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### Page **1** of **15** 

# BMD Analysis **( AUC**  **)**

Iris Camacho Paul Schlosser 

# Saillenfait et al. 2003, fetal body weights Internal Dose, AUC (m g - hr/L) # litters Fetal BW (g) Standard Deviation 0 24 5.671 0.37 93.84 20 5.623 0.358 190.67 19 5.469 0.252 397.28 25 5.393 0.446 **Model Type Risk** 

**Ty pe**  **P**  

** Value** **AI C**  **BMD**

**(BM R=**  **5%) BMD**  **L (BM**  **R= 5%)**  **BMD (BM**  **R= 10%)**  **BMDL (BM**  **R= 10%)**  **Comments** Exponential (M2) Rel. Dev. 0. 9361 - 8 3.661 384 24 2 788 497 Exponential (M3) Rel. Dev. 0.7 571 - 8 1.697 3 89 24 2 728 411 Exponential (M4) Rel. Dev. 0. 9361 - 8 3.661 3 84 1 66 788 497 Sam e best fit , but more fitted parameters than M2 Exponential (M5) Rel. Dev. 0.7571 - 79.79 3 382 99 error error Model did not com pute BMD for BMR = 10% Hill Rel. Dev. NA - 79.793 388 103 error error Chi - square test for fit is not valid . Model did not com pute BMD for BMR = 10% Power Rel. Dev. 0.7 539 - 8 1.695 39 0 2 46 784 466 Polynomial 3° Rel. Dev. 0.7254 - 79.793 336 156 error error Chi - square test for fit is not valid . Model did not com pute BMD for BMR = 10% Polynomial 2° Rel. Dev. 0.7362 - 81.680 3 88 156 697 462 **Linear Rel. Dev.**  **0. 9386**  **- 8**  **3.666 384**  **2 46**  **7 68**  **491** 

### Among models with valid fits, the linear model has the lowest AIC and the BMDL values varied less **than three fold. Therefore the linear model is selected.** 

# BMDL05=24 **6 mg**  **- hr/L was selected for the analysis.**  **Model output files for BMR =5%** 

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**Exponential Model.** (Version: 1.9; Date: 01/29/2013) Input Data File: C:/ Bmds/BMDS240/Data/exp_NMP_Saillenfait_BW.2_Setting.(d) Gnuplot Plotting File: Thu Sep 12 12:20:01 2013 ====================================== ============================== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~ The form of the response function by Model: Model 2: Y[dose] = a * exp{sign * b * dose} Model 3: Y[dose] = a * exp{sign * (b * dose)^d} Model 4: Y[dose] = a * [c - (c - 1) * exp{ - b * dose}] Model 5: Y[dose] = a * [c - (c - 1) * exp{ - (b * dose)^d}] Note: Y[dose] is the median response for exposure = dose; sign = +1 for increasing trend in data; sign = - 1 for decreasing trend. Model 2 is nested within Models 3 and 4. Model 3 is nested within Model 5. Mo del 4 is nested within Model 5. Dependent variable = Mean Independent variable = Dose Data are assumed to be distributed: normally Variance Model: exp(lnalpha +rho *ln(Y[dose])) The variance is t o be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 500 Relative Function Convergence has been set to: 1e - 008 Parameter Convergence has been set to: 1e - 008 MLE solution provided: Exact

Initial Parameter Values Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha - 0.761471 - 0.761471 - 0.761471 - 0.761471 rho - 0.784145 - 0.784145 - 0.784145 - 0.784145 a 5.41 074 5.41074 5.95455 5.95455 b 0.000130807 0.000130807 0.00335347 0.00335347 c -- -- 0.862566 0.862566 d -- 1 -- 1

Parameter Estimates by Model Variable Model 2 Model 3 Model 4 Model 5

-------- ------- - ------ ------- ------- lnalpha 10.5079 11.4881 10.5079 9.88714 rho - 7.33335 - 7.90647 - 7.33335 - 6.9715 a 5.66744 5 .65942 5.66744 5.65863 b 0.000133676 0.000194725 0.000133676 0.00437576 c -- -- 0 0.947666 d -- 1.15149 -- 2.20686

