# BMDs for T and CS from WIL FOB Study

April 1, 2009

# Contents

1 Methods 4 1.1 Recoding T and CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Dose-Response Modeling and BMD Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Results 6 2.1 How to Read This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 B-Cyf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Fenpro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 S-Bio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5 Cyper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.2.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.3.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5.3.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6 L-Cyh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6.2.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6.3.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6.3.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7 Perm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

12.7.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.7.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.7.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.8 Delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.8.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.8.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8.2.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8.3.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8.3.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.9 Pyr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.9.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.9.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.9.2.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.9.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.9.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.10 Resm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.10.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.10.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.10.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.10.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.10.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.10.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.11 Bifen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.11.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.11.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.11.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.11.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.11.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.11.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.12 Esfen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.12.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.12.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.12.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.12.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.12.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.12.3.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.12.3.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.13 Tefl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.13.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.13.2 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.13.2.1 Modeling Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.13.2.2 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.13.3 CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.13.3.1 Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3 Summary Graphs 51 3.1 BMDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2 Relative Potencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 A getData.R 54

2B DRmodelsTCS.R 56

3

# Chapter 1 

# Methods

1.1 Recoding T and CS The variables analyzed here, T and CS , are composites of five other variables measured in the WIL FOB study:
• body temperature: T (hyperthermia) and CS (hypothermia)

• tremors: T

• clonic convulsions: T

• salivation: CS

• mobility: CS Body temperature,was measured and reported as a continuous variable (degrees C, in tenths of a degree), and the remaining are categorical variables, coded 1 . . . 4, except for ’convulsions’, which were coded 1 . . . 7. Clonic convulsions was recoded to 4 for myolonus, and 1 for anything else. Tremors and clonic convulsions were observed as both home cage and open field observations. The value used is the maximum of the two types of observation. Before the composite indices were constructed, body temperature was recoded to two categorical variables, hyperthermia and hypothermia. Each variable is based on the difference between an observation and the concurrent control mean, as a multiple of the standard deviatio of values in the controls. The control standard deviation was calculated as the square root of the within-group mean square error for all control groups:
sd 

### = s ∑m

j=1 ∑nj i=1 

### (yij 

### − yj 

### ) N



### − m where yj 

### = ∑nj i=1 yij nj and N 

### = ∑

j nj . Coding for both variables is as follows. 1 up to 1 sd from the concurrent control mean 2 greater than 1 and less than 1.5 sd from the concurrent control mean 3 between 1.5 and 2 sd from the concurrent control mean 4 greater than 2 sd from the concurrent control mean Hyperthermia flags increases, while hypothermia flags decreases in temperature. So, for example, if an observation is 1.8 sd above its concurrent control mean, hyperthermia would be coded 3, while hypothermia would be coded 1, while if the observation were the same distance below the control mean, hypothermia would be coded 3, while hyperthermia would be coded 1. The variables T and CS are constructed by summing the values of the individual variables of which they are composits. In this analysis, the resulting 12 - state variables was dichotomized, to 1 if T 

### > 4 or CS 

### > 4

. 4

## 1.2 Dose-Response Modeling and BMD Calculation

Before dose-response modeling, each data set was tested for significant trend. Only if a trend was statistically significant was a BMD computed. Dose-response modeling was carried out using the methodology described in Wheeler and Bailer (2007): “Properties of Model-Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation” from Risk Analysis:27, pages 659–670. BMDLs and standard deviations of the (natural) log-transformed BMDs were based on 4999 bootstrap samples. Confidence limits for relative potency ratios are based on 500 random samples from the appropriate distributions. Because of the small sample sizes, the BMR was defined to be 20% extra risk; that is, a BMD in this analysis is the dose estimated to result in 20% extra risk.

5

# Chapter 2 

# Results

2.1 How to Read This Chapter The remaining sections in this chapter give the results for all the chemicals covered in the WIL study. Each sectionhas a section devoted to the data for the T and CS endpoints. This is followed by sections for each of the two endpoints, T and CS. If there is a significant trend for an endpoint, then the output from mabmd.exe is shown, followed by a plot of the data with 95% confidence intervals for the means and the trace of the fitted model, along with indicators for BMD and BMDL. If there is no significant trend, then only the data are shown with their confidence intervals. Within the section labeled "Modeling Details", notice in particular the section giving the results of a goodness-of-fit test for the average model. Also, see the summary table of log-likelihoods and weights at the top of the section, as this gives the contribution of each model to the average model. Finally, there is a separate entry for each component model, giving the parameter estimates for that model to the data. 

## 2.2 B-Cyf 2.2.1 Data dose T n CS 0 0.0 1 20 2 12.5 12.5 0 10 2 25 25.0 2 10 7 45 45.0 0 10 10 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0.0 0 20 1 12.5 12.5 0 10 2 25 25.0 3 10 6 45 45.0 0 10 10

6 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-7

Similar summary of data entered independently for QA;

### 2.2.2 T

2.2.2.1 Figure



### 2.2.3 CS 2.2.3.1 Modeling Details Model Fitting Summary and Weights

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

Weight -2log(L) AIC BIC Multistage 0.012 35.27 43.27 50.92 Logistic 0.338 36.48 40.48 44.31 Probit 0.335 36.50 40.50 44.32 Weibull 0.089 35.24 41.24 46.97 Log-Probit 0.075 35.59 41.59 47.33 Log-Logistic 0.069 35.75 41.75 47.49 Gamma 0.082 35.41 41.41 47.14

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 12.602505925424 BMDL(BCa): 8.460449823594 BMDL(Percentile): 8.184628126452 Acceleration: -0.060599
7Bootstrap Resamples: 4999

Random Seed: 1238590375

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.476716 P.value: 0.637327

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 9.700513e-02 6.136486e-02 BETA(1) 0.000000e+00 NA BETA(2) 0.000000e+00 NA BETA(3) 7.061953e-05 2.867501e-05 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -2.633190 0.721913 BETA 0.139356 0.037137 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -1.484032 0.356103 BETA 0.079560 0.018927 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.100894 0.066933 ALPHA 3.315661 1.966987 BETA 0.000026 0.000162 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.1074275 0.074059 ALPHA -8.7765930 4.785742 BETA 2.8920350 1.467550 Optimization Successful

------------------------------------------------------------
8MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.113403 0.083303 ALPHA -16.611691 15.368976 BETA 5.417968 4.671650 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.104228 0.070214 ALPHA 8.360603 7.930061 BETA 0.380702 0.348166 Optimization Successful

------------------------------------------------------------
2.2.3.2 Figure



## 2.3 Fenpro 2.3.1 Data dose T n CS 0 0 0 10 1
915 15 0 10 0

30 30 3 10 3 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 0 10 1 15 15 0 10 0 30 30 3 10 2 

### 2.3.2 T 2.3.2.1 Modeling Details Model Fitting Summary and Weights

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

Weight -2log(L) AIC BIC Multistage 0.030 13.78 19.78 23.98 Logistic 0.358 12.22 16.22 19.02 Probit 0.359 12.22 16.22 19.02 Weibull 0.065 12.22 18.22 22.42 Log-Probit 0.065 12.22 18.22 22.42 Log-Logistic 0.058 12.47 18.47 22.67 Gamma 0.065 12.24 18.24 22.44

