Document ID: EPA-HQ-OPP-2019-0161-0017
Agency: epa
Document Type: Supporting & Related Material
Title: 
Posted Date: 2019-06-04T04:00Z

Sample Size for Pet Product Studies
                                       
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Table of Contents

Executive Summary	2
1.	Background	3
2.	Simulations and Assumptions	3
3.	Conclusions and Suggested sample sizes based on the results of simulations	6
Simulations of Study Design 1: Narthropods/animal/day = 50+-5 and blood-fed proportion of arthropod on each animal >= 25%	8
Simulations of Study Design 2: Narthropods/animal/day = 50+-5 and blood-fed proportion of arthropod on each animal >= 40%	15
Simulations of Study Design 3: Narthropods/animal/day = 100+-10 and blood-fed proportion of arthropod on each animal >= 40%	21
Simulations of Study Design 4: Narthropods/animal/day = 50+-5 and blood-fed proportion of arthropod on each animal >= 60%	27
Simulations of Study Design 5: Narthropods/animal/day = 100+-10 and blood-fed proportion of arthropod on each animal >= 60%	32
Appendix II: Evaluation of random effects of logit generated from normal distributions and Weibull distribution	37
Appendix III: True blood-fed proportion vs. proportions of animals/datasets meet the required blood-fed proportion	42

SAS Programs of Simulations

                              
 Executive Summary 
This document is directly related to the guideline for Efficacy Testing of Topically Applied Pesticides Used Against Certain Ectoparasitic Pests on Pets, Charge Question #9. 

Briefly, the revision of guideline for testing topically applied pet products provides an opportunity to assess sample sizes from a statistical standpoint. Historically, EPA has recommended 6 animals per treatment, but no statistical simulation or calculation had been conducted to evaluate the statistical power of this experimental design to detect a treatment-related effect. In practice, the agency has often received studies which utilized between 2 and 12 animals per treatment. 

Here we provide statistical simulations based on sections (j)  -  (l) of the draft guideline, which illustrate the potential power of several different experimental designs to detect efficacy of 90% or greater based on the behavior of different types of arthropods. Adequate power is typically considered 80% power to detect a given true effect at a given precision. For the studies in the guideline, EPA determined the sample size which results in 80% power to detect the true efficacy of >=90% with a precision of <= 5% using a normal distribution. The Agency will be soliciting comments of this analysis and how it relates to the draft guideline. 

Specifically: 
 For studies assessing efficacy against ticks (study design 1), 14 animal subjects would be appropriate per treatment.  
 For studies assessing efficacy against fleas, 7 animal subjects per treatment would be appropriate for tests on cats (study design 3), and 6 animal subjects are appropriate for tests on dogs (study design 5). 
 For studies assessing efficacy against mosquitoes, 6 animal subjects per treatment would be appropriate if testing against one species (study design 5), and 8 animal subjects per treatment if testing against three mosquito species simultaneously (study design 4).  
 For studies assessing efficacy against stable flies, horse flies, and deer flies, 8 animal subjects per treatment would be appropriate (study design 4). 
 For studies assessing efficacy against sand flies, black flies, or biting midges, 6 animal subjects would be appropriate (study design 5).

Background
   Purpose
   Historically, the Agency has recommended using a minimum of 6 animals per study group for efficacy testing of topically applied products on pets, however studies have been submitted with 2-12 animals per group. Previously no statistical simulation or calculation had been conducted to evaluate the statistical power associated with the sample size of these experimental designs in detecting a treatment-related effect. Therefore, this document presents the simulations that have been conducted to determine the sample sizes and associated power of the study designs in the proposed guideline. 
   Study design
 2 groups (1 control and 1 treatment) with X animals per group
 Data are collected at 4 different days over the study duration
 Each day, Y arthropods (+-10%) per animal
   Objective of study
 Evaluate the efficacy or effectiveness of the treatment where efficacy or effectiveness of the treatment is defined as ABBOTT's formula:
 (retained or blood-fed proportion of control group  -  retained or blood-fed proportion of treated group)/retained or blood-fed proportion of control group for repellency evaluation. 
 (Survival proportion of control group  -  survival proportion of treated group)/survival proportion of control group for mortality evaluation.
   Objective of Simulations
   Determine the sample size and the power to obtain an observed efficacy >= 90% with a given (suitable) pre-stated level of precision in studies to evaluate repellency of pet products.
   
Simulations and Assumptions
   Assumptions in the simulations
 Given a total number of arthropods tested on an s[th] animal on a specific i[th] day, the number of blood-fed arthropods follows a binomial distribution with p= Psi, where Psi is the true proportion of blood-fed arthropods on the s[th] animal on i[th] day.
         
 Additional to the variation of the arthropods (described by the variation of binomial distribution), animal random effects and day random effects are permitted in the simulation.  These last two sources of variation typically cause the data to be over dispersed.
         
 The results from simulations in Appendix II indicate that the random effects of animal or day can be reasonably assumed to follow normal distributions or Weibull distributions.  Estimated proportions of blood-fed and estimated treatment efficacy of simulated datasets where random animal effects and random day effects generated from normal distributions or Weibull distributions are unbiased estimates of the true values.
 For the purpose of simulation, efficacy was defined as "blood-fed proportion." However, for application in the guideline, the words "mortality" and "blood-fed proportion" can be used interchangeably for each model when determining sample size. 
         
 The true logit of the s[th] animal on a given i[th] day is Qsi = Q + rands + randi, where rands is the random effect of the s[th] animal (on i[th] day), and randi is the random effect of the i[th] day on the s[th] animal. 
         
 The random animal effects were generated as below:
 P is the true blood-fed proportion of a group (on a specific day)
 Logit Q = log(P/(1-P))
 Logit Qs= Q + rands is the logit of s[th] animal 
 When the animal random effects are assumed to be normal distribution, rands = random number from normal distribution with mean = 0 and SD = 0.33.
 When the animal random effects are assumed to follow a Weibull distribution, rands = (random number from Weibull distribution shape a and location b)  -  SubVar, where a = 1/P and b = exp((1/a)xlog(-(SubVar[a])/log(0.5))).  
               
                  Note that the Weibull distribution shape a and location b has a median value SubVar.  If SubVar = 0, then rands is set = 0.
               
                  Since the value of blood-fed proportion P can vary by day (due to the change in efficacy of the treatment, for example), the shape a = 1/P of the Weibull distributions of random effects can differ by day.  Therefore, a same value rands cannot be used for the same s[th] animal on different days.  However, the quantile value of random effect of an animal in the distribution of random effects is assumed to be consistent on different days (for example, one animal has a random effect located at the 75[th] percentile of the random effect distribution on one day; its random effect on any other day is also located at the 75[th] percentile).  
                  
                  A quantile value U that describes the location of random effects of an s[th] animal is randomly generated from the uniform distribution [0,1], and the associated rands of the s[th] animal on each specific i[th] day is then calculated based on the quantile value U and the specific animal random effect Weibull distribution (a, b) on i[th] day.
         
 Similarly, the random day effects were generated as below
 Ps is the blood-fed proportion of arthropods on an s[th] animal (on a specific i[th] day) 
 Logit Qs = log(Ps/(1-Ps))
 Logit Qsi = Qs + randi is the logit of animal s[th] on specific i[th] day 
 When the day random effects are assumed to be normal distribution, randi = random number from normal distribution with mean = 0 and SD = 0.166.
 When the day random effects are assumed to be Weibull distribution, randi = (random number from Weibull distribution shape ai and location bi)  -  DayVar, where ai = 1/Ps and bi = exp((1/ai) xlog(-(DayVar[a][i])/log(0.5))).  
                     Note that the Weibull distribution shape ai and location bi has a median value DayVar.  Also, on a given day, different animals have different value of ai, so they have different Weibull distributions of day effects.  If DayVar = 0, then randi is set = 0.
 Therefore, the logit of the s[th] animal on a given i[th] day is Qsi = Q + rands + randi.  The blood-fed proportion of arthropods on s[th] animal on a specific i[th] day is Psi = exp(Qsi)/(1+exp(Qsi)).
         
 Number of arthropods used on s[th] animal on i[th] day is randomly generated from Uniform distribution Nsi =  U [ NPDayx(1  -  Rndiff), NPDayx (1  -  Rndiff) ]

 Number of blood-fed arthropods on s[th] animal on i[th] day is randomly generated from binomial distribution of Nsi trials and success proportion =  Psi.

 Generalized linear mixed effects model (PROC GLIMMIX) for Poisson distribution data with animal and day as random effects for over-dispersed data (RANDOM Day/subject = animal type = cs; RANDOM _residual_;) is used to analyze each dataset.  For those datasets that have a computational (convergence) issue in the generalized linear mixed effects model, generalized linear model for Poisson distribution data is used to separately analyze the data by Day.  The blood-fed proportion ratio (i.e. adjusted blood-fed proportion of treatment group) and its 95% CI are estimated is by each Day.  The efficacy of the treatment group = 1  -  adjusted blood-fed proportion.  The precision of the estimated efficacy = estimated efficacy  -  lower limit of 95% CI.
         
 The power of a study design is the proportion of datasets that have observed treatment efficacy >= 0.90 and observed precision <= ReqPrecision.
   Important Parameters in simulations
 NminSub = the lowest number of ANIMALS/group
 NmaxSub = the highest number of ANIMALS/group
 NPDay = number of arthropods/animal/day
 RNdiff = allowable proportion of deviation in number arthropods/animal
 CP = true blood-fed proportion of control group
 TE = true efficacy of treatment, (1 - TE is the adjusted blood-fed proportion of treated group)
 ReqTE = required observed efficacy of treatment
 ReqPrecision = required maximum precision value
 SubVar  or SD_sub = degree of variation between ANIMAL
 DayVar or SD_day = degree of variation between DAY
 Nsim = number of simulated datasets per scenario (set to be 2000)
 seed = seed to regenerate the results of simulations

Conclusions and Suggested sample sizes based on the results of simulations
   Conclusions
   The results of power in Appendix I indicate that when the true efficacy is 0.85, the power (i.e. false discovery rate to claim the efficacy >= 0.90) is very low even when the required precision is 0.05.  Therefore, a required precision of 0.05 is suggested for use to optimize the power to detect the products with true efficacy >= 0.90.
   The statistical model used to analyze the simulated data is an acceptable technique for evaluating the efficacy of the products. As mentioned above, when the true efficacy of a product is 0.85 (i.e., less than the required efficacy of 0.90), there is a very low probability (< 0.02) that the product would be incorrectly accepted (i.e., low probability that the estimated efficacy from a study of this product >= 0.90 and the precision <=0.05). When the true efficacy of a product is 0.925 (slightly greater than the required efficacy of 0.90), there is high probability that the product would be correctly accepted based on the results of an adequate sample size study (i.e., there is at least 0.80 power that the study would result an estimated efficacy >= 0.90 and a precision <=0.05).
   Suggested sample sizes
   Below is the summary table including simulation results of all the scenarios analyzed where both animal random effects and day random effects were randomly generated from normal distributions or Weibull distributions (i.e. both animal random effects and day random effects exist in the dataset). From the simulations based on sections (j)-(l) of the draft guideline, EPA determined the sample size which results in 80% power to detect the true efficacy of >=90% with a precision of <= 5% using a normal distribution for the studies in the guideline. For studies assessing efficacy against ticks (study design 1), 14 animal subjects would be appropriate per treatment. For studies assessing efficacy against fleas, 7 animal subjects per treatment would be appropriate for tests on cats (study design 3), and 6 animal subjects are appropriate for tests on dogs (study design 5). For studies assessing efficacy against mosquitoes, 6 animal subjects per treatment would be appropriate if testing against one species (study design 5), and 8 animal subjects per treatment if testing against three mosquito species simultaneously (study design 4).  For studies assessing efficacy against stable flies, horse flies, and deer flies, 8 animal subjects per treatment would be appropriate (study design 4). For studies assessing efficacy against sand flies, black flies, or biting midges, 6 animal subjects would be appropriate (study design 5). EPA will be soliciting comments on this analysis and how it relates to the draft guideline.
   