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### Page **3** of **15** Table of Stats From Input Data Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 24 5.671 0.37 93.84 20 5.623 0.358 190.7 19 5.469 0.252 397.3 25 5.393 0.446 Estimated Values of Interest Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 5.667 0.3306 0.05272 93.84 5.597 0.3462 0.3385 190.7 5.525 0.363 - 0.6702 397.3 5.374 0.4017 0.2326 3 0 5.659 0.3302 0.1718 93.84 5.603 0.3434 0.2565 190.7 5.533 0.3609 - 0.7761 397.3 5.37 0.4063 0.2833 4 0 5.667 0.3306 0.05272 93.84 5.597 0.3462 0.3385 190.7 5.525 0.363 - 0.6702 397.3 5.374 0.4017 0.2326 5 0 5.659 0.3336 0.1816 93.84 5.62 0.3417 0.04083 190.7 5.5 14 0.3651 - 0.5367 397.3 5.372 0.3997 0.2565 Other models for which likelihoods are calculated: Model A1: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma^2 Model A2: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma(i)^2 Model A3: Yij = Mu(i) + e(ij) Var{e(ij)} = exp(lalpha + log(mean(i)) * rho) Model R: Yij = Mu + e(i) Var{e(ij)} = Sigma^2 Likelihoods of Interest Model Log(likelihood) DF AIC

------- ----------------- ---- ------------ A1 45.53621 5 - 81.07243 A2 48.82817 8 - 81.65634 A3 45.89652 6 - 79.79305 R 41.22097 2 - 78.44193 2 45.83051 4 - 83.66102 3 45.8487 5 - 81.69739 4 45.83051 4 - 83.66102 5 45.89652 6 - 79.79305 Additive constant for al l log - likelihoods = - 80. 87. This constant added to the above values gives the log - likelihood including the term that does not depend on the model parameters.

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### Page **4** of **15** Explanation of Tests Test 1: Does response and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A2 vs. A1) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4: Does Model 2 fit the data? (A3 vs. 2) Test 5a: Does Model 3 fit the data? (A3 vs 3) Test 5b: Is Model 3 better than Model 2? (3 vs. 2) Test 6a: Does Model 4 fit the data? (A3 vs 4) Test 6b: Is Model 4 better than Model 2? (4 vs. 2) Test 7a: Does Model 5 fit the data? (A3 vs 5) Test 7b: Is Model 5 better than Model 3? (5 vs. 3) Test 7c: Is Model 5 better than Model 4? (5 vs. 4)

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

-------- ------------------------ ------ -------------- Test 1 15.21 6 0.01865 Test 2 6.584 3 0.08641 Test 3 5.863 2 0.05331 Test 4 0.132 2 0.9361 Test 5a 0.09566 1 0.7571 Test 5b 0.03638 1 0.8487 Test 6a 0 .132 2 0.9361 Test 6b 7.105e - 014 0 N/A Test 7a - 5.37e - 011 0 N/A Test 7b 0.09566 1 0.75 71 Test 7c 0.132 2 0.9361 The p - value for Test 1 is less t han .05. There appears to be a difference between response and/ or var iances among the dose levels, it seems appropriate to model the data. The p - value for Test 2 is l ess than .1. A non - homogeneous variance model appears to be appropriate. The p - value for Test 3 is less than .1. You may want to consider a different variance model. The p - value for Test 4 is greater than .1. Model 2 seems to adequately describe the data. The p - value for Test 5a is greater than .1. Model 3 seems to adequately describe the data. The p - value for Test 5b is greater than .05. Model 3 does not seem to fit the data better than Model 2. The p - value for Test 6a is greater than .1. Model 4 seems to adequately describe the data. Degrees of freedom for Test 6b are less than or equal to 0. The Chi - Square test for fit is not valid. Degrees of freedom for Test 7a are less th an or equal to 0. The Chi - Square test for fit is not valid. The p - value for Test 7b is greater than .05. Model 5 does not seem to fit the data better than Model 3. The p - value for Test 7c is greater than .05. Model 5 does not seem to fit the data better than Model 4.