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 28.952112240473 BMDL(BCa): 27.40278122376 BMDL(Percentile): 26.713650694254 Acceleration: -0.053673 Bootstrap Resamples: 4999 Random Seed: 1238590445

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.028464 P.value: 0.366873

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.0000000000 NA BETA(1) 0.0000000000 NA BETA(2) 0.0003049298 0.000176603 Optimization Successful

------------------------------------------------------------ 10MODEL: Logistic

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

Estimate StdErr ALPHA -18.00000 NA BETA 0.57175 0.023002 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -10.925079 150.014161 BETA 0.346689 5.000492 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0 NA ALPHA 18 NA BETA 0 NA Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 5.138034 0.122517 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 5.029222 0.201122 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

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

Estimate StdErr GAMMA 0.000000 NA ALPHA 18.000000 NA BETA 0.517888 0.053165 Optimization Successful

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

112.3.2.2 Figure

12

### 2.3.3 CS

2.3.3.1 Figure



## 2.4 S-Bio 2.4.1 Data dose T n CS 0 0 1 20 2 150 150 3 10 0 200 200 4 10 1 300 300 7 10 2 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 0 20 1 150 150 3 10 0 200 200 6 10 1 300 300 7 10 2 

### 2.4.2 T 2.4.2.1 Modeling Details Model Fitting Summary and Weights

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

Weight -2log(L) AIC BIC
13Multistage 0.008 45.85 53.85 61.50

Logistic 0.385 45.89 49.89 53.71 Probit 0.391 45.86 49.86 53.68 Weibull 0.055 45.88 51.88 57.61 Log-Probit 0.053 45.93 51.93 57.66 Log-Logistic 0.054 45.92 51.92 57.66 Gamma 0.054 45.90 51.90 57.63

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 134.747692444733 BMDL(BCa): 48.461298780822 BMDL(Percentile): 76.969215951809 Acceleration: -0.026914 Bootstrap Resamples: 4999 Random Seed: 1238590496

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.036528 P.value: 0.980196

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 5.014189e-02 4.885420e-02 BETA(1) 1.320776e-03 1.664475e-03 BETA(2) 0.000000e+00 NA BETA(3) 2.749103e-08 3.024149e-08 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -2.842217 0.813086 BETA 0.012404 0.003893 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -1.640690 0.414383 BETA 0.007171 0.002061 Optimization Successful

------------------------------------------------------------
14MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.050325 0.049041 ALPHA 2.004461 1.113709 BETA 0.000012 0.000074 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.05040726 0.049145 ALPHA -8.98537800 4.974338 BETA 1.65182600 0.924366 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.050495 0.049236 ALPHA -14.613989 8.331084 BETA 2.685795 1.545659 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.050320 0.049058 ALPHA 3.143474 3.150328 BETA 0.012091 0.013879 Optimization Successful

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

152.4.2.2 Figure

16

### 2.4.3 CS 2.4.3.1 Figure



### 0 50 100 150 200 250 300 0.0 0.1 0.2 0.3 0.4 0.5

doseFraction Affected

●
● ● ●



## 2.5 Cyper 2.5.1 Data dose T n CS 0 0 2 20 0 65 65 1 10 1 100 100 2 10 5 150 150 0 10 9 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 2 30 0 65 65 0 10 1 100 100 2 10 3 150 150 0 10 8

17 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-18

Similar summary of data entered independently for QA:

### 2.5.2 T

2.5.2.1 Figure



### 2.5.3 CS 2.5.3.1 Modeling Details Model Fitting Summary and Weights

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

Weight -2log(L) AIC BIC Multistage 0.007 27.23 35.23 42.88 Logistic 0.371 27.20 31.20 35.02 Probit 0.396 27.07 31.07 34.89 Weibull 0.057 27.05 33.05 38.78 Log-Probit 0.062 26.87 32.87 38.61 Log-Logistic 0.045 27.52 33.52 39.26 Gamma 0.062 26.87 32.87 38.61

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 76.310148716412 BMDL(BCa): 55.941045828748 BMDL(Percentile): 60.76106953468 Acceleration: -0.065139
18Bootstrap Resamples: 4999

Random Seed: 1238590564

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.148155 P.value: 0.754151

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.000000e+00 NA BETA(1) 0.000000e+00 NA BETA(2) 0.000000e+00 NA BETA(3) 6.441077e-07 1.860408e-07 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -5.553001 1.679117 BETA 0.053720 0.016379 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -3.148468 0.890986 BETA 0.030268 0.008408 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 3.436636 1.039889 BETA 0.000000 0.000000 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -14.089924 4.212192 BETA 3.063952 0.913437 Optimization Successful

------------------------------------------------------------ 19MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 3.918997 0.094946 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 9.698677 5.646506 BETA 0.092890 0.055873 Optimization Successful

------------------------------------------------------------
2.5.3.2 Figure



## 2.6 L-Cyh 2.6.1 Data dose T n CS 0 0 1 10 0
2010 10 0 10 4 20 20 0 9 9 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 1 10 0 10 10 0 10 4 20 20 0 9 9 

### 2.6.2 T 2.6.2.1 Figure



### 0 5 10 15 20 0.0 0.1 0.2 0.3 0.4

doseFraction Affected

●

● ●



### 2.6.3 CS 2.6.3.1 Modeling Details Model Fitting Summary and Weights

------------------------------------------------------------ Weight -2log(L) AIC BIC Multistage 0.031 15.02 21.02 25.12 Logistic 0.358 13.47 17.47 20.20 Probit 0.359 13.46 17.46 20.19 Weibull 0.067 13.46 19.46 23.56 Log-Probit 0.067 13.46 19.46 23.56 Log-Logistic 0.062 13.59 19.59 23.69 Gamma 0.058 13.74 19.74 23.85

------------------------------------------------------------ 21 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-22

Similar summary of data entered independently for QA:’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 8.867571148113 BMDL(BCa): 7.906543294388 BMDL(Percentile): 7.424462797918 Acceleration: -0.021087 Bootstrap Resamples: 4999 Random Seed: 1238590634

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.029447 P.value: 0.377075

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.00000000 NA BETA(1) 0.00000000 NA BETA(2) 0.00716054 0.002446198 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -9.405114 20.554243 BETA 0.900000 2.053592 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -6.211629 -1 BETA 0.595828 -1 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 5.034649 16.003821 BETA 0.000005 0.000174 Optimization Successful

------------------------------------------------------------
22MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 7.707274 0.174147 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 7.656268 0.27337 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 9.950272 9.081291 BETA 0.900000 0.838877 Optimization Successful

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

232.6.3.2 Figure



### 0 5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0

doseFraction Affected

● ● ●



## 2.7 Perm 2.7.1 Data dose T n CS 0 0 1 10 0 200 200 3 10 1 250 250 6 10 0 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 1 10 0 200 200 3 10 1 250 250 5 10 0 

### 2.7.2 T 2.7.2.1 Modeling Details Model Fitting Summary and Weights

------------------------------------------------------------ Weight -2log(L) AIC BIC Multistage 0.064 32.85 38.85 43.05 Logistic 0.346 32.88 36.88 39.69 Probit 0.333 32.96 36.96 39.76

24 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-25

Similar summary of data entered independently for QA:Weibull 0.090 32.18 38.18 42.38