   
                                 Study design
                         Relevant section of guideline
     Required lowest observed blood-fed proportion on each control animal
                  True blood fed proportion in control group
                       No. arthropods per animal per day
                                    True TE
                          Assumed distribution types
                                  Sample size
                                     Power
               to observe TE >= 0.90 and precision <= 0.050  
                                       1
                         Ticks on cats or dogs, (k)(2)
                                       
                                     0.25
                                     0.45
                                     50+-5
                                     0.925
                                    Normal
                                      14
                                     0.811
                                       
                                       
                                       
                                       
                                       
                                       
                                    Weibull
                                      13
                                     0.828
                                       2
                           Not included in guideline
                                     0.40
                                     0.60
                                     50+-5
                                     0.925
                                    Normal
                                      11
                                     0.834
                                       
                                       
                                       
                                       
                                       
                                       
                                    Weibull
                                      10
                                     0.860
                                       3
                             Fleas on cats, (j)(2)
                                       
                                     0.40
                                     0.60
                                    100+-10
                                     0.925
                                    Normal
                                       7
                                     0.798
                                       
                                       
                                       
                                       
                                       
                                       
                                    Weibull
                                       7
                                     0.875
                                       4
          Mosquitoes or flies on cats or dogs using 50 pests, (l)(2)
                                     0.60
                                     0.80
                                     50+-5
                                     0.925
                                    Normal
                                       8
                                     0.839
                                       
                                       
                                       
                                       
                                       
                                       
                                    Weibull
                                       6
                                     0.801
                                       5
Fleas on dogs, (j)(2) Mosquitoes or flies for cats and dogs using 100 pests, (l)(2)
                                     0.60
                                     0.75
                                    100+-10
                                     0.925
                                    Normal
                                       6
                                     0.834
                                       
                                       
                                       
                                       
                                       
                                       
                                    Weibull
                                       6
                                     0.930
 
Appendix I: Details of study designs and input parameters
     Simulations of Study Design 1: Narthropods/animal/day = 50+-5 and blood-fed proportion of arthropod on each animal >= 25%
 The study design:
 The results of this study design apply to studies that test 1 tick species/animal/day
 Number of arthropods/animal/day = 50+-5
 4 different days
 Inclusion criterion: blood-fed proportion of arthropod on each animal >= 25%
 Input parameters for the simulations:
 From the simulation in SAS program "percent animals or datasets have at least  a certain percent arthropod non-blood-fed.sas" using the criterion that the blood-fed proportion of arthropod on each animal >= 25%, a true blood-fed proportion CP of arthropods in control animals can reasonably be as low as 0.40.
 NPDay = 50 arthropods/animal/day
 RNdiff = 0.1
 True efficacy of treatment is set = 0.95, 0.925, 0.90, and 0.85 for the 1[st], 2[nd], 3[rd], and 4[th] days. 
 Required observed treatment efficacy is ReqTE = 0.90
 Required precision of efficacy is evaluated as ReqPrecision = 0.025, 0.03, 0.04, and 0.05.
 The simulations are set to have 2000 datasets per each sample size = 8, 9, 10, 11, and 15.
         
      Table A1.1-1
 N per Day = 50+-5, CP = 0.45, no animal random effect, no day random effects 
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.010
                                                                          0.078
                                                                          0.433
                                                                          0.825
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.016
                                                                          0.177
                                                                          0.565
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.003
                                                                          0.061
                                                                          0.267
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.026
                                                                          0.135
                                                                          0.632
                                                                          0.923
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.025
                                                                          0.297
                                                                          0.700
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.005
                                                                          0.097
                                                                          0.373
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.023
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.040
                                                                          0.186
                                                                          0.746
                                                                          0.967
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.038
                                                                          0.412
                                                                          0.826
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.007
                                                                          0.134
                                                                          0.439
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.017
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.065
                                                                          0.292
                                                                          0.848
                                                                          0.986
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.010
                                                                          0.069
                                                                          0.553
                                                                          0.883
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.012
                                                                          0.208
                                                                          0.472
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.013
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.094
                                                                          0.388
                                                                          0.922
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.012
                                                                          0.090
                                                                          0.661
                                                                          0.893
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.014
                                                                          0.303
                                                                          0.500
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.008
                                                                          0.017
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.141
                                                                          0.518
                                                                          0.964
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.017
                                                                          0.133
                                                                          0.774
                                                                          0.925
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.025
                                                                          0.353
                                                                          0.494
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.007
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.201
                                                                          0.634
                                                                          0.987
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.023
                                                                          0.186
                                                                          0.840
                                                                          0.926
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.040
                                                                          0.429
                                                                          0.520
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.007
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.274
                                                                          0.751
                                                                          0.995
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.051
                                                                          0.293
                                                                          0.908
                                                                          0.944
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.060
                                                                          0.452
                                                                          0.491
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                          0.007

      Table A1.1-2
Animal random effects and day random effects assumed to be normal distributions
             N per Day = 50+-5, CP = 0.45, SD_sub = 0.33, SD_day=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.004
                                                                          0.039
                                                                          0.292
                                                                          0.669
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.077
                                                                          0.326
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.014
                                                                          0.121
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.008
                                                                          0.069
                                                                          0.401
                                                                          0.805
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.008
                                                                          0.139
                                                                          0.480
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.032
                                                                          0.194
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.008
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.027
                                                                          0.113
                                                                          0.557
                                                                          0.889
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.014
                                                                          0.205
                                                                          0.595
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.050
                                                                          0.260
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.011
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.033
                                                                          0.165
                                                                          0.671
                                                                          0.949
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.020
                                                                          0.292
                                                                          0.703
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.073
                                                                          0.317
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.016
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.048
                                                                          0.234
                                                                          0.809
                                                                          0.975
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.028
                                                                          0.377
                                                                          0.792
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.003
                                                                          0.130
                                                                          0.391
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.017
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.077
                                                                          0.340
                                                                          0.875
                                                                          0.988
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.007
                                                                          0.056
                                                                          0.523
                                                                          0.844
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.004
                                                                          0.176
                                                                          0.407
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.009
                                                                          0.018
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.105
                                                                          0.394
                                                                          0.919
                                                                          0.991
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.008
                                                                          0.078
                                                                          0.606
                                                                          0.862
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.010
                                                                          0.213
                                                                          0.410
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.161
                                                                          0.521
                                                                          0.958
                                                                          0.997
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.014
                                                                          0.114
                                                                          0.722
                                                                          0.894
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.020
                                                                          0.281
                                                                          0.409
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.006

      Table A1.1-3
Animal random effects and day random effects assumed to be Weibull distributions
              N per Day = 50+-5, CP = 0.45, SubVar = 1, DayVar=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.017
                                                                          0.078
                                                                          0.368
                                                                          0.727
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.008
                                                                          0.110
                                                                          0.397
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.030
                                                                          0.168
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.013
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.024
                                                                          0.112
                                                                          0.502
                                                                          0.836
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.002
                                                                          0.012
                                                                          0.181
                                                                          0.541
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.048
                                                                          0.235
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.017
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.043
                                                                          0.156
                                                                          0.619
                                                                          0.905
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.023
                                                                          0.242
                                                                          0.658
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.003
                                                                          0.066
                                                                          0.316
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.019
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.054
                                                                          0.223
                                                                          0.734
                                                                          0.946
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.034
                                                                          0.354
                                                                          0.766
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.109
                                                                          0.415
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.020
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.083
                                                                          0.321
                                                                          0.841
                                                                          0.977
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.009
                                                                          0.057
                                                                          0.478
                                                                          0.861
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.007
                                                                          0.146
                                                                          0.476
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.019
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.123
                                                                          0.409
                                                                          0.907
                                                                          0.985
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.007
                                                                          0.079
                                                                          0.586
                                                                          0.896
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.008
                                                                          0.210
                                                                          0.507
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.012
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.158
                                                                          0.498
                                                                          0.929
                                                                          0.987
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.010
                                                                          0.112
                                                                          0.676
                                                                          0.907
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.013
                                                                          0.291
                                                                          0.522
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.011
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.214
                                                                          0.609
                                                                          0.958
                                                                          0.992
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.019
                                                                          0.152
                                                                          0.762
                                                                          0.917
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.015
                                                                          0.359
                                                                          0.532
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.008
                                                                          0.011

      Table A1.1-4
Animal random effects and day random effects assumed to be normal distributions
            N per Day = 50+-5, CP = 0.45, SD_sub = 0, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.007
                                                                          0.042
                                                                          0.306
                                                                          0.722
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.006
                                                                          0.092
                                                                          0.392
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.031
                                                                          0.184
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.010
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.013
                                                                          0.060
                                                                          0.434
                                                                          0.839
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.002
                                                                          0.009
                                                                          0.156
                                                                          0.553
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.038
                                                                          0.247
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.004
                                                                          0.016
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.017
                                                                          0.113
                                                                          0.594
                                                                          0.918
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.018
                                                                          0.259
                                                                          0.684
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.081
                                                                          0.338
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.011
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.031
                                                                          0.162
                                                                          0.739
                                                                          0.967
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.023
                                                                          0.344
                                                                          0.784
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.004
                                                                          0.115
                                                                          0.408
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.012
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.042
                                                                          0.235
                                                                          0.831
                                                                          0.983
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.041
                                                                          0.478
                                                                          0.857
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.006
                                                                          0.182
                                                                          0.456
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.013
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.073
                                                                          0.335
                                                                          0.907
                                                                          0.995
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.009
                                                                          0.074
                                                                          0.614
                                                                          0.890
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.007
                                                                          0.228
                                                                          0.470
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.009
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.100
                                                                          0.423
                                                                          0.957
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.007
                                                                          0.087
                                                                          0.713
                                                                          0.916
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.016
                                                                          0.300
                                                                          0.476
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.006
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.149
                                                                          0.550
                                                                          0.976
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.015
                                                                          0.137
                                                                          0.797
                                                                          0.920
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.022
                                                                          0.360
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.004

      
      Table A1.1-5
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day = 50+-5, CP = 0.45, SubVar = 0, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.009
                                                                          0.038
                                                                          0.305
                                                                          0.681
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.005
                                                                          0.092
                                                                          0.405
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.024
                                                                          0.166
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.002
                                                                          0.011
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.011
                                                                          0.062
                                                                          0.442
                                                                          0.804
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.002
                                                                          0.011
                                                                          0.160
                                                                          0.542
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.036
                                                                          0.243
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.010
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.014
                                                                          0.107
                                                                          0.563
                                                                          0.904
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.002
                                                                          0.022
                                                                          0.251
                                                                          0.688
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.057
                                                                          0.326
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.016
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.028
                                                                          0.160
                                                                          0.706
                                                                          0.954
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.028
                                                                          0.364
                                                                          0.788
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.103
                                                                          0.406
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.019
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.047
                                                                          0.234
                                                                          0.792
                                                                          0.979
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.040
                                                                          0.461
                                                                          0.859
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.004
                                                                          0.162
                                                                          0.479
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.011
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.068
                                                                          0.320
                                                                          0.898
                                                                          0.991
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.008
                                                                          0.063
                                                                          0.596
                                                                          0.894
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.008
                                                                          0.239
                                                                          0.524
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.014
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.100
                                                                          0.432
                                                                          0.938
                                                                          0.994
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.008
                                                                          0.090
                                                                          0.714
                                                                          0.939
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.013
                                                                          0.307
                                                                          0.531
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.009
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.131
                                                                          0.535
                                                                          0.971
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.012
                                                                          0.141
                                                                          0.798
                                                                          0.945
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.025
                                                                          0.388
                                                                          0.542
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.007
                                                                          0.010

