BMDs for T and CS from WIL FOB Study

April 1, 2009

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-1
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

1

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-2
2.7.1 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

2

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-3
B DRmodelsTCS.R 56

3

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-4
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

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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-6
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 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.

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

0 10 20 30 40

0.0

0.1

0.2

0.3

0.4

0.5

dose

Fraction Affected

●

●

●

●

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

7

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-8
Bootstrap 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

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

8

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-9
MODEL: 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

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

dose

Fraction Affected

●

●

●

●

2.3 Fenpro

2.3.1 Data

dose T n CS

0 0 0 10 1

9

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-10
15 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

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

10

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-11
MODEL: 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

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

11

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-12
2.3.2.2 Figure

0 5 10 15 20 25 30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

dose

Fraction Affected

● ●

●

12

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-13
2.3.3 CS

2.3.3.1 Figure

0 5 10 15 20 25 30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

dose

Fraction Affected

●

●

●

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

13

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-14
Multistage 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

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

14

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-15
MODEL: 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

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

15

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-16
2.4.2.2 Figure

0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

dose

Fraction Affected

●

●

●

●

16

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-17
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

dose

Fraction 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

0 50 100 150

0.0

0.1

0.2

0.3

0.4

0.5

dose

Fraction Affected

● ●

●

●

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

18

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-19
Bootstrap 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

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

19

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-20
MODEL: 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

0 50 100 150

0.0

0.2

0.4

0.6

0.8

1.0

dose

Fraction Affected

●

●

●

●

2.6 L-Cyh

2.6.1 Data

dose T n CS

0 0 1 10 0

20

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-21
10 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

dose

Fraction 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

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

22

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-23
MODEL: 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

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

23

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-24
2.6.3.2 Figure

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

dose

Fraction 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

25

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-26
ALPHA 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

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

26

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-27
2.7.2.2 Figure

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

dose

Fraction Affected

●

●

●

27

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-28
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

dose

Fraction 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

0 5 10 15 20 25 30 35

0.0

0.1

0.2

0.3

0.4

0.5

dose

Fraction Affected

● ● ●

●

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

29

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-30
Bootstrap 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

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

30

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-31
MODEL: 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

0 5 10 15 20 25 30 35

0.0

0.2

0.4

0.6

0.8

1.0

dose

Fraction Affected

●

●

●

●

2.9 Pyr

2.9.1 Data

dose T n CS

0 0 0 9 1

31

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-32
400 400 0 10 1

800 800 2 10 1

2.9.2 T

2.9.2.1 Figure

0 200 400 600 800

0.0

0.1

0.2

0.3

0.4

0.5

dose

Fraction Affected

● ●

●

32

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-33
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

dose

Fraction 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

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

34

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-35
MODEL: 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

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

35

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-36
2.10.2.2 Figure

0 200 400 600

0.0

0.2

0.4

0.6

0.8

1.0

dose

Fraction Affected

●

●

●

●

36

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-37
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

dose

Fraction 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

38

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-39
GAMMA 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

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

39

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-40
2.11.2.2 Figure

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

dose

Fraction Affected

●

●

●

40

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-41
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

dose

Fraction 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

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

42

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-43
MODEL: 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

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

43

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-44
2.12.2.2 Figure

0 10 20 30 40 50

0.0

0.1

0.2

0.3

0.4

0.5

0.6

dose

Fraction Affected

●

●

●

●

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

44

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-45
Random 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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-46
------------------------------------------------------------

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

0 10 20 30 40 50

0.0

0.1

0.2

0.3

0.4

0.5

0.6

dose

Fraction Affected

●

●

●

●

2.13 Tefl

2.13.1 Data

dose T n CS

0 0 0 10 1

10 10 2 10 1

46

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-47
15 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

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

48

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-49
2.13.2.2 Figure

0 5 10 15

0.0

0.2

0.4

0.6

dose

Fraction Affected

●

●

●

49

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-50
2.13.3 CS

2.13.3.1 Figure

0 5 10 15

0.0

0.1

0.2

0.3

0.4

dose

Fraction Affected

● ● ●

50

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-51
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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-52
0.5 1.0 2.0 5.0 20.0 50.0 200.0

BMD

●

●

●

●

●

●

●

●

●

●

●

●

Pyr

Cyper

Delta

B−Cyf

L−Cyh

Resm

Perm

S−Bio

Esfen

Fenpro

Bifen

Tefl

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.

52

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-53
1e−05 1e−03 1e−01 1e+01

Relative Potency

●

●

●

●

●

●

●

●

●

●

●

●

Pyr

L−Cyh

B−Cyf

Delta

Cyper

Tefl

Bifen

Fenpro

Esfen

S−Bio

Perm

Resm

53

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-54
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)

54

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-55
dta <- 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 5. BMDs for T and CS from WIL FOB Study Page A-56
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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-57
"\\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,

57

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-58
direction=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]

58

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-59
Y <- 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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-60
## 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)) {

60

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-61
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 {

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)

61

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-62
writeChem <- 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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-63
}

### 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

63

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-64
cn <- 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)

64

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-65
tmp <- 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,

65

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-66
paste("\\","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

Appendix 5. BMDs for T and CS from WIL FOB Study Page A-67