Log-Probit 0.004 38.19 44.19 48.39 Log-Logistic 0.072 32.63 38.63 42.83 Gamma 0.090 32.18 38.18 42.38

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 155.472984143356 BMDL(BCa): 73.028044424238 BMDL(Percentile): 80.410717728741 Acceleration: -0.030554 Bootstrap Resamples: 4999 Random Seed: 1238590688

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.466719 P.value: 0.341468

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 9.198646e-02 8.722756e-02 BETA(1) 0.000000e+00 NA BETA(2) 1.018379e-05 4.455432e-06 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -2.435285 1.117981 BETA 0.010095 0.005287 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -1.382745 0.548359 BETA 0.005695 0.002708 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.100000 0.090549
25ALPHA 5.249889 0.083305

BETA 0.000000 NA Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.3333333 0.086067 ALPHA -18.0000000 NA BETA 0.0000110 0.003088 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.092802 0.087641 ALPHA -18.000000 NA BETA 3.249044 0.104494 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

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

Estimate StdErr GAMMA 0.100000 0.094868 ALPHA 17.561547 26.877834 BETA 0.071259 0.113334 Optimization Successful

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

262.7.2.2 Figure

27

### 2.7.3 CS 2.7.3.1 Figure



### 0 50 100 150 200 250 0.0 0.1 0.2 0.3 0.4

doseFraction Affected

● ●

●



## 2.8 Delta 2.8.1 Data dose T n CS 0 0.0 0 19 1 12.5 12.5 0 10 1 25 25.0 0 9 7 35 35.0 1 9 9 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0.0 1 29 0 12.5 12.5 0 10 2 25 25.0 0 9 5 35 35.0 2 9 9

28 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-29

Similar summary of data entered independently for QA:

### 2.8.2 T

2.8.2.1 Figure



### 2.8.3 CS 2.8.3.1 Modeling Details Model Fitting Summary and Weights

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

Weight -2log(L) AIC BIC Multistage 0.011 24.99 32.99 40.39 Logistic 0.305 26.10 30.10 33.80 Probit 0.226 26.70 30.70 34.40 Weibull 0.135 23.88 29.88 35.43 Log-Probit 0.118 24.15 30.15 35.70 Log-Logistic 0.099 24.49 30.49 36.04 Gamma 0.107 24.35 30.35 35.90

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 14.523864366883 BMDL(BCa): 10.508910488967 BMDL(Percentile): 9.889283851677 Acceleration: -0.062764
29Bootstrap Resamples: 4999

Random Seed: 1238590739

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.687989 P.value: 0.520704

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 4.230535e-02 4.079831e-02 BETA(1) 0.000000e+00 NA BETA(2) 0.000000e+00 NA BETA(3) 9.058667e-05 3.046528e-05 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -3.955773 1.129567 BETA 0.206862 0.055040 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -2.061216 0.490155 BETA 0.110771 0.024778 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.053399 0.051307 ALPHA 4.949825 3.244907 BETA 0.000000 0.000002 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.06862262 0.047008 ALPHA -18.00000000 NA BETA 5.82036300 0.145575 Optimization Successful

------------------------------------------------------------
30MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.051004 0.045735 ALPHA -18.000000 NA BETA 6.020438 0.231923 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

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

Estimate StdErr GAMMA 0.047928 0.045750 ALPHA 10.605697 6.729212 BETA 0.514286 0.315394 Optimization Successful

------------------------------------------------------------
2.8.3.2 Figure



## 2.9 Pyr 2.9.1 Data dose T n CS 0 0 0 9 1
31400 400 0 10 1

800 800 2 10 1 

### 2.9.2 T 2.9.2.1 Figure

32

### 2.9.3 CS 2.9.3.1 Figure



### 0 200 400 600 800 0.0 0.1 0.2 0.3 0.4 0.5

doseFraction Affected

● ● ●



## 2.10 Resm 2.10.1 Data dose T n CS 0 0 0 19 1 350 350 4 10 0 500 500 9 10 0 750 750 10 10 0 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 1 29 0 350 350 4 10 1 500 500 10 10 0 750 750 10 10 0 

### 2.10.2 T 2.10.2.1 Modeling Details Model Fitting Summary and Weights

------------------------------------------------------------ Weight -2log(L) AIC BIC
33 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-34

Similar summary of data entered independently for QA:Multistage 0.007 20.46 28.46 36.03

Logistic 0.409 20.04 24.04 27.82 Probit 0.423 19.97 23.97 27.75 Weibull 0.061 19.96 25.96 31.64 Log-Probit 0.043 20.65 26.65 32.33 Log-Logistic 0.012 23.19 29.19 34.87 Gamma 0.046 20.52 26.52 32.20

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 291.236665494815 BMDL(BCa): 203.355604431669 BMDL(Percentile): 226.648147002643 Acceleration: -0.025408 Bootstrap Resamples: 4999 Random Seed: 1238590813

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.031184 P.value: 0.773755

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.000000e+00 NA BETA(1) 0.000000e+00 NA BETA(2) 0.000000e+00 NA BETA(3) 1.539193e-08 4.605681e-09 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -6.809086 2.903910 BETA 0.018191 0.007352 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -3.856251 1.771505 BETA 0.010285 0.004325 Optimization Successful

------------------------------------------------------------ 34MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 4.222329 0.052558 BETA 0.000000 NA Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 3.064206 0.049804 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -18.000000 NA BETA 3.123761 0.076464 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 8.969755 7.168128 BETA 0.024000 0.018416 Optimization Successful

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

352.10.2.2 Figure

36

### 2.10.3 CS 2.10.3.1 Figure



### 0 200 400 600 0.00 0.05 0.10 0.15 0.20 0.25 0.30

doseFraction Affected

●
● ● ●



## 2.11 Bifen 2.11.1 Data dose T n CS 0 0 0 10 1 40 40 8 10 1 55 55 9 10 3 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 0 10 1 40 40 9 10 1 55 55 10 10 3 

### 2.11.2 T 2.11.2.1 Modeling Details Model Fitting Summary and Weights

------------------------------------------------------------ Weight -2log(L) AIC BIC Multistage 0.085 16.51 22.51 26.71 Logistic 0.289 17.48 21.48 24.28
37 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-38

Similar summary of data entered independently for QA:Probit 0.285 17.50 21.50 24.30

Weibull 0.085 16.51 22.51 26.71 Log-Probit 0.085 16.51 22.51 26.71 Log-Logistic 0.085 16.51 22.51 26.71 Gamma 0.085 16.51 22.51 26.71

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 14.324456046211 BMDL(BCa): 0.452076409196 BMDL(Percentile): 0.648629563182 Acceleration: -0.020141 Bootstrap Resamples: 4999 Random Seed: 1238590885

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.299386 P.value: 0.261452

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.0000000000 NA BETA(1) 0.0358913100 0.073382650 BETA(2) 0.0001086158 0.001546523 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -4.003572 2.116348 BETA 0.125501 0.050427 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -2.182651 0.988300 BETA 0.068975 0.022827 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr
38GAMMA 0.000000 NA

ALPHA 1.124656 1.791507 BETA 0.025404 0.174943 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -4.254541 8.408739 BETA 1.381493 2.199496 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -8.007310 15.718938 BETA 2.546465 4.129419 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 1.292895 4.525451 BETA 0.050802 0.148237 Optimization Successful