      Table A1.1-6
Animal random effects and day random effects assumed to be normal distributions
           N per Day = 50+-5, CP = 0.45, SD_sub = 0.33, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.003
                                                                          0.017
                                                                          0.196
                                                                          0.540
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.042
                                                                          0.224
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.012
                                                                          0.078
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.008
                                                                          0.029
                                                                          0.275
                                                                          0.686
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.005
                                                                          0.077
                                                                          0.335
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.012
                                                                          0.125
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.008
                                                                          0.050
                                                                          0.414
                                                                          0.809
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.000
                                                                          0.006
                                                                          0.112
                                                                          0.450
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.026
                                                                          0.186
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.012
                                                                          0.083
                                                                          0.525
                                                                          0.879
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.000
                                                                          0.011
                                                                          0.171
                                                                          0.575
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.043
                                                                          0.230
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.013
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.023
                                                                          0.124
                                                                          0.637
                                                                          0.938
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.014
                                                                          0.246
                                                                          0.678
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.055
                                                                          0.289
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.011
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.037
                                                                          0.195
                                                                          0.762
                                                                          0.965
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.026
                                                                          0.348
                                                                          0.751
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.003
                                                                          0.095
                                                                          0.333
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.014
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.048
                                                                          0.246
                                                                          0.826
                                                                          0.977
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.005
                                                                          0.032
                                                                          0.437
                                                                          0.811
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.133
                                                                          0.371
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.002
                                                                          0.008
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.078
                                                                          0.339
                                                                          0.895
                                                                          0.986
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.053
                                                                          0.519
                                                                          0.845
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.169
                                                                          0.382
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.012

      Table A1.1-7
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day = 50+-5, CP = 0.45, SubVar = 1, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.010
                                                                          0.037
                                                                          0.254
                                                                          0.604
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.001
                                                                          0.005
                                                                          0.066
                                                                          0.292
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.012
                                                                          0.113
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.010
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.008
                                                                          0.049
                                                                          0.361
                                                                          0.727
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.000
                                                                          0.004
                                                                          0.100
                                                                          0.397
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.021
                                                                          0.156
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.011
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.015
                                                                          0.096
                                                                          0.503
                                                                          0.851
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.000
                                                                          0.012
                                                                          0.178
                                                                          0.553
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.030
                                                                          0.232
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.017
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.023
                                                                          0.140
                                                                          0.622
                                                                          0.926
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.020
                                                                          0.247
                                                                          0.657
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.063
                                                                          0.312
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.021
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.047
                                                                          0.216
                                                                          0.725
                                                                          0.954
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.024
                                                                          0.319
                                                                          0.767
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.092
                                                                          0.415
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.018
                                                                             13
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.065
                                                                          0.277
                                                                          0.822
                                                                          0.972
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.043
                                                                          0.441
                                                                          0.828
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.142
                                                                          0.481
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.019
                                                                             14
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.088
                                                                          0.352
                                                                          0.878
                                                                          0.981
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.053
                                                                          0.534
                                                                          0.877
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.004
                                                                          0.194
                                                                          0.509
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.013
                                                                             15
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.120
                                                                          0.430
                                                                          0.905
                                                                          0.979
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.081
                                                                          0.621
                                                                          0.899
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.011
                                                                          0.243
                                                                          0.534
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.006
                                                                          0.019
                                                                             20
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.359
                                                                          0.756
                                                                          0.958
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.043
                                                                          0.276
                                                                          0.858
                                                                          0.945
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.050
                                                                          0.471
                                                                          0.555
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.007

Comment:
 If the true efficacy is 92.5%, the recommended sample size is 14.

     Simulations of Study Design 2: Narthropods/animal/day = 50+-5 and blood-fed proportion of arthropod on each animal >= 40%

 The study design:
 The results of this study design apply to studies that test 3 mosquito species/case/day and 50+-5 mosquitoes/species/case/day (data are separately analyzed by species) or studies that test a single species of stable flies, horse flies, or deer flies on an animal per day, with the number of arthropods/species/animal/day = 50+-5
 4 different days
 Inclusion criterion: blood-fed proportion of arthropod on each animal >= 40%
 Input parameters for the simulations:
 From the simulation in SAS program "percent animals or datasets have at least a certain percent arthropod non-blood-fed.sas" using the criterion that the blood-fed proportion of arthropod on each animal >= 40%, a true blood-fed proportion CP of arthropod in control animals can be reasonably as low as 0.60.
 N arthropods/animal/day = 50+-5
 True efficacy of treatment is set = 0.95, 0.925, 0.90, and 0.85 for the 1[st], 2[nd], 3[rd], and 4[th] days. 
 Required observed treatment efficacy is ReqTE = 0.90
 Required precision of efficacy is evaluated as ReqPrecision = 0.025, 0.03, and 0.04.
 The simulations are set to have 2000 datasets per each sample size = 6, 7, ... , 12.
         
      Table A1.2-1
 N per Day = 50+-5, CP = 0.60, no animal random effect, no day random effects
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.061
                                                                          0.179
                                                                          0.551
                                                                          0.843
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.012
                                                                          0.042
                                                                          0.274
                                                                          0.620
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.015
                                                                          0.108
                                                                          0.303
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.006
                                                                          0.020
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.076
                                                                          0.238
                                                                          0.715
                                                                          0.930
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.021
                                                                          0.073
                                                                          0.409
                                                                          0.757
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.007
                                                                          0.019
                                                                          0.159
                                                                          0.386
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.016
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.117
                                                                          0.382
                                                                          0.866
                                                                          0.972
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.022
                                                                          0.114
                                                                          0.612
                                                                          0.873
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.030
                                                                          0.269
                                                                          0.470
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.008
                                                                          0.015
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.191
                                                                          0.541
                                                                          0.944
                                                                          0.992
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.033
                                                                          0.184
                                                                          0.750
                                                                          0.896
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.037
                                                                          0.340
                                                                          0.470
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.008
                                                                          0.010
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.282
                                                                          0.667
                                                                          0.975
                                                                          0.997
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.059
                                                                          0.291
                                                                          0.834
                                                                          0.923
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.013
                                                                          0.073
                                                                          0.421
                                                                          0.501
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.011
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.402
                                                                          0.787
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.075
                                                                          0.410
                                                                          0.907
                                                                          0.945
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.016
                                                                          0.117
                                                                          0.476
                                                                          0.515
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.004
                                                                          0.005
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.535
                                                                          0.890
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.148
                                                                          0.553
                                                                          0.937
                                                                          0.953
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.026
                                                                          0.178
                                                                          0.504
                                                                          0.527
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.006
                                                                          0.006

      Table A1.2-2
Animal random effects and day random effects assumed to be normal distributions
             N per Day =50+-5, CP = 0.60, SD_sub = 0, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.061
                                                                          0.234
                                                                          0.764
                                                                          0.966
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.046
                                                                          0.431
                                                                          0.788
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.014
                                                                          0.161
                                                                          0.408
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.012
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.094
                                                                          0.365
                                                                          0.882
                                                                          0.989
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.012
                                                                          0.094
                                                                          0.614
                                                                          0.867
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.019
                                                                          0.247
                                                                          0.445
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.007
                                                                          0.012
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.172
                                                                          0.508
                                                                          0.939
                                                                          0.992
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.022
                                                                          0.156
                                                                          0.730
                                                                          0.902
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.038
                                                                          0.349
                                                                          0.482
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.006
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.241
                                                                          0.630
                                                                          0.983
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.034
                                                                          0.242
                                                                          0.826
                                                                          0.915
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.048
                                                                          0.398
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.006
                                                                          0.006
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.339
                                                                          0.758
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.062
                                                                          0.345
                                                                          0.901
                                                                          0.936
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.007
                                                                          0.078
                                                                          0.434
                                                                          0.469
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.008
                                                                          0.008

      Table A1.2-3
Animal random effects and day random effects assumed to be Weibull distributions
              N per Day =50+-5, CP = 0.60, SubVar = 0, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.015
                                                                          0.059
                                                                          0.335
                                                                          0.699
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.012
                                                                          0.122
                                                                          0.428
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.042
                                                                          0.193
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.014
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.029
                                                                          0.116
                                                                          0.520
                                                                          0.838
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.021
                                                                          0.230
                                                                          0.629
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.006
                                                                          0.077
                                                                          0.311
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.017
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.047
                                                                          0.180
                                                                          0.701
                                                                          0.941
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.042
                                                                          0.352
                                                                          0.763
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.009
                                                                          0.125
                                                                          0.409
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.016
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.075
                                                                          0.282
                                                                          0.831
                                                                          0.983
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.071
                                                                          0.514
                                                                          0.879
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.010
                                                                          0.211
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.016
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.109
                                                                          0.399
                                                                          0.925
                                                                          0.995
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.017
                                                                          0.110
                                                                          0.669
                                                                          0.908
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.020
                                                                          0.282
                                                                          0.530
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.011
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.162
                                                                          0.526
                                                                          0.965
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.016
                                                                          0.161
                                                                          0.786
                                                                          0.935
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.035
                                                                          0.388
                                                                          0.556
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.008
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.253
                                                                          0.686
                                                                          0.992
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.033
                                                                          0.246
                                                                          0.875
                                                                          0.954
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.054
                                                                          0.459
                                                                          0.552
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.005
                                                                          0.007

      Table A1.2-4
Animal random effects and day random effects assumed to be normal distributions
             N per Day =50+-5, CP = 0.60, SD_sub = 0.33, SD_day=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.049
                                                                          0.196
                                                                          0.698
                                                                          0.940
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.006
                                                                          0.036
                                                                          0.313
                                                                          0.700
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.006
                                                                          0.104
                                                                          0.322
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.017
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.075
                                                                          0.290
                                                                          0.825
                                                                          0.981
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.009
                                                                          0.067
                                                                          0.474
                                                                          0.799
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.008
                                                                          0.158
                                                                          0.388
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.012
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.144
                                                                          0.438
                                                                          0.914
                                                                          0.992
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.014
                                                                          0.105
                                                                          0.614
                                                                          0.851
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.017
                                                                          0.239
                                                                          0.407
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.003
                                                                          0.009
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.212
                                                                          0.564
                                                                          0.962
                                                                          0.997
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.019
                                                                          0.162
                                                                          0.715
                                                                          0.873
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.024
                                                                          0.300
                                                                          0.415
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.006
                                                                          0.009
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.292
                                                                          0.703
                                                                          0.987
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.034
                                                                          0.216
                                                                          0.813
                                                                          0.893
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.049
                                                                          0.353
                                                                          0.426
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.007

      Table A1.2-5
Animal random effects and day random effects assumed to be Weibull distributions
               N per Day =50+-5, CP = 0.60, SubVar = 1, DayVar=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.038
                                                                          0.121
                                                                          0.452
                                                                          0.757
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.017
                                                                          0.163
                                                                          0.453
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.005
                                                                          0.059
                                                                          0.202
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.018
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.048
                                                                          0.163
                                                                          0.580
                                                                          0.869
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.027
                                                                          0.227
                                                                          0.600
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.071
                                                                          0.285
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.016
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.091
                                                                          0.282
                                                                          0.745
                                                                          0.951
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.009
                                                                          0.051
                                                                          0.387
                                                                          0.768
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.010
                                                                          0.135
                                                                          0.407
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.023
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.135
                                                                          0.396
                                                                          0.862
                                                                          0.975
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.014
                                                                          0.089
                                                                          0.520
                                                                          0.851
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.011
                                                                          0.193
                                                                          0.470
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.007
                                                                          0.019
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.203
                                                                          0.525
                                                                          0.928
                                                                          0.988
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.026
                                                                          0.149
                                                                          0.667
                                                                          0.906
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.025
                                                                          0.272
                                                                          0.502
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.008
                                                                          0.018
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.282
                                                                          0.649
                                                                          0.961
                                                                          0.989
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.034
                                                                          0.216
                                                                          0.768
                                                                          0.920
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.032
                                                                          0.391
                                                                          0.536
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.008
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.386
                                                                          0.750
                                                                          0.979
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.062
                                                                          0.297
                                                                          0.848
                                                                          0.938
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.051
                                                                          0.449
                                                                          0.553
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.007
                                                                          0.010