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### Page **5** of **15** Benchmark Dose Computations: Specified Effect = 0.050000 Risk Type = Relative deviation Confidence Level = 0.950000 BMD and BMDL by Model Model BMD BMDL

------- ------------ ---------- 2 383.715 241.79 3 389.358 242.411 4 383.715 165.531 5 382.145 98.9937

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Exponential Model 2, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

15:59 09/12 2013 BMD BMDL Exponential

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Exponential Model 3, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

15:59 09/12 2013 BMD BMDL Exponential

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Exponential Model 4, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

15:59 09/12 2013 BMD BMDL Exponential

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Exponential Model 5, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

15:59 09/12 2013 BMD BMDL Exponential

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**Hill Model.** (Version: 2.17; Date: 01/28/2013) Input Data File: C:/ Bmds/BMDS240/Data/hil_NMP_Saillenfait_BW.2_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/hil_NMP_Saillenfait_BW.2_Opt.plt Thu Sep 12 13:04:24 2013 ==================================================================== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = intercept + v*dose^n/(k^n + dose^n) Dependent variable = Mean Independent variable = Dose Power parameter restricted to be greater than 1 The variance is to be modeled as Var(i) = exp(lalpha + rho * ln(mean(i))) Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 500 Relative Function Convergence ha s been set to: 1e - 008 Parameter Conv ergence has been set to: 1e - 008 Default Initial Parameter Values lalpha = - 1.98839 rho = 0 intercept = 5.671 v = - 0.278 n = 3.74441 k = 151.058 Asymptotic Correlation Matrix of Parameter Estimates lalpha rho i ntercept v n k lalpha 1 - 1 - 0.35 - 0.23 - 0.19 0.43 rho - 1 1 0.36 0.23 0.19 - 0.43 intercept - 0.35 0.36 1 - 0.32 - 0.34 - 0.021 v - 0.23 0.23 - 0.32 1 0.93 - 0.92 n - 0.19 0.19 - 0.34 0.93 1 - 0.85 k 0.43 - 0.43 - 0.021 - 0.92 - 0.85 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 9.88714 14.1954 - 17.9353 37.7096 rho - 6.97151 8.29351 - 23.2265 9.28348 intercept 5.65863 0.071347 5.5188 5.79847 v - 0.356526 0.463103 - 1.26419 0.551139 n 2.43 4.62921 - 6.64308 11.5031 k 223.068 318.717 - 401.606 847.742 Table of Data and Estimated Values of Interest Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res.

------ --- -------- -------- ----------- ----------- ---------- 0 24 5.67 5.66 0.37 0.334 0.182 93.84 20 5.62 5.62 0.358 0.342 0.0408 190.7 19 5.47 5.51 0.252 0.365 - 0.537 397.3 25 5.39 5.37 0. 446 0.4 0.257 Warning: Likelihood for fitted model larger than the Li kelihood for model A3. Model Descriptions for likelihoods calculated

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### Page **7** of **15** Model A1: Yij = Mu(i) + e(i j) Var{e(ij)} = Sigma^2 Model A2: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma(i)^2 Model A3: Yij = Mu(i) + e(ij) Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) Model A3 uses any fixed variance parameters that were specified by the user Model R: Yi = Mu + e(i) Var{e(i)} = Sigma^2 Likelihoods of Interest Model Log(likelihood) # Param's AIC A1 45.536214 5 - 81.072428 A2 48.828168 8 - 81.656336 A3 45.896524 6 - 79.793047 fitted 45.896524 6 - 79.793047 R 41.220967 2 - 78.441934 Explanation of Tests Test 1: Do responses and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A1 vs A2) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4 : Does the Model for the Mean Fit? (A3 vs. fitted) (Note: When rho=0 the results of Test 3 and Test 2 will be the same.)