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

392.11.2.2 Figure

40

### 2.11.3 CS 2.11.3.1 Figure



### 0 10 20 30 40 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6

doseFraction Affected

● ● ●



## 2.12 Esfen 2.12.1 Data dose T n CS 0 0 0 20 1 15 15 1 10 0 25 25 0 10 2 50 50 3 10 3 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 1 20 2 15 15 1 10 1 25 25 3 10 2 50 50 5 10 3 

### 2.12.2 T 2.12.2.1 Modeling Details Model Fitting Summary and Weights

------------------------------------------------------------ Weight -2log(L) AIC BIC
41 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-42

Similar summary of data entered independently for QA:Multistage 0.009 21.10 29.10 36.75

Logistic 0.386 21.44 25.44 29.27 Probit 0.386 21.45 25.45 29.27 Weibull 0.057 21.37 27.37 33.11 Log-Probit 0.052 21.56 27.56 33.29 Log-Logistic 0.055 21.42 27.42 33.16 Gamma 0.055 21.41 27.41 33.15

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 43.213915333116 BMDL(BCa): 26.77701717019 BMDL(Percentile): 32.083978629096 Acceleration: -0.060748 Bootstrap Resamples: 4999 Random Seed: 1238590939

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 2.292697 P.value: 0.133227

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.000000e+00 NA BETA(1) 2.515154e-03 3.176256e-03 BETA(2) 0.000000e+00 NA BETA(3) 1.574971e-06 2.073566e-06 Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -4.618523 1.481826 BETA 0.074586 0.034966 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -2.425696 0.633009 BETA 0.037263 0.016636 Optimization Successful

------------------------------------------------------------
42MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 1.603046 1.171478 BETA 0.000577 0.002458 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -3.929307 2.114856 BETA 0.831319 0.606559 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -7.653107 4.471076 BETA 1.686990 1.244263 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 1.704430 1.630899 BETA 0.015303 0.027516 Optimization Successful

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

432.12.2.2 Figure



### 2.12.3 CS 2.12.3.1 Modeling Details Model Fitting Summary and Weights

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

Weight -2log(L) AIC BIC Multistage 0.008 32.20 40.20 47.85 Logistic 0.376 32.36 36.36 40.19 Probit 0.376 32.36 36.36 40.18 Weibull 0.058 32.20 38.20 43.93 Log-Probit 0.063 32.02 38.02 43.76 Log-Logistic 0.059 32.15 38.15 43.89 Gamma 0.059 32.14 38.14 43.87

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 40.497794666185 BMDL(BCa): 24.378180504341 BMDL(Percentile): 27.583100831625 Acceleration: -0.053137 Bootstrap Resamples: 4999

44Random Seed: 1238591007

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 1.420257 P.value: 0.418484

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

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

Estimate StdErr GAMMA 0.0412702900 3.877431e-02 BETA(1) 0.0000000000 NA BETA(2) 0.0001394037 8.266066e-05 BETA(3) 0.0000000000 NA Optimization Successful

------------------------------------------------------------ MODEL: Logistic

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

Estimate StdErr ALPHA -3.148835 0.861267 BETA 0.047384 0.023813 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -1.764806 0.410953 BETA 0.025371 0.012574 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.041087 0.039613 ALPHA 1.970129 1.423513 BETA 0.000156 0.000838 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.04006911 0.038646 ALPHA -5.18551300 2.777312 BETA 1.19252100 0.765436 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic
45------------------------------------------------------------ Estimate StdErr GAMMA 0.040631 0.039239 ALPHA -9.269580 5.570416 BETA 2.148311 1.495522 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.040918 0.039392 ALPHA 2.547387 2.554875 BETA 0.030641 0.047134 Optimization Successful

------------------------------------------------------------
2.12.3.2 Figure



## 2.13 Tefl 2.13.1 Data dose T n CS 0 0 0 10 1 10 10 2 10 1
4615 15 4 10 1 Similar summary of data entered by Ginger, for sanity check: dose T n CS 0 0 0 10 1 10 10 3 10 1 15 15 6 10 1 

### 2.13.2 T 2.13.2.1 Modeling Details Model Fitting Summary and Weights

------------------------------------------------------------ Weight -2log(L) AIC BIC Multistage 0.069 23.47 29.47 33.67 Logistic 0.313 23.86 27.86 30.66 Probit 0.341 23.69 27.69 30.49 Weibull 0.069 23.47 29.47 33.67 Log-Probit 0.069 23.47 29.47 33.67 Log-Logistic 0.069 23.47 29.47 33.67 Gamma 0.069 23.47 29.47 33.67

------------------------------------------------------------ ’Average-Model’ Benchmark Dose Estimate

------------------------------------------------------------ Nominally Specified Confidence Limit: 0.95 Weighting Criterion: BIC BMD Calculation: Extra Risk BMR: 0.2 BMD: 10.696668720962 BMDL(BCa): 4.376647944949 BMDL(Percentile): 6.397027088121 Acceleration: -0.058722 Bootstrap Resamples: 4999 Random Seed: 1238591077

------------------------------------------------------------ ’Average-Model’ Pearson Goodness of Fit Test

------------------------------------------------------------ X2: 0.107198 P.value: 0.363673

------------------------------------------------------------ Model Parameters

------------------------------------------------------------ MODEL: Multistage

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000000 NA BETA(1) 0.000000000 NA BETA(2) 0.002257068 0.0009287071 Optimization Successful

------------------------------------------------------------ MODEL: Logistic
47 

## Appendix 5. BMDs for T and CS from WIL FOB Study Page A-48

Similar summary of data entered independently for QA:------------------------------------------------------------ Estimate StdErr ALPHA -4.342516 2.010630 BETA 0.269533 0.152153 Optimization Successful

------------------------------------------------------------ MODEL: Probit

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

Estimate StdErr ALPHA -2.482959 1.085366 BETA 0.152574 0.084562 Optimization Successful

------------------------------------------------------------ MODEL: Weibull

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 2.042624 2.142450 BETA 0.002023 0.011174 Optimization Successful

------------------------------------------------------------ MODEL: Log-Probit

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -4.182356 3.784783 BETA 1.450863 1.491594 Optimization Successful

------------------------------------------------------------ MODEL: Log-Logistic

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

Estimate StdErr GAMMA 0.000000 NA ALPHA -6.956392 6.421249 BETA 2.419062 2.514596 Optimization Successful

------------------------------------------------------------ MODEL: Gamma

------------------------------------------------------------ Estimate StdErr GAMMA 0.000000 NA ALPHA 2.907765 4.951848 BETA 0.146691 0.327839 Optimization Successful

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

482.13.2.2 Figure

49

### 2.13.3 CS

2.13.3.1 Figure

50

# Chapter 3 

# Summary Graphs

3.1 BMDs This figure indicates the estimates of BMD for each compound, for each endpoint for which there was a dose-related trend. BMDs for T are in red, and for CS are in blue. The BMD is indicated by the solid colored point, and the error bars indicate 95% confidence intervals. The small black point in each row is the BMDL.

51

## 3.2 Relative Potencies

Permethrin is used here as the index chemical for T (Type I response), Deltamethrin the as index chemical for CS (Type II response). This choice does not reflect the final regulatory choice of index chemical. The solid vertical lines indicate the range of relative potency estimates.