      
      
      Table A1.2-6
Animal random effects and day random effects assumed to be normal distributions
           N per Day = 50+-5, CP = 0.60, SD_sub = 0.33, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.026
                                                                          0.120
                                                                          0.567
                                                                          0.897
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.017
                                                                          0.210
                                                                          0.597
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.003
                                                                          0.067
                                                                          0.279
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.015
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.036
                                                                          0.179
                                                                          0.712
                                                                          0.952
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.030
                                                                          0.319
                                                                          0.723
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.100
                                                                          0.324
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.013
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.067
                                                                          0.291
                                                                          0.833
                                                                          0.977
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.008
                                                                          0.052
                                                                          0.451
                                                                          0.784
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.009
                                                                          0.159
                                                                          0.371
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.002
                                                                          0.014
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.108
                                                                          0.402
                                                                          0.910
                                                                          0.993
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.010
                                                                          0.088
                                                                          0.589
                                                                          0.834
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.015
                                                                          0.212
                                                                          0.382
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.010
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.165
                                                                          0.496
                                                                          0.954
                                                                          0.990
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.014
                                                                          0.119
                                                                          0.711
                                                                          0.868
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.018
                                                                          0.258
                                                                          0.379
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.008

      Table A1.2-7
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day = 50+-5, CP = 0.60, SubVar = 1, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.015
                                                                          0.054
                                                                          0.303
                                                                          0.656
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.002
                                                                          0.010
                                                                          0.097
                                                                          0.340
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.024
                                                                          0.144
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.014
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.025
                                                                          0.090
                                                                          0.435
                                                                          0.772
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.003
                                                                          0.016
                                                                          0.159
                                                                          0.475
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.044
                                                                          0.203
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.018
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.038
                                                                          0.156
                                                                          0.597
                                                                          0.893
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.025
                                                                          0.248
                                                                          0.619
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.076
                                                                          0.310
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.017
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.065
                                                                          0.243
                                                                          0.743
                                                                          0.951
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.004
                                                                          0.045
                                                                          0.371
                                                                          0.766
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.000
                                                                          0.005
                                                                          0.122
                                                                          0.411
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.021
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.091
                                                                          0.333
                                                                          0.841
                                                                          0.979
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.008
                                                                          0.059
                                                                          0.496
                                                                          0.860
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.007
                                                                          0.167
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.019
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.133
                                                                          0.433
                                                                          0.909
                                                                          0.989
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.015
                                                                          0.092
                                                                          0.620
                                                                          0.905
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.017
                                                                          0.259
                                                                          0.540
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.004
                                                                          0.012
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.214
                                                                          0.579
                                                                          0.958
                                                                          0.994
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.020
                                                                          0.156
                                                                          0.732
                                                                          0.930
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.001
                                                                          0.023
                                                                          0.323
                                                                          0.560
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.016
                                                                             20
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.815
                                                                          0.941
                                                                          0.998
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.282
                                                                          0.767
                                                                          0.961
                                                                          0.983
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.033
                                                                          0.321
                                                                          0.567
                                                                          0.590
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001

Comment:
 If the true efficacy is 92.5%, the recommended sample size is 11

Simulations of Study Design 3: Narthropods/animal/day = 100+-10 and blood-fed proportion of arthropod on each animal >= 40%
 The study design:
 The results of this study design apply to studies that test a single species of mosquitoes, fleas, sand flies, black flies, or biting midges per case per day.
 Number of arthropods/species/animal/day = 100+-10
 4 different days
 Inclusion criterion: blood-fed proportion of arthropod on each animal >= 40%
               
 Input parameters for the simulations:
 From the simulation in SAS program "percent animals or datasets have at least a certain percent arthropod non-blood-fed.sas" using the criterion that the blood-fed proportion of arthropod on each animal >= 40%, a true blood-fed proportion CP of arthropods in control animal can be reasonably as low as 0.60.
 N arthropods/animal/day = 100+-10
 True efficacy of treatment is set = 0.95, 0.925, 0.90, and 0.85 for the 1[st], 2[nd], 3[rd], and 4[th] days. 
 Required observed treatment efficacy is ReqTE = 0.90
 Required precision of efficacy is evaluated as ReqPrecision = 0.025, 0.03, and 0.04.
 The simulations are set to have 2000 datasets per each sample size = 6, 7, ..., 12.
      Table A1.3-1
N per Day = 100+-10, CP = 0.60, no animal random effect, no day random effects
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.499
                                                                          0.797
                                                                          0.974
                                                                          0.994
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.183
                                                                          0.486
                                                                          0.868
                                                                          0.931
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.054
                                                                          0.179
                                                                          0.432
                                                                          0.492
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.004
                                                                          0.004
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.667
                                                                          0.903
                                                                          0.988
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.293
                                                                          0.675
                                                                          0.931
                                                                          0.953
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.083
                                                                          0.268
                                                                          0.468
                                                                          0.493
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.005
                                                                          0.005
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.844
                                                                          0.968
                                                                          0.998
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.499
                                                                          0.844
                                                                          0.970
                                                                          0.977
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.140
                                                                          0.380
                                                                          0.501
                                                                          0.510
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.932
                                                                          0.989
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.666
                                                                          0.924
                                                                          0.980
                                                                          0.982
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.214
                                                                          0.432
                                                                          0.485
                                                                          0.489
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.002
                                                                          0.002
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.966
                                                                          0.994
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.808
                                                                          0.957
                                                                          0.983
                                                                          0.984
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.314
                                                                          0.480
                                                                          0.505
                                                                          0.505
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.990
                                                                          0.999
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.901
                                                                          0.972
                                                                          0.984
                                                                          0.984
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.417
                                                                          0.509
                                                                          0.521
                                                                          0.522
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.994
                                                                          1.000
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.955
                                                                          0.989
                                                                          0.992
                                                                          0.992
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.465
                                                                          0.517
                                                                          0.524
                                                                          0.525
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

      Table A1.3-2
Animal random effects and day random effects assumed to be normal distributions
           N per Day = 100+-10, CP = 0.60, SD_sub = 0, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.232
                                                                          0.542
                                                                          0.929
                                                                          0.990
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.072
                                                                          0.244
                                                                          0.743
                                                                          0.900
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.015
                                                                          0.073
                                                                          0.337
                                                                          0.441
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.004
                                                                          0.005
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.388
                                                                          0.746
                                                                          0.975
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.116
                                                                          0.384
                                                                          0.865
                                                                          0.936
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.027
                                                                          0.118
                                                                          0.431
                                                                          0.499
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.004
                                                                          0.004
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.576
                                                                          0.880
                                                                          0.993
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.176
                                                                          0.565
                                                                          0.922
                                                                          0.948
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.043
                                                                          0.195
                                                                          0.461
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.005
                                                                          0.005
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.744
                                                                          0.950
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.313
                                                                          0.738
                                                                          0.956
                                                                          0.963
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.064
                                                                          0.291
                                                                          0.472
                                                                          0.481
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.873
                                                                          0.984
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.444
                                                                          0.866
                                                                          0.966
                                                                          0.967
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.095
                                                                          0.375
                                                                          0.477
                                                                          0.479
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.946
                                                                          0.995
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.610
                                                                          0.933
                                                                          0.970
                                                                          0.971
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.164
                                                                          0.411
                                                                          0.453
                                                                          0.453
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.978
                                                                          0.998
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.760
                                                                          0.964
                                                                          0.984
                                                                          0.984
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.258
                                                                          0.453
                                                                          0.467
                                                                          0.468
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

      
      
      
      Table A1.3-3
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day =100+-10, CP = 0.60, SubVar = 0, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.222
                                                                          0.516
                                                                          0.890
                                                                          0.972
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.052
                                                                          0.195
                                                                          0.695
                                                                          0.887
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.010
                                                                          0.053
                                                                          0.323
                                                                          0.498
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.005
                                                                          0.007
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.358
                                                                          0.677
                                                                          0.951
                                                                          0.990
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.097
                                                                          0.343
                                                                          0.835
                                                                          0.947
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.019
                                                                          0.097
                                                                          0.427
                                                                          0.531
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.007
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.502
                                                                          0.833
                                                                          0.987
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.159
                                                                          0.482
                                                                          0.917
                                                                          0.969
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.030
                                                                          0.156
                                                                          0.499
                                                                          0.542
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.003
                                                                          0.003
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.664
                                                                          0.910
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.250
                                                                          0.648
                                                                          0.956
                                                                          0.983
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.049
                                                                          0.256
                                                                          0.541
                                                                          0.563
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.794
                                                                          0.957
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.375
                                                                          0.787
                                                                          0.972
                                                                          0.983
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.092
                                                                          0.347
                                                                          0.570
                                                                          0.577
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.861
                                                                          0.973
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.486
                                                                          0.862
                                                                          0.984
                                                                          0.988
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.135
                                                                          0.431
                                                                          0.568
                                                                          0.572
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.929
                                                                          0.991
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.643
                                                                          0.921
                                                                          0.988
                                                                          0.989
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.205
                                                                          0.483
                                                                          0.567
                                                                          0.571
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001

      Table A1.3-4
Animal random effects and day random effects assumed to be normal distributions
            N per Day = 100+-10, CP = 0.60, SD_sub = 0.33, SD_day=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.196
                                                                          0.460
                                                                          0.871
                                                                          0.975
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.030
                                                                          0.136
                                                                          0.528
                                                                          0.783
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.028
                                                                          0.194
                                                                          0.367
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.008
                                                                          0.018
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.303
                                                                          0.651
                                                                          0.958
                                                                          0.995
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.064
                                                                          0.238
                                                                          0.707
                                                                          0.886
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.009
                                                                          0.054
                                                                          0.304
                                                                          0.441
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                          0.012
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.466
                                                                          0.781
                                                                          0.990
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.107
                                                                          0.361
                                                                          0.804
                                                                          0.897
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.014
                                                                          0.089
                                                                          0.350
                                                                          0.432
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.006
                                                                          0.007
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.623
                                                                          0.900
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.157
                                                                          0.480
                                                                          0.887
                                                                          0.926
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.027
                                                                          0.144
                                                                          0.385
                                                                          0.426
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.005
                                                                          0.006
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.754
                                                                          0.953
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.260
                                                                          0.634
                                                                          0.925
                                                                          0.937
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.034
                                                                          0.210
                                                                          0.418
                                                                          0.438
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.003
                                                                          0.003
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.866
                                                                          0.980
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.339
                                                                          0.752
                                                                          0.934
                                                                          0.942
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.074
                                                                          0.249
                                                                          0.404
                                                                          0.409
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.928
                                                                          0.991
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.482
                                                                          0.831
                                                                          0.948
                                                                          0.951
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.090
                                                                          0.301
                                                                          0.412
                                                                          0.416
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001