Tests of Interest Test - 2*log(Likelihood Ratio) Test df p - value Test 1 1 5.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 - 5.51097e - 011 0 NA The p - value for Test 1 is less t han .05. There appears to be a difference between response and/or variances among the dose levels. It seems appropriate to model the data The p - value for Test 2 is less than . 1. A non - homogeneous variance model appears to be appropriate The p - value for Test 3 is less than . 1. You may want to consider a different variance model NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi - Square test for fit is not valid Benchmark Dose Computation Specified effect = 0.05 Ri sk Type = Relative deviation Confidence level = 0.95 BMD = 388.251 BMDL = 103.239

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Hill Model, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Limit for the BMDL

13:04 09/12 2013 BMD BMDL Hill

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**Power Model** . (Version: 2.17; Date: 01/28/2013) Input Data File: C:/Bmds/BMDS240/Data/pow_NMP_Saillenfait_BW.2_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/pow_NMP_Saillenfait_BW.2_Opt.plt Thu Sep 12 12:51:23 2013 ====================================== ========= ===================== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = control + slope * dose^power Dependent variable = Mean Independent variable = Dose The power is restricted to be greater than or equal to 1 The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 500 Relative Function Convergence has been set to: 1e - 008 Parameter Convergence has been set to: 1e - 008 Default Initial Parameter Values lalpha = - 1.98839 rho = 0 control = 5.671 slope = - 3189.28 power = - 1.56195 Asymptotic Correlatio n Matrix of Parameter Estimates lalpha rho co ntrol slope power lalpha 1 - 1 - 0.41 0.42 0.4 rho - 1 1 0.41 - 0.42 - 0.4 control - 0.41 0.41 1 - 0.68 - 0.64 slope 0.42 - 0.42 - 0.68 1 1 power 0.4 - 0.4 - 0.64 1 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 11.5119 13.3283 - 14.6112 37.6349 rho - 7.92031 7.78614 - 23.1809 7.34024 control 5.65939 0.0692321 5.5237 5.79508 slope - 0.000326476 0.00170611 - 0.00367039 0.00301744 power 1.13409 0.856156 - 0.54394 2.81213 Table of Data a nd Estimated Values of Interest Dose N Obs Mean Est Mea n Obs Std Dev Est Std Dev Scaled Res.

------ --- -------- -------- ------ ----- ----------- ---------- 0 24 5.67 5.66 0.37 0.33 0.172 93.84 20 5.62 5.6 0.358 0 .343 0.26 190.7 19 5.47 5.53 0.252 0.361 - 0.779 397.3 25 5.39 5.37 0.446 0.406 0.283

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### Page **9** of **15** Model Descriptions for likelihoods calculated Model A1: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma^2 Model A2: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma(i)^2 Model A3: Yij = Mu(i) + e(ij) Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) Model A3 uses any fixed variance parameters tha t were specified by the user Model R: Yi = Mu + e(i) Var{e(i)} = Sigma^2 Likelihoods of Interest Model Log(likelihood) # Param's AIC A1 45.536214 5 - 81.072428 A2 48.828168 8 - 81.656336 A3 45.896524 6 - 79.793047 fitted 45.847392 5 - 81.694784 R 41.220 967 2 - 78.441934 Explanation of Tests Test 1: Do responses and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A1 vs A2) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) (Note: When rho=0 the results of Test 3 and Test 2 will be the same.)