5253

# Appendix A 

# getData.R

Code for reading data from Excel spreadsheet: library(gdata) dta <- vector("list", 8) names(dta) <- nm <- LETTERS[1:9][-5] ## Arrays to convert Dose Group (DOSEGP) codes to a chemical name ## and dose level Chems <- matrix("A",nrow=7, ncol=8, dimnames=list(NULL, nm)) Doses <- matrix(0.0, nrow=7, ncol=8, dimnames=list(NULL, nm)) Chems[1,] <- rep("Control", 8) Chems[2,] <- c("B-Cyf","L-Cyh","Resm","Tefl","B-Cyf","Resm","Esfen","Cyper") Doses[2,] <- c(25, 10, 500, 10, 12.5, 350, 15, 65) Chems[3,] <- c("B-Cyf","L-Cyh","Resm","Tefl","S-Bio","Delta","","") Doses[3,] <- c(45, 20, 750, 15, 150, 12.5, NA, NA) Chems[4,] <- c("S-Bio","Cyper","Delta","Esfen",rep("",4)) Doses[4,] <- c(200, 100, 25, 25, rep(NA, 4)) Chems[5,] <- c("S-Bio","Cyper","Delta","Esfen",rep("",4)) Doses[5,] <- c(300, 150, 35, 50, rep(NA, 4)) Chems[6,] <- c("Fenpro","Perm","Pyr","Bifen", rep("", 4)) Doses[6,] <- c(15, 200, 400, 40, rep(NA, 4)) Chems[7,] <- c("Fenpro","Perm","Pyr","Bifen", rep("", 4)) Doses[7,] <- c(30, 250, 800, 55, rep(NA, 4)) for (i in 1:8) { dta[[i]] <- read.xls("409002_FOB.xls", sheet=i) dta[[i]]$BLOCK <- factor(rep(nm[i], nrow(dta[[i]])), levels=nm) dta[[i]]$TIME <- c(A = 2, B=4, C=4, D=8, F=2, G=4, H=8, I=4)[as.character(dta[[i]]$BLOCK)] dta[[i]]$DOSE <- Doses[cbind(dta[[i]]$DOSEGP, match(as.character(dta[[i]]$BLOCK),nm))] dta[[i]]$CHEMICAL <- factor(Chems[cbind(dta[[i]]$DOSEGP, match(as.character(dta[[i]]$BLOCK),nm))]) } dta <- do.call("rbind",dta) ### categorical and measurement tests may use ’0’ as NA; counts cannot ### So, read in the test type, and set up NAs for the "right" variables. TTypes <- read.table("TESTtypes.txt", header=TRUE, as.is=TRUE, row.names=1) ### Just keep the tests we want to look at (the ones in TTypes)
54dta <- subset(dta, TEST %in% rownames(TTypes))

### Three kinds of variables: categorical (c), measurement (m), and counts(z). ### 0’s in c and m types indicate NA (I think); counts can be 0. indx <- as.character(TTypes[as.character(dta$TEST),"type"]) %in% c("c","m") dta$RESULT[indx & dta$RESULT == 0] <- NA ### Ginger independently manually entered data from the WIL study appendices ### Here we read and process that data, for comparison with the "official" ### WIL electronic file. I use the names from above, rather than the ones ### Ginger has used in the spreadsheet. Ginger’s names are paired after ### a ’#’ symbol. Gdta <- vector("list", 11) names(Gdta) <- c("B-Cyf", # BCYF "Bifen", # BIFEN "Tefl", # TEF "S-Bio", # SBIO "Resm", # RESME "Perm", # PERM "L-Cyh", # LCYH "Fenpro", # FEN "Esfen", # ESF "Delta", # DELTA "Cyper" # CYPER ) ### Note, Ginger has no Pyr data for (i in seq(along=Gdta)) { Gdta[[i]] <- read.xls("pyrethroid WIL domain data v1.xls", sheet=i, na.strings=c(".", ". ", " . ")) } save(dta, Gdta, file="data.Rdata")

55

# Appendix B 

# DRmodelsTCS.R

Code for doing the dose-response analysis: ### Use mabmd to get BMDs for each endpoint in the FOB. Do trend test, ### first, and only do model if trend is significant. ### Need to save MA BMD, and var of log(BMD) from bootstrap distribution. library(RMADr) library(xtable) makeHeader <- function(name){ c( "\\documentclass[letterpaper]{report}", "\\usepackage{longtable}", "\\usepackage{lastpage, fancyhdr, mathpazo, courier}", "\\usepackage[scaled=0.92]{helvet}", "\\usepackage[T1]{fontenc}", "\\renewcommand{\\familydefault}{\\sfdefault}", "\\renewcommand{\\headrulewidth}{0pt}", "\\setlength{\\hoffset}{0pt}", "\\setlength{\\oddsidemargin}{0pt}", "\\setlength{\\voffset}{0pt}", "\\setlength{\\headheight}{0pt}", "\\setlength{\\headsep}{0pt}", "\\setlength{\\marginparsep}{0pt}", "\\setlength{\\marginparwidth}{0pt}", "\\setlength{\\textwidth}{468pt}", "\\setlength{\\textheight}{648pt}", "\\pagestyle{fancy}", "\\rhead{}", "\\lhead{}", "\\chead{}", "\\setcounter{secnumdepth}{5}", "\\setcounter{tocdepth}{5}", "\\usepackage{graphicx}", "\\usepackage[colorlinks=true]{hyperref}", paste("\\title{",name,"}",sep=""), "\\author{}", "\\begin{document}", "\\maketitle", "\\thispagestyle{fancy}", "\\tableofcontents", "\\chapter{Methods}",
56"\\input{Methods.tex}",

"\\chapter{Results}", "\\section{How to Read This Chapter}", "The remaining sections in this chapter give the results for", "all the chemicals covered", "in the WIL study. Each section has a section devoted to the", "data for the T and CS endpoints.", "This is followed by sections for each of the two endpoints, T and CS.", "If there is a significant trend for an endpoint, then the", "output from mabmd.exe is shown,", "followed by a plot of the data with 95\\% confidence intervals", "for the means and the trace", "of the fitted model, along with indicators for BMD and BMDL.", "If there is no significant", "trend, then only the data are shown with their confidence", "intervals. Within the section", "labeled \"Modeling Details\", notice in particular the section", "giving the results of a", "goodness-of-fit test for the average model. Also, see the summary", "table of log-likelihoods", "and weights at the top of the section, as this gives the", "contribution of each model to the", "average model. Finally, there is a separate entry for each", "component model, giving the", "parameter estimates for that model to the data." ) } makeClose <- function(){ c("\\end{document}") } ## Modification of prop.trend.test to return direction of trend: my.prop.trend.test <- function (x, n, score = 1:length(x),

alternative=c("two.sided","decreasing","increasing") ) { alternative <- match.arg(alternative) method <- "Chi-squared Test for Trend in Proportions" dname <- paste(deparse(substitute(x)), "out of", deparse(substitute(n))) dname <- paste(dname, ",\n using scores:", paste(score, collapse = " ")) x <- as.vector(x) n <- as.vector(n) score <- as.vector(score) freq <- x/n p <- sum(x)/sum(n) w <- n/p/(1 - p) res <- lm(freq ~ score, weight = w) direction <- sign(coef(res)[2]) a <- anova(res) chisq <- a["score", "Sum Sq"] names(chisq) <- "X-squared" df <- c(df = 1) pval <- pchisq(chisq, 1, lower.tail = FALSE) rval <- list(statistic = chisq, parameter = df, p.value = as.numeric(pval),

