DDVP Dog ‐ Week 13 ‐ RBC ChE ‐ Females

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 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: 

C:/Users/jliccion/Desktop/BMDS230/Data/exp_TestContinuous1_Setting.(d) 

 Gnuplot Plotting File: 

 Wed May 21 09:02:54 2014 

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 BMDS Model Run 

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 The form of the response function by Model: 

 Model 2: Y[dose] = a * exp{sign * b * dose} 

 Model 3: Y[dose] = a * exp{sign * (b * dose)^d} 

 Model 4: Y[dose] = a * [c-(c-1) * exp{-b * dose}] 

 Model 5: Y[dose] = a * [c-(c-1) * exp{-(b * dose)^d}] 

 Note: Y[dose] is the median response for exposure = dose; 

 sign = +1 for increasing trend in data; 

 sign = -1 for decreasing trend. 

 Model 2 is nested within Models 3 and 4. 

 Model 3 is nested within Model 5. 

 Model 4 is nested within Model 5. 

 Dependent variable = Mean 

 Independent variable = Dose 

 Data are assumed to be distributed: normally 

 Variance Model: exp(lnalpha +rho *ln(Y[dose])) 

 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) 

 Total number of dose groups = 4 

 Total number of records with missing values = 0 

 Maximum number of iterations = 250 

 Relative Function Convergence has been set to: 1e-008 

 Parameter Convergence has been set to: 1e-008 

 MLE solution provided: Exact 

 Initial Parameter Values 

 Variable Model 2 Model 3 Model 4 Model 5 

 -------- ------- ------- ------- ------- 

 lnalpha -3.337 -3.337 -3.337 -3.337 

 rho 2.13506 2.13506 2.13506 2.13506 

 a 2.61954 2.61954 9.345 9.345 

 b 0.543931 0.543931 0.806855 0.806855 

 c -- -- 0.0856073 

0.0856073 

 d -- 1 -- 1 

 Parameter Estimates by Model 

 Variable Model 2 Model 3 Model 4 Model 5 

 -------- ------- ------- ------- ------- 
 lnalpha -3.13476 -3.13476 -3.3699 -3.3699 

 rho 2.11969 2.11969 2.16696 2.16696 

 a 7.90215 7.90215 8.3663 8.3663 

 b 0.54289 0.54289 0.971055 0.971055 

 c -- -- 0.147844 0.147844 

 d -- 1 -- 1 

 Table of Stats From Input Data 

 Dose N Obs Mean Obs Std Dev 

 ----- --- ---------- ------------- 

 0 4 8.9 2.47 

 0.05 4 7.3 1.86 

 1 4 4.1 0.42 

 3 4 1.6 0.42 

 Estimated Values of Interest 

 Model Dose Est Mean Est Std Scaled Residual 

 ------- ------ ---------- --------- ---------------- 

 2 0 7.902 1.865 1.07 

 0.05 7.691 1.812 -0.4309 

 1 4.592 1.049 -0.9372 

 3 1.55 0.332 0.2993 

 3 0 7.902 1.865 1.07 

 0.05 7.691 1.812 -0.4309 

 1 4.592 1.049 -0.9372 

 3 1.55 0.332 0.2993 

 4 0 8.366 1.853 0.5762 

 0.05 8.028 1.772 -0.8223 

 1 3.937 0.8186 0.399 

 3 1.624 0.3136 -0.1534 

 5 0 8.366 1.853 0.5762 

 0.05 8.028 1.772 -0.8223 

 1 3.937 0.8186 0.399 

 3 1.624 0.3136 -0.1534 

 Other models for which likelihoods are calculated: 

 Model A1: Yij = Mu(i) + e(ij) 

 Var{e(ij)} = Sigma^2 

 Model A2: Yij = Mu(i) + e(ij) 

 Var{e(ij)} = Sigma(i)^2 

 Model A3: Yij = Mu(i) + e(ij) 

 Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) 

 Model R: Yij = Mu + e(i) 

 Var{e(ij)} = Sigma^2 

 Likelihoods of Interest 

 Model Log(likelihood) DF AIC 

 ------- ----------------- ---- ------------ 

 A1 -12.95921 5 35.91841 

 A2 -4.857717 8 25.71543 

 A3 -6.674776 6 25.34955 
 R -26.30027 2 56.60055 

 2 -8.654198 4 25.3084 

 3 -8.654198 4 25.3084 

 4 -7.315069 5 24.63014 

 5 -7.315069 5 24.63014 

 Additive constant for all log-likelihoods = -14.7. This constant added to the 

 above values gives the log-likelihood including the term that does not 

 depend on the model parameters. 