Tests of Interest Test - 2*log(Likelihood Rat io) T est df p - value Test 1 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 0.0982629 1 0.753 9 The p - value for Test 1 is less than .05. There appears to be a difference between response and/or variances among the dose levels It seems appropriate to model the data The p - value for Test 2 is less than .1. A non - homogeneous variance model appears to be appropriate The p - value for Test 3 is less than .1. You may want to consider a different variance model The p - value for Test 4 is greater than .1. The model chosen seems to adequately describe the data Benchmark Dose C omputation S pecified effect = 0.05 Risk Type = Relative deviation C onfidence level = 0.95 BMD = 389.506 BMDL = 246.217 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Power Model, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Limit for the BMDL

12:51 09/12 2013 BMD BMDL Power

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**Polynomial Model –**  **3 rd**  **degree.** (Version: 2.17; Date: 01/28/2013) Input Data File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW2_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW2_Opt.plt Thu Sep 12 13:33:47 2013 ========================================================= =========== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = beta_0 + be ta_1*dose + bet a_2*dose^2 + ... Dependent variable = Mean Independent variable = Dose Signs of the polynomial coefficients are not restricted The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 500 Relative Function Convergence has been set to: 1e - 008 Parameter Convergence has been set to: 1e - 008 Default Initial Parameter Values lalpha = - 1.98839 rho = 0 beta_0 = 5.671 beta_1 = 0.000455788 beta_2 = - 1.25962e - 005 be ta_3 = 2.43847e - 008 Asymptotic Correlation Matrix of Paramet er Estimates lalpha rho beta_0 b eta_1 beta_2 beta_3 lalpha 1 - 1 - 0.17 - 0.18 0.34 - 0.41 rho - 1 1 0.17 0.18 - 0.34 0.41 beta_0 - 0.17 0.17 1 - 0.44 0.24 - 0.16 beta_1 - 0.18 0.18 - 0.44 1 - 0.95 0.91 beta_2 0.34 - 0.34 0.24 - 0.95 1 - 0.99 beta_3 - 0.41 0.41 - 0.16 0.91 - 0.99 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 9.88714 15.0342 - 19.5793 39.3536 rho - 6.97151 8.77078 - 24.1619 10.2189 beta_0 5.65863 0.0697728 5.52188 5.79539 beta_1 0.000143739 0.00262457 - 0.00500033 0.00528781 beta_2 - 7.09479e - 006 2.18836e - 005 - 4.99859e - 005 3.57963e - 005 beta_3 1.23843e - 008 4.00862e - 008 - 6 .61832e - 008 9.09518e - 008 Table of Data a nd Estimated Values of Interest Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res.

------ --- -------- -------- ------ ----- ----------- ---------- 0 24 5.67 5.66 0.37 0.334 0.182 93.84 20 5.62 5.62 0.358 0.342 0.0408 190.7 19 5.47 5.51 0.252 0.365 - 0.537 397.3 25 5.39 5.37 0.446 0.4 0.257

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### Page **11** of **15** Warning: Likelihood for fitted model larger th an the Likelihood for model A3. Model Descriptions for likelihoods calculated Model A1: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma^2 Model A2: Yij = Mu(i) + e(i j) Var{e(ij)} = Sigma(i)^2 Model A3: Yij = Mu(i) + e(ij) Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) Model A3 uses any fixed variance parameters that were specified by the user Model R: Yi = Mu + e(i) Var{e(i)} = Sigma^2 Likelihoods of Interest Model Log(likelihood) # Param's AIC A1 45.536214 5 - 81.072428 A2 48.828168 8 - 81.656336 A3 45.896524 6 - 79.793047 fitted 45.896524 6 - 79.793047 R 41.220967 2 - 78.441934 Explanation of Tests Test 1: Do response s and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A1 vs A2) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) (Note: When rho=0 the re sults of Test 3 and Test 2 will be the same.)