method = method, data.name = dname,
57direction=c("decreasing","increasing")[1 + (direction+1)/2])

class(rval) <- "htest" return(rval) } ### trend test a la Tukey et al, NOSTASOT. Currently ### for quantal independent only. hasTrend <- function(model, data, criterion=0.05) { dose <- data[,as.character(model[[3]])] indx <- order(dose) dose <- dose[indx] ldose <- ifelse(dose > 0, log(dose),

log(dose[2]) - ((dose[2] - dose[1])/(dose[3] - dose[2])) * (log(dose[3])- log(dose[2])) ) resp <- data[,as.character(model[[2]][[2]])][indx] N <- data[,as.character(model[[2]][[3]])][indx] ## If any of three carriers gives a significantly positive ## trend, we have a trend. ## If any of the three carriers gives a significantly NEGATIVE ## trend, we have a negative trend (and don’t want to even try ## fitting our monotonic increasing models to the data, since ## they are likely to hang. ## ## first run the tests, and save significance decisions and direction signifs <- logical(3) directions <- character(3) x <- my.prop.trend.test(resp,N,dose) signifs[1] <- x$p.value <= criterion directions[1] <- x$direction x <- my.prop.trend.test(resp,N,rank(dose)) signifs[2] <- x$p.value <= criterion directions[2] <- x$direction x <- my.prop.trend.test(resp,N,ldose) signifs[3] <- x$p.value <= criterion directions[3] <- x$direction
c(any(signifs & directions == "increasing"), any(signifs & directions == "decreasing")) } plot.QData <- function(x, Confidence = 0.95, plotBoot=FALSE, ...) { RHS <- all.vars(x$model[[3]]) LHSvars <- all.vars(x$model[[2]]) llim <- ulim <- numeric(nrow(x$data)) for (i in 1:nrow(x$data)) { CL <- binom.test(x$data[i, LHSvars[1]], x$data[i, LHSvars[2]], conf.level = Confidence)$conf.int llim[i] <- CL[1] ulim[i] <- CL[2] } X <- x$data[, RHS]
58Y <- x$data[, LHSvars[1]]/x$data[, LHSvars[2]]

YLAB <- "Fraction Affected" yrange <- range(llim, ulim, na.rm = TRUE) plot(X, Y, type = "n", xlab = RHS, ylab = YLAB, ylim = yrange,

las = 1, ...) points(X, Y, pch = 19) segments(X, llim, X, ulim) } load("data.RData") ### Construct an array to hold the result: ### rows are chemicals ### columns are TESTS ### depth is lBMD, var(lBMD) chems <- levels(dta$CHEMICAL) ## Drop the control group chems <- setdiff(chems, "Control") ### Some tests are repeated in different subcategories, and ### we want to keep those separate, so construct a new variable ### concatenating SUBCAT and TEST dta$newTEST <- factor(paste("{",dta$SUBCAT,"}",as.character(dta$TEST),sep="")) Tests <- levels(dta$newTEST) Answers <- array(dim=c(length(chems),2,2), dimnames=list(chems,c("T","CS"), c("lBMD","var(lBMD)"))) Models <- vector("list",length(chems) * 2) dim(Models) <- c(length(chems),2) dimnames(Models) <- list(chems, c("T","CS")) T.Score.Tests <- c("{6}BODY_TEMPERATURE_(degrees_F)", "{1}TREMORS", "{3}TREMORS", "{1}CONVULSIONS_-_CLONIC", "{3}CONVULSIONS_-_CLONIC" ) CS.Score.Tests <- c("{6}BODY_TEMPERATURE_(degrees_F)","{2}SALIVATION", "{3}MOBILITY") ### Loop through chemicals, and extract a dataset with all the data ### for each chemical, along with all the controls in the blocks that have ### that chemical. for (ch in chems) { tdta <- subset(dta, CHEMICAL %in% c("Control", ch)) ## Which blocks contain this chemical? tbl <- table(tdta$BLOCK, tdta$CHEMICAL)[,ch] blocks <- names(tbl)[tbl > 0] tdta <- subset(tdta, BLOCK %in% blocks) ## First construct a dataset with T-score and CS-score ## for each individual. ## - Extract the component tests ndta <- subset(tdta, newTEST %in% c(T.Score.Tests, CS.Score.Tests),

select=c("ANIMLNUM","RESULT","BLOCK","DOSE","newTEST")) ## - reshape the dataframe so each test is a separate column t2 <- na.omit(reshape(ndta, v.names="RESULT", timevar="newTEST",

direction="wide", idvar="ANIMLNUM")) ## Construct CLONUS and TREMORS ## - Recode the CLONIC endpoints so that 5 -> 4, and everything else -> 1
59## per Ginger Moser, 10/30/07

t2$‘RESULT.{1}CONVULSIONS_-_CLONIC‘ <- ifelse( t2$‘RESULT.{1}CONVULSIONS_-_CLONIC‘ == 5, 4, 1) t2$‘RESULT.{3}CONVULSIONS_-_CLONIC‘ <- ifelse( t2$‘RESULT.{3}CONVULSIONS_-_CLONIC‘ == 5, 4, 1) t2$CLONUS <- pmax(t2$‘RESULT.{1}CONVULSIONS_-_CLONIC‘, t2$‘RESULT.{3}CONVULSIONS_-_CLONIC‘) t2$TREMORS <- pmax(t2$‘RESULT.{1}TREMORS‘, t2$‘RESULT.{3}TREMORS‘) ## Construct Hyperthermia ## - temperature t2$Temp <- t2$‘RESULT.{6}BODY_TEMPERATURE_(degrees_F)‘ ## - pooled estimate of sd Cdta <- subset(dta,

CHEMICAL == "Control" & newTEST == "{6}BODY_TEMPERATURE_(degrees_F)" & RESULT > 0) sd <- summary(lm(RESULT ~ factor(BLOCK), data=Cdta))$sigma ## - Get the block control group means t2c <- subset(t2, DOSE == 0) mns <- tapply(t2c$Temp, factor(t2c$BLOCK), mean) bg <- mns[as.character(t2$BLOCK)] ## - Create Hyperthermia t2$Hyperthermia <- as.numeric(cut((t2$Temp - bg)/sd, breaks=c(-Inf, 1, 1.5, 2, Inf), right=FALSE)) ## Now, the scores t2$T <- with(t2, Hyperthermia + TREMORS + CLONUS) ## Hypothermia t2$Hypothermia <- as.numeric(cut(-(t2$Temp - bg)/sd, breaks=c(-Inf, 1, 1.5, 2, Inf), right=FALSE)) t2$CS <- t2$Hypothermia + t2$‘RESULT.{2}SALIVATION‘ + t2$‘RESULT.{3}MOBILITY‘ ## Aggregated datasets for MAbmd: indx <- order(t2$DOSE) t2 <- t2[indx,] adta <- data.frame(dose=unique(t2$DOSE), T=tapply(t2$T, factor(t2$DOSE), function(x) sum(x > 5)), n=tapply(t2$T, factor(t2$DOSE), length), CS=tapply(t2$CS, factor(t2$DOSE), function(x) sum(x > 4)) ) ## Model T if (sum(adta$T) == 0) { Answers[ch,"T",] <- rep(.Machine$double.xmax,2) Models[[ch,"T"]] <- list(data=adta, model = cbind(T,n) ~ dose) class(Models[[ch,"T"]]) <- "QData" } else { tmp <- hasTrend(cbind(T, n) ~ dose, data=adta) ## If DECREASING, set resp = n - T if (tmp[2]) adta$resp <- adta$n - adta$T if (!any(tmp)) {
60Answers[ch,"T",] <- rep(.Machine$double.xmax,2) Models[[ch,"T"]] <- list(data=adta, model = cbind(T,n) ~ dose) class(Models[[ch,"T"]]) <- "QData" } else { Models[[ch,"T"]] <- out <- try(MAbmd(cbind(T,n) ~ dose, data=adta, Nboot=4999,BMR=0.2,