 Explanation of Tests 

 Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) 

 Test 2: Are Variances Homogeneous? (A2 vs. A1) 

 Test 3: Are variances adequately modeled? (A2 vs. A3) 

 Test 4: Does Model 2 fit the data? (A3 vs. 2) 

 Test 5a: Does Model 3 fit the data? (A3 vs 3) 

 Test 5b: Is Model 3 better than Model 2? (3 vs. 2) 

 Test 6a: Does Model 4 fit the data? (A3 vs 4) 

 Test 6b: Is Model 4 better than Model 2? (4 vs. 2) 

 Test 7a: Does Model 5 fit the data? (A3 vs 5) 

 Test 7b: Is Model 5 better than Model 3? (5 vs. 3) 

 Test 7c: Is Model 5 better than Model 4? (5 vs. 4) 

 Tests of Interest 

 Test -2*log(Likelihood Ratio) D. F. p-value 

 -------- ------------------------ ------ -------------- 

 Test 1 42.89 6 < 0.0001 

 Test 2 16.2 3 0.00103 

 Test 3 3.634 2 0.1625 

 Test 4 3.959 2 0.1381 

 Test 5a 3.959 2 0.1381 

 Test 5b 3.197e-014 0 N/A 

 Test 6a 1.281 1 0.2578 

 Test 6b 2.678 1 0.1017 

 Test 7a 1.281 1 0.2578 

 Test 7b 2.678 1 0.1017 

 Test 7c 2.558e-013 0 N/A 

 The p-value for Test 1 is less than .05. There appears to be a 

 difference between response and/or variances among the dose 

 levels, it seems appropriate to model the data. 

 The p-value for Test 2 is less than .1. A non-homogeneous 

 variance model appears to be appropriate. 

 The p-value for Test 3 is greater than .1. The modeled 

 variance appears to be appropriate here. 

 The p-value for Test 4 is greater than .1. Model 2 seems 

 to adequately describe the data. 

 The p-value for Test 5a is greater than .1. Model 3 seems 

 to adequately describe the data. 
 Degrees of freedom for Test 5b are less than or equal to 0. 

 The Chi-Square test for fit is not valid. 

 The p-value for Test 6a is greater than .1. Model 4 seems 

 to adequately describe the data. 

 The p-value for Test 6b is greater than .05. Model 4 does 

 not seem to fit the data better than Model 2. 

 The p-value for Test 7a is greater than .1. Model 5 seems 

 to adequately describe the data. 

 The p-value for Test 7b is greater than .05. Model 5 does 

 not seem to fit the data better than Model 3. 

 Degrees of freedom for Test 7c are less than or equal to 0. 

 The Chi-Square test for fit is not valid. 

 Benchmark Dose Computations: 

 Specified Effect = 0.100000 

 Risk Type = Relative deviation 

 Confidence Level = 0.950000 

 BMD and BMDL by Model 

 Model BMD BMDL 

 ------- ------------ ---------- 

 2 0.194073 0.165103 

 3 0.194073 0.165103 

 4 0.128547 0.0946144 

 5 0.128547 0.0946144 
 0

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 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

09:02 05/21 2014

BMDL BMD

 

Exponential
 0

 2

 4

 6

 8

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 12

 14

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

09:02 05/21 2014

BMDL BMD

 

Exponential
 0

 2

 4

 6

 8

 10

 12

 14

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

09:02 05/21 2014

BMDL BMD

 

Exponential
 0

 2

 4

 6

 8

 10

 12

 14

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 5 with 0.95 Confidence Level

09:02 05/21 2014

BMDL BMD

 

Exponential