Tests of Interest Test - 2*log(Likelihood Rat io) Test df p - value Test 1 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 - 5.48823e - 011 0 NA The p - value for Test 1 is less t han .05. There appears to be a difference between response and/or variances among the dose l evel. It seems appropriate to model the data The p - value for Test 2 is less than .1. A non - homogeneous vari ance model appears to be appropriate The p - value for Test 3 is less than . 1. You may want to consider a different variance model NA - Degrees of freedom for Test 4 are less than or equal to 0. The Chi - Square test for fit is not valid Benchmark Dose Computation S pecified effect = 0.05 Risk Type = Relative deviation C onfidence level = 0.95 BMD = 336.067 BMDL = 156.263 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Polynomial Model, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Limit for the BMDL

13:33 09/12 2013 BMD BMDL Polynomial

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**Polynomial Model –**  **2 nd**  **Order** . (Version: 2.17; Date: 01/28/2013) Input Data File: C:/ Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW2_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW2_Opt.plt Thu Sep 12 13:16:42 2013 ====================================== ============================== BMDS Model Run

~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... Dependent variable = Mean Independent variable = Dose Signs of the polynomial coefficients are not restricted The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 500 Relative Function Convergence has been set to: 1e - 008 Parameter Convergence has been set to: 1e - 008 Default Initial Parameter Values lalpha = - 1.98839 rho = 0 beta_0 = 5.68648 beta_1 = - 0.00121037 beta_2 = 1.15923e - 006 Asymptotic Correlatio n Matrix of Parameter Estimates lalpha rho b et a_0 beta_1 beta_2 lalpha 1 - 1 - 0.26 0.49 - 0.53 rho - 1 1 0.26 - 0.49 0.53 beta_0 - 0.26 0.26 1 - 0.72 0.59 beta_1 0.49 - 0.49 - 0.72 1 - 0.97 beta_2 - 0.53 0.53 0.59 - 0.97 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 11.3659 13.6638 - 15.4147 38.1465 rho - 7.8349 7.97466 - 23.465 7.79515 beta_0 5.66143 0.068493 5.52719 5.79568 beta_1 - 0.000624567 0.0010711 - 0.00272388 0.00147474 beta_2 - 2.68501e - 007 2.63938e - 006 - 5 .44159e - 006 4.90459e - 006 Table of Data a nd Estimated Values of Interest Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res.

------ --- -------- ---- ---- ------ ----- ----------- ---------- 0 24 5.67 5.66 0.37 0.33 0.142 93.84 20 5.62 5.6 0.358 0.344 0.293 190.7 19 5.47 5.53 0.252 0 .361 - 0.767 397.3 25 5.39 5.37 0.446 0.406 0.272

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### Page **13** of **15** Model Descriptions for likelihoods calculated Model A1: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma^2 Model A2: Yij = Mu(i) + e(ij ) Var{e(ij)} = Sigma(i)^2 Model A3: Yij = Mu(i) + e(ij) Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) Model A3 uses any fixed variance parameters that were specified by the user Model R: Yi = Mu + e(i) Var{e(i)} = Sigma^2 Likelihoods of Interest Model Log(likelihood) # Param's AIC A1 45.536214 5 - 81.072428 A2 48.828168 8 - 81.656336 A3 45.896524 6 - 79.793047 fitted 45.839777 5 - 81.679555 R 41.220967 2 - 78.441934 Explanation of Tests Test 1: Do responses and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A1 vs A2) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4: Does the Model for the Mean Fit? (A3 vs. fitted) (Note: When rho=0 the results of Test 3 and Test 2 will be the same.)

Tests of Interest Test - 2*log(Likelihood Rat io) Test df p - value Test 1 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 0.113493 1 0.7362 The p - value for Test 1 is less t han .05. There appears to be a difference between response and/or variances amon g the dose levels . It seems appropriate to model the data The p - value for Test 2 is less than .1. A non - homogeneous variance model appears to be appropriate The p - value for Test 3 is less than . 1. You may want to consider a different variance model The p - value for Test 4 is greater th an .1. The model chosen seems to adequately describe the data Benchmark Dose Computation S pecified effect = 0.05 Risk Type = Relative deviation C onfidence level = 0.95 BMD = 388.382 BMDL = 155.967 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Polynomial Model, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Limit for the BMDL

13:16 09/12 2013 BMD BMDL Polynomial

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### Page **14** of **15** ====================================================================