Degree=nrow(adta) - 1)) if (!inherits(out, "try-error")) { Answers[ch,"T","lBMD"] <- mean(log(out$BootStrapBMDs)) Answers[ch,"T",2] <- var(log(out$BootStrapBMDs)) } else { Answers[ch,"T",] <- c(NA,NA) Models[[ch,"T"]] <- list(data=adta, model = cbind(T,n) ~ dose) class(Models[[ch,"T"]]) <- "QData" } } } ## Model CS if (sum(adta$CS) == 0) { Answers[ch,"CS",] <- rep(.Machine$double.xmax,2) Models[[ch,"CS"]] <- list(data=adta, model = cbind(CS,n) ~ dose) class(Models[[ch,"CS"]]) <- "QData" } else { tmp <- hasTrend(cbind(CS, n) ~ dose, data=adta) ## If DECREASING, set resp = n - CS if (tmp[2]) adta$resp <- adta$n - adta$CS if (!any(tmp)) { Answers[ch,"CS",] <- rep(.Machine$double.xmax,2) Models[[ch,"CS"]] <- list(data=adta, model = cbind(CS,n) ~ dose) class(Models[[ch,"CS"]]) <- "QData" } else { Models[[ch,"CS"]] <- out <- try(MAbmd(cbind(CS,n) ~ dose, data=adta, Nboot=4999,BMR=0.2,

Degree=nrow(adta) - 1)) if (!inherits(out, "try-error")) { Answers[ch,"CS","lBMD"] <- mean(log(out$BootStrapBMDs)) Answers[ch,"CS",2] <- var(log(out$BootStrapBMDs)) } else { Answers[ch,"CS",] <- c(NA,NA) Models[[ch,"CS"]] <- list(data=adta, model = cbind(CS,n) ~ dose) class(Models[[ch,"CS"]]) <- "QData" } } } save(Answers, Models, file="Answers.RData") } ### -------------------------------------------------------------- ### Construct Report ### -------------------------------------------------------------- ### Open File and header output <- file("T_CSBMDs.tex", open="wt") writeLines(makeHeader("BMDs for T and CS from WIL FOB Study"), con=output)
61writeChem <- function(ch, endpt) {

writeLines(paste("\\subsection{",endpt,"}",sep=""),con=output) if (Answers[ch,endpt,"lBMD"] < .Machine$double.xmax) { writeLines(c("\\subsubsection{Modeling Details}",

paste("\\","begin","{","verbatim","}",sep="") ), con=output) sink(file=output, append=TRUE) print(Models[[ch,endpt]]) sink() writeLines(paste("\\","end","{","verbatim","}",sep=""),

con=output) } graphfile <- file.path("graphs",paste(ch,"-",endpt,".pdf",sep="")) writeLines(c("\\subsubsection{Figure}",

"\\begin{center}", paste("\\includegraphics{",graphfile,"}",sep=""), "\\end{center}"), con=output) pdf(file=graphfile, width=5, height=4, pointsize=11) plot(Models[[ch, endpt]]) dev.off() } ### Chemical-specific outputs for (ch in chems) { writeLines(paste("\\section{",ch,"}"), con=output) writeLines(c("\\subsection{Data}",

"\\begin{verbatim}"), con=output) sink(file=output, append=TRUE) print(Models[[ch,"T"]]$data) sink() writeLines(paste("\\","end","{","verbatim","}",sep=""), con=output) if (ch %in% names(Gdta)) { writeLines(c("Similar summary of data entered by Ginger, for sanity",

"check:", "\\begin{verbatim}"), con=output) aGdta <- data.frame(dose=unique(Gdta[[ch]]$Dose),

T=tapply(Gdta[[ch]]$T, factor(Gdta[[ch]]$Dose), function(x) sum(x > 5, na.rm=TRUE)), n=tapply(Gdta[[ch]]$T, factor(Gdta[[ch]]$Dose), function(x) sum(!is.na(x))), CS=tapply(Gdta[[ch]]$CS, factor(Gdta[[ch]]$Dose), function(x) sum(x > 4,na.rm=TRUE)) ) sink(file=output, append=TRUE) print(aGdta) sink() writeLines(paste("\\","end","{","verbatim","}",sep=""),

con=output) } writeChem(ch, "T") writeChem(ch, "CS")
62}

### Summary ## BMDplot writeLines(c("\\chapter{Summary Graphs}",

"\\section{BMDs}", "This figure indicates the estimates of BMD for each", "compound, for each", "endpoint for which there was a dose-related trend.", "BMDs for T are in red, and", "for CS are in blue. The BMD is indicated by the solid", "colored point, and", "the error bars indicate", "95\\% confidence intervals. The small black point in each", "row is the BMDL.", "\\begin{center}", "\\includegraphics{graphs/BMDs.pdf}", "\\end{center}"), con=output) ## Build the table BMDs to hold the output ColNames <- c("Max Dose","T GoF P value","T.BMDLse","T.BMDLq","T.BMD",

"T.llim","T.ulim","CS GoF P value", "CS.BMDLse","CS.BMDLq","CS.BMD","CS.llim","CS.ulim") BMDs <- matrix(nrow=length(chems), ncol=length(ColNames),

dimnames=list(chems, ColNames)) for (ch in chems) { BMDs[ch,"Max Dose"] <- max(Models[[ch,"T"]]$data$dose) if (Answers[ch,"T","lBMD"] < .Machine$double.xmax) { BMDs[ch,"T GoF P value"] <- Models[[ch,"T"]]$GOF$P.value BMDs[ch,"T.BMDLse"] <- exp(Answers[ch,"T","lBMD"] + qnorm(0.05) * sqrt(Answers[ch,"T","var(lBMD)"])) BMDs[ch,"T.BMDLq"] <- BMD(Models[[ch,"T"]])["BMDL"] BMDs[ch,"T.BMD"] <- BMD(Models[[ch,"T"]])["BMD"] lims <- quantile(Models[[ch,"T"]]$BootStrapBMDs, prob=c(0.025, 0.975)) BMDs[ch, "T.llim"] <- lims[1] BMDs[ch, "T.ulim"] <- lims[2] } if (Answers[ch,"CS","lBMD"] < .Machine$double.xmax) { BMDs[ch,"CS GoF P value"] <- Models[[ch,"CS"]]$GOF$P.value BMDs[ch,"CS.BMDLse"] <- exp(Answers[ch,"CS","lBMD"] + qnorm(0.05) * sqrt(Answers[ch,"CS","var(lBMD)"])) BMDs[ch,"CS.BMDLq"] <- BMD(Models[[ch,"CS"]])["BMDL"] BMDs[ch,"CS.BMD"] <- BMD(Models[[ch,"CS"]])["BMD"] lims <- quantile(Models[[ch,"CS"]]$BootStrapBMDs, prob=c(0.025, 0.975)) BMDs[ch, "CS.llim"] <- lims[1] BMDs[ch, "CS.ulim"] <- lims[2] } } indx <- order(BMDs[,"T.BMD"],BMDs[,"CS.BMD"], na.last=FALSE,decreasing=TRUE) BMDs <- BMDs[indx,] ## save BMDs into a spreadsheet library(xlsReadWrite) ## get around a bug in write.xls tmp <- BMDs
63cn <- colnames(tmp)