      Table A1.3-5
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day = 100+-10, CP = 0.60, SubVar = 1, DayVar=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.271
                                                                          0.578
                                                                          0.927
                                                                          0.994
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.041
                                                                          0.180
                                                                          0.629
                                                                          0.881
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.011
                                                                          0.048
                                                                          0.269
                                                                          0.481
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.008
                                                                          0.015
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.392
                                                                          0.718
                                                                          0.973
                                                                          0.991
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.075
                                                                          0.278
                                                                          0.786
                                                                          0.924
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.013
                                                                          0.067
                                                                          0.358
                                                                          0.511
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.008
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.545
                                                                          0.860
                                                                          0.991
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.142
                                                                          0.431
                                                                          0.895
                                                                          0.947
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.022
                                                                          0.124
                                                                          0.466
                                                                          0.545
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.005
                                                                          0.006
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.728
                                                                          0.946
                                                                          0.989
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.209
                                                                          0.578
                                                                          0.946
                                                                          0.963
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.032
                                                                          0.184
                                                                          0.507
                                                                          0.525
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.005
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.833
                                                                          0.967
                                                                          0.995
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.342
                                                                          0.732
                                                                          0.964
                                                                          0.970
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.057
                                                                          0.261
                                                                          0.534
                                                                          0.540
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.002
                                                                          0.003
                                                                          0.005
                                                                          0.005
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.911
                                                                          0.984
                                                                          0.994
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.459
                                                                          0.847
                                                                          0.968
                                                                          0.972
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.092
                                                                          0.371
                                                                          0.548
                                                                          0.550
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.953
                                                                          0.990
                                                                          0.997
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.586
                                                                          0.918
                                                                          0.980
                                                                          0.984
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.127
                                                                          0.437
                                                                          0.550
                                                                          0.552
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001

      Table A1.3-6
Animal random effects and day random effects assumed to be normal distributions
          N per Day = 100+-10, CP = 0.60, SD_sub = 0.33, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.094
                                                                          0.270
                                                                          0.753
                                                                          0.940
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.012
                                                                          0.062
                                                                          0.361
                                                                          0.706
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.017
                                                                          0.142
                                                                          0.327
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.014
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.155
                                                                          0.422
                                                                          0.877
                                                                          0.975
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.024
                                                                          0.115
                                                                          0.535
                                                                          0.798
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.017
                                                                          0.207
                                                                          0.373
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                          0.013
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.256
                                                                          0.592
                                                                          0.953
                                                                          0.993
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.031
                                                                          0.190
                                                                          0.681
                                                                          0.873
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.041
                                                                          0.288
                                                                          0.413
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.008
                                                                          0.010
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.378
                                                                          0.734
                                                                          0.976
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.066
                                                                          0.303
                                                                          0.795
                                                                          0.894
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.008
                                                                          0.073
                                                                          0.323
                                                                          0.394
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.003
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.510
                                                                          0.859
                                                                          0.995
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.098
                                                                          0.409
                                                                          0.865
                                                                          0.911
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.014
                                                                          0.100
                                                                          0.367
                                                                          0.410
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.003
                                                                          0.003
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.636
                                                                          0.925
                                                                          0.996
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.141
                                                                          0.545
                                                                          0.908
                                                                          0.925
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.017
                                                                          0.150
                                                                          0.393
                                                                          0.407
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.002
                                                                          0.002
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.782
                                                                          0.967
                                                                          0.998
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.231
                                                                          0.659
                                                                          0.923
                                                                          0.931
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.041
                                                                          0.216
                                                                          0.381
                                                                          0.391
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.002
                                                                          0.002

      
      Table A1.3-7
Animal random effects and day random effects assumed to be Weibull distributions
            N per Day = 100+-10, CP = 0.60, SubVar = 1, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.143
                                                                          0.365
                                                                          0.802
                                                                          0.949
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.019
                                                                          0.093
                                                                          0.453
                                                                          0.782
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.016
                                                                          0.176
                                                                          0.432
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.017
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.219
                                                                          0.505
                                                                          0.884
                                                                          0.961
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.031
                                                                          0.157
                                                                          0.608
                                                                          0.875
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.035
                                                                          0.242
                                                                          0.485
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.016
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.330
                                                                          0.644
                                                                          0.917
                                                                          0.961
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.052
                                                                          0.236
                                                                          0.728
                                                                          0.897
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.047
                                                                          0.357
                                                                          0.536
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.009
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.461
                                                                          0.779
                                                                          0.955
                                                                          0.974
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.089
                                                                          0.338
                                                                          0.840
                                                                          0.933
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.011
                                                                          0.082
                                                                          0.440
                                                                          0.541
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.006
                                                                          0.006
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.576
                                                                          0.866
                                                                          0.954
                                                                          0.981
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.128
                                                                          0.468
                                                                          0.892
                                                                          0.936
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.016
                                                                          0.120
                                                                          0.495
                                                                          0.548
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.004
                                                                          0.004
                                                                             11
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.689
                                                                          0.898
                                                                          0.963
                                                                          0.984
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.195
                                                                          0.593
                                                                          0.917
                                                                          0.949
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.027
                                                                          0.174
                                                                          0.523
                                                                          0.551
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             12
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.804
                                                                          0.922
                                                                          0.968
                                                                          0.994
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.293
                                                                          0.694
                                                                          0.924
                                                                          0.957
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.047
                                                                          0.258
                                                                          0.548
                                                                          0.569
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.004
                                                                          0.005
                                                                             20
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.951
                                                                          0.979
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.901
                                                                          0.950
                                                                          0.992
                                                                          0.996
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.451
                                                                          0.559
                                                                          0.596
                                                                          0.601
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

Comment:
 If the true efficacy is 92.5, the recommended sample size is 7.

Simulations of Study Design 4: Narthropods/animal/day = 50+-5 and blood-fed proportion of arthropod on each animal >= 60%
 The study design:
 The results of this study design apply to studies that test 3 mosquito species/case/day (data are separately analyzed by species) or a single species of stable flies, horse flies, or deer flies/case/day.
 Number of each arthropod species per animal per day = 50+-5
 4 different days
 Inclusion criterion: blood-fed proportion of arthropod on each animal >= 60%
 Input parameters for the simulations:
 From the simulation in SAS program "percent animals or datasets have at least a certain percent arthropod non-blood-fed.sas" using the criterion that the observed proportion of blood-fed on each animal >= 60%, the true percent blood-fed arthropods CP in control animal used in the simulation are reasonably assumed to be 0.80.
 N arthropods/animal/day = 50+-5
 True efficacy of treatment is set = 0.95, 0.925, 0.90, and 0.85 for the 1[st], 2[nd], 3[rd], and 4[th] days. 
 Required observed treatment efficacy is ReqTE = 0.90
 Required precision of efficacy is evaluated as ReqPrecision = 0.025, 0.03, and 0.04.
 The simulations are set to have 2000 datasets per each sample size = 6, 7, ..., 10.
         
      Table A1.4-1
 N per Day = 50+-5, CP = 0.80, no animal random effect, no day random effects
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.305
                                                                          0.558
                                                                          0.864
                                                                          0.950
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.102
                                                                          0.283
                                                                          0.667
                                                                          0.841
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.030
                                                                          0.099
                                                                          0.336
                                                                          0.460
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.008
                                                                          0.013
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.417
                                                                          0.698
                                                                          0.927
                                                                          0.984
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.152
                                                                          0.400
                                                                          0.788
                                                                          0.890
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.042
                                                                          0.138
                                                                          0.384
                                                                          0.470
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.008
                                                                          0.011
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.561
                                                                          0.836
                                                                          0.975
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.252
                                                                          0.577
                                                                          0.892
                                                                          0.944
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.079
                                                                          0.229
                                                                          0.468
                                                                          0.511
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.003
                                                                          0.004
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.705
                                                                          0.906
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.348
                                                                          0.697
                                                                          0.929
                                                                          0.952
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.103
                                                                          0.295
                                                                          0.469
                                                                          0.491
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.003
                                                                          0.003
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.806
                                                                          0.943
                                                                          0.996
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.485
                                                                          0.813
                                                                          0.947
                                                                          0.962
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.161
                                                                          0.365
                                                                          0.494
                                                                          0.508
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.004
                                                                          0.004

      Table A1.4-2
Animal random effects and day random effects assumed to be normal distributions
            N per Day = 50+-5, CP = 0.80, SD_sub = 0, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.197
                                                                          0.433
                                                                          0.822
                                                                          0.951
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.062
                                                                          0.208
                                                                          0.604
                                                                          0.800
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.015
                                                                          0.065
                                                                          0.277
                                                                          0.408
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.009
                                                                          0.012
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.308
                                                                          0.615
                                                                          0.914
                                                                          0.983
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.094
                                                                          0.299
                                                                          0.723
                                                                          0.875
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.038
                                                                          0.114
                                                                          0.376
                                                                          0.479
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.008
                                                                          0.012
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.435
                                                                          0.747
                                                                          0.962
                                                                          0.992
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.152
                                                                          0.421
                                                                          0.835
                                                                          0.916
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.039
                                                                          0.154
                                                                          0.432
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.009
                                                                          0.011
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.588
                                                                          0.857
                                                                          0.988
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.235
                                                                          0.578
                                                                          0.885
                                                                          0.933
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.067
                                                                          0.228
                                                                          0.448
                                                                          0.484
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.002
                                                                          0.002
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.711
                                                                          0.930
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.328
                                                                          0.724
                                                                          0.929
                                                                          0.944
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.088
                                                                          0.289
                                                                          0.466
                                                                          0.482
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.002
                                                                          0.002

      Table A1.4-3
Animal random effects and day random effects assumed to be Weibull distributions
              N per Day =50+-5, CP = 0.80, SubVar = 0, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.121
                                                                          0.368
                                                                          0.833
                                                                          0.956
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.026
                                                                          0.143
                                                                          0.576
                                                                          0.842
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.035
                                                                          0.277
                                                                          0.473
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.009
                                                                          0.015
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.221
                                                                          0.566
                                                                          0.926
                                                                          0.986
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.058
                                                                          0.226
                                                                          0.779
                                                                          0.920
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.010
                                                                          0.064
                                                                          0.382
                                                                          0.509
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.009
                                                                          0.014
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.363
                                                                          0.738
                                                                          0.975
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.086
                                                                          0.364
                                                                          0.864
                                                                          0.941
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.025
                                                                          0.118
                                                                          0.466
                                                                          0.532
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.005
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.513
                                                                          0.872
                                                                          0.991
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.161
                                                                          0.546
                                                                          0.945
                                                                          0.967
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.029
                                                                          0.193
                                                                          0.515
                                                                          0.540
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.003
                                                                          0.003
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.704
                                                                          0.944
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.252
                                                                          0.704
                                                                          0.947
                                                                          0.962
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.061
                                                                          0.283
                                                                          0.545
                                                                          0.556
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.003
                                                                          0.003

      Table A1.4-4
Animal random effects and day random effects assumed to be normal distributions
             N per Day = 50+-5, CP = 0.80, SD_sub = 0.33, SD_day=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.111
                                                                          0.297
                                                                          0.753
                                                                          0.939
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.023
                                                                          0.089
                                                                          0.425
                                                                          0.716
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.002
                                                                          0.021
                                                                          0.158
                                                                          0.342
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.008
                                                                          0.023
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.181
                                                                          0.460
                                                                          0.871
                                                                          0.979
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.040
                                                                          0.162
                                                                          0.590
                                                                          0.818
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.035
                                                                          0.259
                                                                          0.433
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.009
                                                                          0.015
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.283
                                                                          0.615
                                                                          0.952
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.063
                                                                          0.261
                                                                          0.731
                                                                          0.865
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.009
                                                                          0.066
                                                                          0.313
                                                                          0.425
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.008
                                                                          0.009
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.420
                                                                          0.770
                                                                          0.985
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.100
                                                                          0.363
                                                                          0.831
                                                                          0.894
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.020
                                                                          0.109
                                                                          0.372
                                                                          0.427
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.006
                                                                          0.008
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.548
                                                                          0.862
                                                                          0.993
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.163
                                                                          0.495
                                                                          0.894
                                                                          0.917
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.021
                                                                          0.143
                                                                          0.400
                                                                          0.428
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.003
                                                                          0.005
                                                                          0.005