**Linear Model** ( Polynomial Model , 1 st order) . (Version: 2.17; Date: 01/28/2013) Input Data File: C:/Bmds/ BMDS240/Data/lin_NMP_Saillenfait_BW2_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/lin_NMP_Saillenfait_BW2_Opt.plt Thu Sep 12 13:44:42 2013 ========================================= =========================== BMDS Model Run

~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = beta_0 + beta_1*dose + beta_2*dose^2 + ... Dependent variable = Mean Independent variable = Dose Signs of the polynomial coefficients are not restricted The variance is to be modeled as Var(i) = exp(lalpha + log(mean(i)) * rho) Total number of dose groups = 4 Total number of records with missing values = 0 Maximum number of iterations = 500 Relative Function Convergence has been set to: 1e - 008 Parameter Conv ergence has been set to: 1e - 008 Default Initial Parameter Values lalpha = - 1.98839 rho = 0 beta_0 = 5.66365 beta_1 = - 0.000731332 Asymptotic Correlatio n Matrix of Parameter Estimates lalpha rho beta_0 be ta_1 lalpha 1 - 1 0.079 - 0.11 rho - 1 1 - 0.079 0.11 beta_0 0.079 - 0.079 1 - 0.72 beta_1 - 0.11 0.11 - 0.72 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 10.6377 11.5633 - 12.0259 33.3013 rho - 7.40923 6.75646 - 20.6517 5.8332 beta_0 5.66658 0.055234 5.55832 5.77484 beta_1 - 0.000737251 0.000261912 - 0.00125059 - 0.000223912 Table of Data a nd Estimated Values of Interest Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res.

------ --- -------- --- ----- ------ ----- ----------- ---------- 0 24 5.67 5.67 0.37 0.331 0.0655 93.84 20 5.62 5.6 0.358 0.346 0.331 190.7 19 5.47 5.53 0.252 0.363 - 0.685 397.3 25 5.39 5.37 0.446 0.402 0.24 Model Descriptions for likelihoods calculated Model A1: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma^2

### Version: 09/12/13 BMCL AUC — Fetal BW — Saillenfait et al.(2003)



### Page **15** of **15** Model A2: Yij = Mu(i) + e(ij) Var{e(ij)} = Sigma(i)^2 Model A3: Yij = Mu(i) + e(ij) Var{e(ij)} = exp(lalpha + rho*ln(Mu(i))) Model A3 uses any fixed variance parameters that were specified by the user Model R: Yi = Mu + e(i) Var{e(i)} = Sigma^2 Likelihoods of Interest Model Log(likelihood) # Param's AIC A1 45.536214 5 - 81.072428 A2 48.828168 8 - 81.656336 A3 45.896524 6 - 79.793047 fitted 45.833158 4 - 83.666316 R 41.220967 2 - 78.441934 Explanation of Tests Test 1: Do responses and/or variances differ among Dose levels? (A2 vs. R) Test 2: Are Variances Homogeneous? (A1 vs A2) Test 3: Are variances adequately modeled? (A2 vs. A3) Test 4: Does the M odel for the Mean Fit? (A3 vs. fitted) (Note: When rho=0 the results of Test 3 and Test 2 will be the same.)

Tests of Interest Test - 2*log(Likelihood Rat io) Test df p - value Test 1 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 0.126732 2 0.9386 The p - value for Test 1 is less t han .05. There appears to b e a difference between response and/or variances among the dose levels. It seems appropriate to model the data The p - value for Test 2 is less than . 1. A non - homogeneous variance model appears to be appropriate The p - value for Test 3 is less than . 1. Y ou may want to consider a different variance model The p - value for Test 4 is greater than .1. The model chose n seems to adequately describe the data Benchmark Dose Computation S pecified effect = 0.05 Risk Type = Relative deviation C onfidence level = 0.95 BMD = 384.305 BMDL = 245.743 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 50 100 150 200 250 300 350 400MeanResponse

dose Linear Model, with BMR of 0.05 Rel. Dev. for the BMD and 0.95 Lower Confidence Limit for the BMDL

13:44 09/12 2013 BMD BMDL Linear