cn[1] <- "Chemical" colnames(tmp) <- cn write.xls(tmp, file="BMDs.xls", rowNames=rownames(BMDs)) ### Plot the BMDs, BMDLqs, and CIs pdf(file="graphs/BMDs.pdf", width=5, height=7, pointsize=11) y <- seq(1, nrow(BMDs)) par(mar=c(5,6,1,1)+0.1) lims <- BMDs[,c("T.llim","T.ulim","CS.llim","CS.ulim")] xlims <- range(lims[lims < 1e6], na.rm=TRUE) plot(BMDs[,"T.BMD"],y,type="n", xlab="BMD", yaxt="n", log="x", xlim=xlims, ylab="") abline(h = y, col="lightgray",lty="dotted") points(BMDs[,"T.BMD"],y + 0.1,pch=19, col="red") points(BMDs[,"T.BMDLq"], y + 0.1, pch=18) arrows(BMDs[,"T.BMD"], y + 0.1, BMDs[,"T.llim"],y+0.1,

length=0.1, angle=90, col="red") arrows(BMDs[,"T.BMD"], y + 0.1, BMDs[,"T.ulim"],y+0.1,

length=0.1, angle=90, col="red") points(BMDs[,"CS.BMD"], y - 0.1, pch=19, col="blue") points(BMDs[,"CS.BMDLq"], y - 0.1, pch=18) arrows(BMDs[,"CS.BMD"], y - 0.1, BMDs[,"CS.llim"],y - 0.1,

length=0.1, angle=90, col="blue") arrows(BMDs[,"CS.BMD"], y - 0.1, BMDs[,"CS.ulim"],y - 0.1,

length=0.1, angle=90, col="blue") axis(side=2, at=y, labels=rownames(BMDs), las=1) dev.off() writeLines(c("\\section{Relative Potencies}",

"Permethrin is used here as the index chemical for T (Type I response),", "Deltamethrin the as index chemical for CS (Type II response).", "This choice does not reflect the final", "regulatory choice of index chemical.", "The solid vertical lines indicate the range of", "relative potency estimates.", "\\begin{center}", "\\includegraphics{graphs/RelativePotencies.pdf}", "\\end{center}"), con=output) ### Calculate relative potencies and CIs: For T use Perm; for CS use Delta ColNames <- c("T","Tllim","Tulim","CS","CSllim","CSulim") RelPot <- matrix(nrow=length(chems), ncol=length(ColNames), dimnames=list(chems, ColNames)) Tindex <- Models[["Perm","T"]]$BootStrapBMDs Tindex[Tindex == 1e06] <- Inf CSindex <- Models[["Delta","CS"]]$BootStrapBMDs CSindex[CSindex == 1e06] <- Inf for (ch in chems) { if (Answers[ch, "T","lBMD"] < .Machine$double.xmax) { Tratiodist <- sample(Tindex, size=4999, replace=TRUE)/ sample(Models[[ch,"T"]]$BootStrapBMDs, size=4999, replace=TRUE)
64tmp <- quantile(Tratiodist, prob=c(0.025, 0.5, 0.975))

RelPot[ch, c("T","Tllim","Tulim")] <- tmp[c(2,1,3)] } else { RelPot[ch, c("T","Tllim","Tulim")] <- rep(NA,3) } if (Answers[ch, "CS","lBMD"] < .Machine$double.xmax) { CSratiodist <- sample(CSindex, size=4999, replace=TRUE)/ sample(Models[[ch,"CS"]]$BootStrapBMDs, size=4999, replace=TRUE) tmp <- quantile(CSratiodist, prob=c(0.025, 0.5, 0.975)) RelPot[ch, c("CS","CSllim","CSulim")] <- tmp[c(2,1,3)] } else { RelPot[ch, c("CS","CSllim","CSulim")] <- rep(NA, 3) } } indx <- order(RelPot[,"T"], RelPot[,"CS"], na.last=FALSE, decreasing=TRUE) RelPot <- RelPot[indx,] ### Plot relative potencies pdf(file="graphs/RelativePotencies.pdf", width=5, height=7, pointsize=11) y <- seq(1, nrow(RelPot)) par(mar=c(5,6,1,1)+0.1) xlims <- range(RelPot[,c("Tllim","Tulim","CSllim","CSulim")], na.rm=TRUE) plot(RelPot[,"T"],y,type="n", xlab="Relative Potency", yaxt="n", log="x", xlim=xlims, ylab="") points(RelPot[,"T"],y + 0.1,pch=19, col="red") doit <- rownames(RelPot) != "Perm" arrows(RelPot[doit,"T"], y[doit] + 0.1,

RelPot[doit,"Tllim"],y[doit]+0.1, length=0.1, angle=90, col="red") arrows(RelPot[doit,"T"], y[doit] + 0.1,

RelPot[doit,"Tulim"],y[doit]+0.1, length=0.1, angle=90, col="red") doit <- rownames(RelPot) != "Delta" points(RelPot[,"CS"], y - 0.1, pch=19, col="blue") arrows(RelPot[doit,"CS"], y[doit] - 0.1,

RelPot[doit,"CSllim"],y[doit] - 0.1, length=0.1, angle=90, col="blue") arrows(RelPot[doit,"CS"], y[doit] - 0.1,

RelPot[doit,"CSulim"],y[doit] - 0.1, length=0.1, angle=90, col="blue") axis(side=2, at=y, labels=rownames(RelPot), las=1) abline(h = y, col="lightgray",lty="dotted") abline(v = max(RelPot[,c("T","CS")], na.rm=TRUE)) abline(v=min(RelPot[,c("T","CS")], na.rm=TRUE)) dev.off() save(RelPot, file="RelativePotencies.RData") ### Close ### Include this file and getData.R in appendices getCode <- function(nm, section="chapter",comment=NULL) { code <- scan(file=nm, character(0), sep="\n") c(paste("\\",section,"{",nm,"}",sep=""), comment,
65paste("\\","begin","{","verbatim","}",sep=""),

code, paste("\\","end","{","verbatim","}",sep="") ) } writeLines(c("\\appendix",

getCode("getData.R",

comment="Code for reading data from Excel spreadsheet:"), getCode("DRmodelsTCS.R",

comment="Code for doing the dose-response analysis:") ),con=output) writeLines(makeClose(), con=output) close(output)

66