      Table A1.4-5
Animal random effects and day random effects assumed to be Weibull distributions
               N per Day =50+-5, CP = 0.80, SubVar = 1, DayVar=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.208
                                                                          0.481
                                                                          0.889
                                                                          0.983
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.033
                                                                          0.151
                                                                          0.597
                                                                          0.859
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.008
                                                                          0.044
                                                                          0.268
                                                                          0.482
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.010
                                                                          0.020
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.283
                                                                          0.634
                                                                          0.964
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.051
                                                                          0.224
                                                                          0.774
                                                                          0.916
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.008
                                                                          0.054
                                                                          0.358
                                                                          0.510
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.008
                                                                          0.013
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.457
                                                                          0.787
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.101
                                                                          0.398
                                                                          0.894
                                                                          0.940
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.020
                                                                          0.109
                                                                          0.465
                                                                          0.525
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.010
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.611
                                                                          0.913
                                                                          0.995
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.176
                                                                          0.536
                                                                          0.928
                                                                          0.946
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.025
                                                                          0.177
                                                                          0.486
                                                                          0.507
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.008
                                                                          0.008
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.755
                                                                          0.957
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.298
                                                                          0.714
                                                                          0.952
                                                                          0.959
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.054
                                                                          0.264
                                                                          0.514
                                                                          0.524
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.002
                                                                          0.003
                                                                          0.006
                                                                          0.006

      Table A1.4-6
Animal random effects and day random effects assumed to be normal distributions
           N per Day = 50+-5, CP = 0.80, SD_sub = 0.33, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.069
                                                                          0.217
                                                                          0.675
                                                                          0.908
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.015
                                                                          0.055
                                                                          0.338
                                                                          0.658
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.005
                                                                          0.017
                                                                          0.130
                                                                          0.326
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.005
                                                                          0.018
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.124
                                                                          0.356
                                                                          0.821
                                                                          0.966
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.023
                                                                          0.107
                                                                          0.502
                                                                          0.780
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.006
                                                                          0.024
                                                                          0.194
                                                                          0.360
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.007
                                                                          0.016
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.211
                                                                          0.520
                                                                          0.932
                                                                          0.989
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.032
                                                                          0.166
                                                                          0.652
                                                                          0.839
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.004
                                                                          0.041
                                                                          0.285
                                                                          0.404
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.015
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.314
                                                                          0.645
                                                                          0.967
                                                                          0.995
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.060
                                                                          0.274
                                                                          0.762
                                                                          0.876
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.008
                                                                          0.067
                                                                          0.314
                                                                          0.392
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.006
                                                                          0.008
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.416
                                                                          0.788
                                                                          0.989
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.095
                                                                          0.368
                                                                          0.836
                                                                          0.885
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.015
                                                                          0.108
                                                                          0.369
                                                                          0.410
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.005
                                                                          0.005

      
      Table A1.4-7
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day = 50+-5, CP = 0.80, SubVar = 1, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.100
                                                                          0.315
                                                                          0.797
                                                                          0.966
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.018
                                                                          0.093
                                                                          0.478
                                                                          0.801
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.003
                                                                          0.016
                                                                          0.194
                                                                          0.446
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.009
                                                                          0.021
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.177
                                                                          0.475
                                                                          0.911
                                                                          0.986
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.036
                                                                          0.155
                                                                          0.669
                                                                          0.909
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.007
                                                                          0.043
                                                                          0.302
                                                                          0.510
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.009
                                                                          0.018
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.297
                                                                          0.660
                                                                          0.968
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.053
                                                                          0.253
                                                                          0.795
                                                                          0.926
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.007
                                                                          0.063
                                                                          0.422
                                                                          0.550
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.009
                                                                          0.013
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.433
                                                                          0.802
                                                                          0.986
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.108
                                                                          0.394
                                                                          0.910
                                                                          0.967
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.018
                                                                          0.126
                                                                          0.481
                                                                          0.541
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.008
                                                                          0.009
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.605
                                                                          0.910
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.149
                                                                          0.561
                                                                          0.938
                                                                          0.956
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.027
                                                                          0.167
                                                                          0.534
                                                                          0.554
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.005
                                                                          0.005
                                                                             20
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.999
                                                                          1.000
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.966
                                                                          0.992
                                                                          0.993
                                                                          0.993
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.514
                                                                          0.545
                                                                          0.548
                                                                          0.548
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

Comment:
 If the true efficacy is 92.5%, the recommended sample size is 8

Simulations of Study Design 5: Narthropods/animal/day = 100+-10 and blood-fed proportion of arthropod on each animal >= 60%
 The study design:
 The results of this study design apply to studies that test a single species of mosquitoes, fleas, sand flies, black flies, or biting midges per case per day.
 Number of arthropod/species/animal/day = 100+-10
 4 different days
 Inclusion criterion: blood-fed proportion of arthropod on each animal >= 60%
               
 Input parameters for the simulations:
 From the simulation in SAS program "percent animals or datasets have at least a certain percent arthropod non-blood-fed.sas" using the criterion that the blood-fed proportion of arthropod on each animal >= 60%, the true percent blood-fed arthropods CP in control animal used in the simulation are reasonably assumed to be 0.75.
 N arthropods/animal/day = 100+-10
 True efficacy of treatment is set = 0.95, 0.925, 0.90, and 0.85 for the 1[st], 2[nd], 3[rd], and 4[th] days. 
 Required observed treatment efficacy is ReqTE = 0.90
 Required precision of efficacy is evaluated as ReqPrecision = 0.025, 0.03, 0.04, and 0.05
 The simulations are set to have 2000 datasets per each sample size = 6, 7, ..., 10.
               
      Table A1.5-1
N per Day = 100+-10, CP = 0.75, no animal random effect, no day random effects
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.814
                                                                          0.933
                                                                          0.987
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.522
                                                                          0.801
                                                                          0.942
                                                                          0.963
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.190
                                                                          0.367
                                                                          0.479
                                                                          0.497
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.900
                                                                          0.970
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.691
                                                                          0.903
                                                                          0.969
                                                                          0.976
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.265
                                                                          0.425
                                                                          0.494
                                                                          0.502
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.963
                                                                          0.992
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.853
                                                                          0.960
                                                                          0.987
                                                                          0.989
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.377
                                                                          0.489
                                                                          0.513
                                                                          0.516
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.985
                                                                          0.998
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.925
                                                                          0.981
                                                                          0.991
                                                                          0.992
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.426
                                                                          0.470
                                                                          0.482
                                                                          0.482
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.995
                                                                          1.000
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.958
                                                                          0.987
                                                                          0.991
                                                                          0.991
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.481
                                                                          0.509
                                                                          0.515
                                                                          0.515
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

      Table A1.5-2
Animal random effects and day random effects assumed to be normal distributions
           N per Day = 100+-10, CP = 0.75, SD_sub = 0, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.624
                                                                          0.871
                                                                          0.988
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.296
                                                                          0.636
                                                                          0.891
                                                                          0.942
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.079
                                                                          0.249
                                                                          0.424
                                                                          0.454
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.002
                                                                          0.002
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.811
                                                                          0.944
                                                                          0.995
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.453
                                                                          0.780
                                                                          0.946
                                                                          0.963
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.147
                                                                          0.357
                                                                          0.500
                                                                          0.513
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.002
                                                                          0.002
                                                                          0.002
                                                                          0.002
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.915
                                                                          0.983
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.651
                                                                          0.894
                                                                          0.961
                                                                          0.967
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.234
                                                                          0.429
                                                                          0.483
                                                                          0.486
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.003
                                                                          0.003
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.959
                                                                          0.996
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.794
                                                                          0.945
                                                                          0.976
                                                                          0.978
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.313
                                                                          0.446
                                                                          0.473
                                                                          0.475
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.987
                                                                          0.998
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.900
                                                                          0.977
                                                                          0.987
                                                                          0.987
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.381
                                                                          0.463
                                                                          0.474
                                                                          0.475
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

      Table A1.5-3
Animal random effects and day random effects assumed to be Weibull distributions
             N per Day =100+-10, CP = 0.75, SubVar = 0, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.491
                                                                          0.792
                                                                          0.974
                                                                          0.996
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.184
                                                                          0.496
                                                                          0.890
                                                                          0.957
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.052
                                                                          0.184
                                                                          0.491
                                                                          0.551
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.002
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.695
                                                                          0.922
                                                                          0.994
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.331
                                                                          0.697
                                                                          0.962
                                                                          0.983
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.093
                                                                          0.292
                                                                          0.521
                                                                          0.547
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.003
                                                                          0.003
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.859
                                                                          0.972
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.479
                                                                          0.843
                                                                          0.979
                                                                          0.987
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.145
                                                                          0.405
                                                                          0.544
                                                                          0.554
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.001
                                                                          0.001
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.926
                                                                          0.992
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.668
                                                                          0.940
                                                                          0.995
                                                                          0.996
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.229
                                                                          0.482
                                                                          0.555
                                                                          0.559
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.975
                                                                          0.998
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.793
                                                                          0.960
                                                                          0.991
                                                                          0.991
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.321
                                                                          0.540
                                                                          0.580
                                                                          0.581
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

      Table A1.5-4
Animal random effects and day random effects assumed to be normal distributions
            N per Day = 100+-10, CP = 0.75, SD_sub = 0.33, SD_day=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.451
                                                                          0.743
                                                                          0.967
                                                                          0.997
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.126
                                                                          0.349
                                                                          0.739
                                                                          0.862
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.030
                                                                          0.110
                                                                          0.320
                                                                          0.417
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.007
                                                                          0.009
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.626
                                                                          0.872
                                                                          0.993
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.234
                                                                          0.521
                                                                          0.854
                                                                          0.923
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.051
                                                                          0.172
                                                                          0.400
                                                                          0.460
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.006
                                                                          0.008
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.778
                                                                          0.950
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.338
                                                                          0.665
                                                                          0.903
                                                                          0.932
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.084
                                                                          0.231
                                                                          0.408
                                                                          0.443
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.005
                                                                          0.005
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.892
                                                                          0.984
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.469
                                                                          0.774
                                                                          0.938
                                                                          0.946
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.125
                                                                          0.290
                                                                          0.411
                                                                          0.427
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.004
                                                                          0.004
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.939
                                                                          0.995
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.592
                                                                          0.867
                                                                          0.955
                                                                          0.958
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.179
                                                                          0.338
                                                                          0.439
                                                                          0.443
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.002
                                                                          0.002
                                                                          0.002
                                                                          0.002

      Table A1.5-5
Animal random effects and day random effects assumed to be Weibull distributions
              N per Day =100+-10, CP = 0.75, SubVar = 1, DayVar=0
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.646
                                                                          0.896
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.216
                                                                          0.533
                                                                          0.920
                                                                          0.951
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.052
                                                                          0.189
                                                                          0.484
                                                                          0.533
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.004
                                                                          0.005
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.805
                                                                          0.970
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.328
                                                                          0.707
                                                                          0.960
                                                                          0.966
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.071
                                                                          0.255
                                                                          0.519
                                                                          0.534
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.003
                                                                          0.003
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.919
                                                                          0.996
                                                                          0.999
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.514
                                                                          0.871
                                                                          0.973
                                                                          0.973
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.136
                                                                          0.375
                                                                          0.522
                                                                          0.524
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.002
                                                                          0.002
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.978
                                                                          0.997
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.681
                                                                          0.947
                                                                          0.982
                                                                          0.983
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.203
                                                                          0.451
                                                                          0.505
                                                                          0.506
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                          0.001
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.989
                                                                          0.998
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.827
                                                                          0.975
                                                                          0.985
                                                                          0.986
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.307
                                                                          0.505
                                                                          0.526
                                                                          0.526
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.002
                                                                          0.002

      Table A1.5-6
Animal random effects and day random effects assumed to be normal distributions
          N per Day = 100+-10, CP = 0.75, SD_sub = 0.33, SD_day=0.166
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.272
                                                                          0.598
                                                                          0.929
                                                                          0.986
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.057
                                                                          0.221
                                                                          0.659
                                                                          0.834
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.016
                                                                          0.063
                                                                          0.277
                                                                          0.409
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.007
                                                                          0.010
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.445
                                                                          0.778
                                                                          0.978
                                                                          0.995
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.119
                                                                          0.361
                                                                          0.785
                                                                          0.870
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.024
                                                                          0.107
                                                                          0.340
                                                                          0.413
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.006
                                                                          0.008
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.612
                                                                          0.892
                                                                          0.995
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.178
                                                                          0.504
                                                                          0.868
                                                                          0.909
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.038
                                                                          0.162
                                                                          0.382
                                                                          0.421
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.005
                                                                          0.005
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.748
                                                                          0.947
                                                                          0.998
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.306
                                                                          0.645
                                                                          0.904
                                                                          0.929
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.066
                                                                          0.214
                                                                          0.367
                                                                          0.393
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.002
                                                                          0.003
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.876
                                                                          0.984
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.400
                                                                          0.773
                                                                          0.935
                                                                          0.939
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.099
                                                                          0.263
                                                                          0.398
                                                                          0.409
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.002
                                                                          0.002
                                                                          0.002
      
      
      
      Table A1.5-7
Animal random effects and day random effects assumed to be Weibull distributions
            N per Day = 100+-10, CP = 0.75, SubVar = 1, DayVar=0.5
                                       N
                                      Day
                                    true_TE
                                     ReqTE
                             Precision <= 0.025
                             Precision <= 0.030
                             Precision <= 0.040
                             Precision <= 0.050
                                                                              6
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.385
                                                                          0.722
                                                                          0.960
                                                                          0.987
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.097
                                                                          0.313
                                                                          0.787
                                                                          0.930
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.016
                                                                          0.094
                                                                          0.407
                                                                          0.539
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.006
                                                                          0.008
                                                                              7
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.547
                                                                          0.845
                                                                          0.977
                                                                          0.991
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.163
                                                                          0.461
                                                                          0.917
                                                                          0.962
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.036
                                                                          0.136
                                                                          0.491
                                                                          0.549
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.002
                                                                          0.005
                                                                          0.006
                                                                              8
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.728
                                                                          0.935
                                                                          0.991
                                                                          0.998
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.256
                                                                          0.629
                                                                          0.951
                                                                          0.973
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.052
                                                                          0.245
                                                                          0.548
                                                                          0.564
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.001
                                                                          0.002
                                                                          0.003
                                                                              9
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.851
                                                                          0.966
                                                                          0.992
                                                                          0.999
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.389
                                                                          0.794
                                                                          0.971
                                                                          0.982
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.101
                                                                          0.343
                                                                          0.551
                                                                          0.560
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.001
                                                                          0.003
                                                                          0.003
                                                                          0.003
                                                                             10
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          0.923
                                                                          0.979
                                                                          0.997
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.552
                                                                          0.887
                                                                          0.974
                                                                          0.982
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.131
                                                                          0.435
                                                                          0.565
                                                                          0.570
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                             20
                                                                              1
                                                                           0.95
                                                                            0.9
                                                                          1.000
                                                                          1.000
                                                                          1.000
                                                                          1.000
                                                                               
                                                                              2
                                                                          0.925
                                                                            0.9
                                                                          0.988
                                                                          0.997
                                                                          0.999
                                                                          0.999
                                                                               
                                                                              3
                                                                            0.9
                                                                            0.9
                                                                          0.575
                                                                          0.582
                                                                          0.584
                                                                          0.584
                                                                               
                                                                              4
                                                                           0.85
                                                                            0.9
                                                                          0.000
                                                                          0.000
                                                                          0.000
                                                                          0.000

Comment:
 if the true efficacy is 92.5%, the recommended sample size is 6
Appendix II: Evaluation of random effects of logit generated from normal distributions and Weibull distribution
Due to the variation between animals, the blood-fed proportion of an arthropod species may be different between different animals; and due to the variation of unknown factors, the blood-fed proportion of an arthropod species on a specific animal can be different between days.  To create the random effects due to the variation between animals or variation between days given the overall blood-fed proportion of population P, an animal random effect rands and a day random effect randi are added to the population logit.
Specifically, if P is the blood-fed proportion of the animal population, the population logit is
      Logit Q = log(P/(1-P)), and
the logit of an s[th] animal on i[th] day is:
      Qs= Q + rands + randi
Since we don't know the true values of rands and randi, we assume that the range of lower half distribution (from minimum value to median) of rands distribution is 1 and the range of lower half distribution of randi is 0.5.  With these assumed values, if the population proportion is 0.95, the population logit is = ln(0.95/(1-0.95)) = 2.9444, the logit of true proportion of an animal on a day at low range can be = 2.9444  -  1  -  0.5 = 1.444, and the true proportion of the animal on the day is = exp(1.444)/(1+exp(1.444) = 0.8091.   Similarly, if the population proportion is 0.4, the true proportion of an animal on a day can be as low as 0.1294.
Since we don't exactly know the underlying distributions of rands and randi of these effects, we evaluate and determine whether normal distributions or Weibull distributions is a better assumption for these random effects.  Basically, we would evaluate the estimated blood-fed proportions and the estimated treatment efficacy from the simulated datasets where rands and randi are generated from normal distributions or Weibull distribution, given the population blood-fed proportions and the treatment efficacy.  
Details simulations
The study design for each dataset includes 2 groups: control and treatment.  There are 4 different testing days and the blood-fed proportions in the control are P = 0.95, 0.60, 0.40, and 0.20.  The treatment effect (efficacy) are TE = 0.95, 0.925, 0.90, and 0.85.  The blood-fed proportions of treated group are calculated as P*(1-TE) and equal 0.0475, 0.045, 0.04, and 0.3.  Within each dataset, the numbers of animals in control group and treatment group are the same.
When the animal random effects and day random effects are assumed to follow normal distributions, the logit of the s[th] animal on i[th] day is Qsi= Q + rands + randi, where the animal random effect rands is randomly generated from normal distribution with mean = 0 and standard deviation SD_sub =0.33 and day random effect is randomly generated from normal distribution mean =0 and standard deviation SD_day = 0.166 (the standard deviation of the distribution is estimated as the half range of distribution divided by 3).  Each animal would have same value of rands for different days and different values of randi for different days.
When the animal random effects and day random effects are assumed to follow Weibull distributions, the logit of the s[th] animal on i[th] day is Qsi= Q + rands + randi, where the animal random effect rands is randomly generated as
 Randomly generated u from uniform distribution U(0,1).  Each animal has same value u for all days.
 Derive the temps associated with the quantile value u of the Weibull distribution (a, b), where a = 1/P and b = exp((1/a)xlog(-(SubVar[a])/log(0.5))), with SubVar = 1
 the animal random effect of s[th] animal on i[th] day is rands = temps  -  SubVar.  Since value of P is different on different day, value of a is different on different days and value of rands of same s[th] animal is different on different days.
 For each i[th] day, compute Ps = exp(Qs)/(1 + exp(Qs)), where Qs = Q + rands
 Randomly generated tempi from Weibull distribution shape ai and location bi, where ai = 1/Ps and bi = exp((1/ai) xlog(-(DayVar[ai])/log(0.5))), with DayVar = 0.5.
 The random day effect of s[th] animal on i[th] day is randi = tempi  -  DayVar, 
From the logit of the s[th] animal on i[th] day is Qsi= Q + rands + randi, we can compute the blood-fed proportion of the s[th] animal on i[th] day as Psi = exp(Qsi)/(1 + exp(Qsi)).
The total arthropod used for each animal on a day is randomly generated from a uniform distribution Nsi = U[0.9*Narthropod, 1.1*Narthropod), where Narthropod = 100 is target number of arthropod/animal/day.
The number of blood-fed arthropods for the s[th] animal on i[th] day is randomly generated from binomial distribution B(Nsi, Psi).
The number of animals per group is set to be 10 (expected sample size for actual studies) and 100 (large but unpractical sample size).
The simulations will include 2000 datasets for each scenario.  Generalized linear mixed effects model (PROC GLIMMIX) for overdispersion Poisson distribution data with animal and day as random effects (RANDOM Day/subject = animal type = cs; RANDOM _residual_;) is used to analyze each dataset.  For those datasets that the generalized linear mixed effects model has a computational (convergence) issue, generalized linear model for Poisson distribution data is used to separately analyze the data by Day.  The point estimated blood-fed proportions and blood-fed proportions ratio (i.e. adjusted blood-fed proportion of treatment group) for each day are obtained.  The efficacy of the treatment group = 1  -  adjusted blood-fed proportion.  Medians of observed blood-fed proportions and treatment efficacy will be compared to the true value to determine whether normal distributions or Weibull distributions for the random animal effect and random day effect would have less bias in the estimates.

Results
Table A2.1
Observed blood-fed proportions
Random animal effect and day effect randomly generated from Normal distribution, N = 100 animal/group
Group
Day
TrueP
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
0
1
0.95
2000
0.9328454
0.9402728
0.9421845
0.9443784
0.9466070
0.9484965
0.9553941

2
0.6
2000
0.5651210
0.5817944
0.5879972
0.5945176
0.6013941
0.6078380
0.6315579

3
0.4
2000
0.3700825
0.3882950
0.3938229
0.4009357
0.4074620
0.4137459
0.4370733

4
0.2
2000
0.1812036
0.1958686
0.2000952
0.2050870
0.2099574
0.2145404
0.2324107
1
1
0.0475
2000
0.0415714
0.0464748
0.0481624
0.0500982
0.0519519
0.0537152
0.0596553

2
0.045
2000
0.0374002
0.0442125
0.0457950
0.0475080
0.0493431
0.0511296
0.0591684

3
0.04
2000
0.0337842
0.0390285
0.0404892
0.0422281
0.0439873
0.0455478
0.0518940

4
0.03
2000
0.0248943
0.0292099
0.0305113
0.0318165
0.0330973
0.0344033
0.0385632

Table A2.2
Observed blood-fed proportions
Random animal effect and day effect randomly generated from Weibull distribution, N = 100 animal/group

Group
Day
TrueP
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
0
1
0.95
2000
0.9303659
0.9393636
0.9423884
0.9461275
0.9492810
0.9521507
0.9632905

2
0.6
2000
0.5585443
0.5907012
0.6004746
0.6119333
0.6231649
0.6331901
0.6720473

3
0.4
2000
0.3611335
0.3928335
0.4004552
0.4091731
0.4180852
0.4263132
0.4574537

4
0.2
2000
0.1778586
0.1912323
0.1945159
0.1986015
0.2026500
0.2062123
0.2223280
1
1
0.0475
2000
0.0402851
0.0440981
0.0455001
0.0469498
0.0484082
0.0497623
0.0537063

2
0.045
2000
0.0369101
0.0417713
0.0430978
0.0445859
0.0460477
0.0472637
0.0519586

3
0.04
2000
0.0330633
0.0371344
0.0382563
0.0395118
0.0407533
0.0419070
0.0495017

4
0.03
2000
0.0236409
0.0276042
0.0285592
0.0296799
0.0308359
0.0318953
0.0349423

Table A2.3
Observed Treatment Efficacy TE
Random animal effect and day effect randomly generated from Normal distribution, N = 100 animal/group
Day
TrueTE
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
1
0.95
2000
0.9368674
0.9431031
0.9449707
0.9469610
0.9490180
0.9507364
0.9558333
2
0.925
2000
0.9006239
0.9137789
0.9168844
0.9200212
0.9231180
0.9257359
0.9381344
3
0.9
2000
0.8662430
0.8855087
0.8898869
0.8946578
0.8992225
0.9033674
0.9165963
4
0.85
2000
0.8044660
0.8301122
0.8374219
0.8448203
0.8521580
0.8592251
0.8822268

Table A2.4
Observed Treatment Efficacy TE
Random animal effect and day effect randomly generated from Weibull distribution, N = 100 animal/group
Day
TrueTE
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
1
0.95
2000
0.9431504
0.9473898
0.9487798
0.9503326
0.9518947
0.9533259
0.9576572
2
0.925
2000
0.9125166
0.9219001
0.9245417
0.9271314
0.9298943
0.9323712
0.9397698
3
0.9
2000
0.8820273
0.8963840
0.8995518
0.9034971
0.9073198
0.9106829
0.9197308
4
0.85
2000
0.8200519
0.8374681
0.8434998
0.8502472
0.8571217
0.8627663
0.8798294

Table A2.5
Observed blood-fed proportions
Random animal effect and day effect randomly generated from Normal distribution, N = 10 animal/group
Group
Day
TrueP
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
0
1
0.95
2000
0.9088040
0.9327243
0.9395808
0.9461810
0.9522739
0.9572993
0.9703017

2
0.6
2000
0.4765415
0.5533382
0.5738590
0.5958000
0.6160173
0.6351628
0.7020218

3
0.4
2000
0.3031381
0.3611132
0.3816398
0.4020775
0.4221412
0.4423258
0.5187859

4
0.2
2000
0.1319066
0.1779262
0.1905663
0.2045801
0.2202250
0.2341645
0.3004032
1
1
0.0475
2000
0.0261650
0.0389766
0.0439661
0.0496388
0.0551633
0.0610804
0.0796229

2
0.045
2000
0.0267567
0.0367934
0.0412758
0.0470691
0.0531056
0.0588088
0.0853381

3
0.04
2000
0.0216858
0.0322226
0.0368126
0.0416141
0.0467908
0.0529292
0.0727324

4
0.03
2000
0.0157180
0.0236748
0.0272710
0.0315263
0.0359851
0.0402597
0.0593183

Table A2.6
Observed blood-fed proportions
Random animal effect and day effect randomly generated from Weibull distribution, N = 10 animal/group

Group
Day
TrueP
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
0
1
0.95
2000
0.8837114
0.9256713
0.9363142
0.9475478
0.9574173
0.9665922
0.9899296

2
0.6
2000
0.4474323
0.5449825
0.5762213
0.6104993
0.6453740
0.6790745
0.7876322

3
0.4
2000
0.2898584
0.3605328
0.3823695
0.4089170
0.4390268
0.4638160
0.5571623

4
0.2
2000
0.1364718
0.1775665
0.1863037
0.1985275
0.2101781
0.2220527
0.2583755
1
1
0.0475
2000
0.0281432
0.0386449
0.0425075
0.0467563
0.0516444
0.0559265
0.0725646

2
0.045
2000
0.0230692
0.0361864
0.0399485
0.0443134
0.0488494
0.0527465
0.0660680

3
0.04
2000
0.0182927
0.0316249
0.0353893
0.0395499
0.0436574
0.0475643
0.0632315

4
0.03
2000
0.0132069
0.0230203
0.0258402
0.0294418
0.0333539
0.0366646
0.0519890

Table A2.7
Observed Treatment Efficacy TE
Random animal effect and day effect randomly generated from Normal distribution, N = 10 animal/group
Day
TrueTE
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
1
0.95
2000
0.9164632
0.9356072
0.9416649
0.9474740
0.9534573
0.9587734
0.9717145
2
0.925
2000
0.8614778
0.9000384
0.9096871
0.9211580
0.9307886
0.9388335
0.9571959
3
0.9
2000
0.7878601
0.8658581
0.8813963
0.8961819
0.9092991
0.9213917
0.9514290
4
0.85
2000
0.6470266
0.7950162
0.8212458
0.8461488
0.8692246
0.8876879
0.9301326

Table A2.8
Observed Treatment Efficacy TE
Random animal effect and day effect randomly generated from Weibull distribution, N = 10 animal/group
Day
TrueTE
N Obs
Minimum
10th Pctl
25th Pctl
50th Pctl
75th Pctl
90th Pctl
Maximum
1
0.95
2000
0.9248519
0.9407501
0.9454142
0.9506733
0.9551289
0.9593058
0.9704267
2
0.925
2000
0.8735442
0.9107129
0.9186265
0.9273257
0.9357941
0.9422458
0.9637692
3
0.9
2000
0.8063440
0.8789001
0.8914272
0.9034103
0.9150339
0.9252431
0.9523135
4
0.85
2000
0.7311387
0.8102500
0.8302189
0.8514160
0.8710503
0.8881022
0.9405302

Conclusions
 The medians of estimated blood-fed proportions from simulated datasets are very close to the true values, when the animal random effects and day random effects are assumed to follow normal distributions or Weibull distributions.
         
 When the random animal effects and random day effects are randomly generated from Weibull distributions, the observed efficacy is slightly over-estimated.  When the random animal effects and random day effects are randomly generated from normal distributions, the observed efficacy is slightly under-estimated.

 Both assumptions that random animal effects and random day effects follow normal distributions and Weibull distributions are reasonable for the simulation of sample size/power of Pet Product studies.  

Appendix III: True blood-fed proportion vs. proportions of animals/datasets meet the required blood-fed proportion
One of the criteria for an animal to be selected for a study is that the observed blood-fed proportion of the animal from the screening test is greater than certain required value to ensure the attractiveness of the animal to the arthropods.  It also requires that the observed blood-fed proportion of each control animal is greater than certain required value during the study period.  This simulation is simply to determine the lowest blood-fed proportion such that a low probability for an animal to have an observed blood-fed proportion below the required blood-fed proportion and a low probability for a dataset (single measurement/animal) to have at least 1 animal with observed blood-fed proportion below the required blood-fed proportion.  It is worth mentioning that the lowest true blood-fed proportions obtained from these simulations are used for simulations of sample size and used for the purpose of helping experts to determine whether the required blood-fed proportions are reasonable or not.  In reality, we cannot assign a value for true blood-fed proportion for animals and we don't exactly know these values.  We determine the lowest true blood-fed for simulations because the power of the study will increase if the true blood-fed proportion is greater.
Two Tables A3.1 and A3.2 below present the results of simulations.  From these simulations, we conclude that the lowest blood-fed proportion are assumed to be:
 When the required blood-fed proportion for an animal is 0.25 and the number of arthropods/animal = 50, the lowest true value for blood-fed-proportion that can be used is 0.45
         
 When the required blood-fed proportion for an animal is 0.40 and the number of arthropods/animal = 50, the lowest true value for blood-fed- proportion that can be used is 0.60
         
 When the required blood-fed proportion for an animal is 0.40 and the number of arthropods/animal = 100, the lowest true value for blood-fed- proportion that can be used is 0.60
         
 When the required blood-fed proportion for an animal is 0.60 and the number of arthropods/animal = 50, the lowest true value for blood-fed- proportion that can be used is 0.80
         
 When the required blood-fed proportion for an animal is 0.60 and the number of arthropods/animal = 100, the lowest true value for blood-fed- proportion that can be used is 0.75
Note that if the true blood-fed proportion is greater than the assumed value in the simulations, the true power of the study design is greater than the power observed from the simulations.

TableA3.1: Proportion of animals with observed blood-fed proportion < require blood fed proportion
                                          True             blood-fed proportion
                                         Required          blood-fed proportion
                                                   Number arthropods per animal
                                                                 Total animals 
Proportion of animals with observed blood-fed proportion < require blood fed proportion
                                                                           0.75
                                                                            0.6
                                                                             50
                                                                         460000
                                                                        0.01065
                                                                            0.8
                                                                            0.6
                                                                             50
                                                                         460000
                                                                        0.00073
                                                                            0.7
                                                                            0.6
                                                                            100
                                                                         460000
                                                                        0.01759
                                                                           0.75
                                                                            0.6
                                                                            100
                                                                         460000
                                                                        0.00060
                                                                           0.55
                                                                            0.4
                                                                             50
                                                                         460000
                                                                        0.01845
                                                                            0.6
                                                                            0.4
                                                                             50
                                                                         460000
                                                                        0.00255
                                                                           0.55
                                                                            0.4
                                                                            100
                                                                         460000
                                                                        0.00152
                                                                            0.6
                                                                            0.4
                                                                            100
                                                                         460000
                                                                        0.00005
                                                                            0.4
                                                                           0.25
                                                                             50
                                                                         460000
                                                                        0.01486
                                                                           0.45
                                                                           0.25
                                                                             50
                                                                         460000
                                                                        0.00209

Table A3.2: Proportion of datasets having at least one animal with observed blood-fed proportion < require blood fed proportion
                                          True             blood-fed proportion
                                         Required          blood-fed proportion
                                                   Number arthropods per animal
                                                       Number animals per group
                                                             Number of datasets
Proportion of datasets having  at least one animal with observed blood-fed proportion < require blood fed proportion 
                                                                           0.75
                                                                            0.6
                                                                             50
                                                                              8
                                                                           5000
                                                                        0.08320
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.08700
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.09940
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.11240
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.12300
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.12660
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.13780
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.15900
                                                                            0.8
                                                                            0.6
                                                                             50
                                                                              8
                                                                           5000
                                                                        0.00600
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.00560
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.00560
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.00820
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.00860
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.00960
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.01000
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.01280
                                                                            0.7
                                                                            0.6
                                                                            100
                                                                              8
                                                                           5000
                                                                        0.13320
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.14680
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.15900
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.18220
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.19080
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.20140
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.21840
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.23560
                                                                           0.75
                                                                            0.6
                                                                            100
                                                                              8
                                                                           5000
                                                                        0.00540
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.00420
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.00600
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.00660
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.00680
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.00780
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.00860
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.00980
                                                                           0.55
                                                                            0.4
                                                                             50
                                                                              8
                                                                           5000
                                                                        0.13720
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.15300
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.16420
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.18760
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.20140
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.21180
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.23020
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.24400
                                                                            0.6
                                                                            0.4
                                                                             50
                                                                              8
                                                                           5000
                                                                        0.01900
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.02140
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.02040
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.02600
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.03100
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.03260
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.03460
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.04520
                                                                           0.55
                                                                            0.4
                                                                            100
                                                                              8
                                                                           5000
                                                                        0.01260
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.01260
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.01340
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.01780
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.01680
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.01880
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.02160
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.02540
                                                                            0.6
                                                                            0.4
                                                                            100
                                                                              8
                                                                           5000
                                                                        0.00000
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.00020
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.00080
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.00040
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.00060
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.00080
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.00060
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.00120
                                                                            0.4
                                                                           0.25
                                                                             50
                                                                              8
                                                                           5000
                                                                        0.11520
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.12620
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.14180
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.14640
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.16220
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.17880
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.18600
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.19780
                                                                           0.45
                                                                           0.25
                                                                             50
                                                                              8
                                                                           5000
                                                                        0.01580
                                                                               
                                                                               
                                                                               
                                                                              9
                                                                           5000
                                                                        0.02000
                                                                               
                                                                               
                                                                               
                                                                             10
                                                                           5000
                                                                        0.02060
                                                                               
                                                                               
                                                                               
                                                                             11
                                                                           5000
                                                                        0.02380
                                                                               
                                                                               
                                                                               
                                                                             12
                                                                           5000
                                                                        0.02280
                                                                               
                                                                               
                                                                               
                                                                             13
                                                                           5000
                                                                        0.02720
                                                                               
                                                                               
                                                                               
                                                                             14
                                                                           5000
                                                                        0.02840
                                                                               
                                                                               
                                                                               
                                                                             15
                                                                           5000
                                                                        0.03140