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



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

# BMD Analysis **( Cmax**  **)**

Iris Camacho Paul Schlosser 

# Saillenfait et al. 2003, fetal body weights Internal Dose, Cmax (m g /L) # litters Fetal BW (g) Standard Deviation 0 24 5.671 0.37 11.90 20 5.623 0.358 24.05 19 5.469 0.252 49.57 25 5.393 0.446

**Model Ty**  **pe 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. 93 37 - 8 3.6 56 47.8 30.2 98.3 62.0 Exponential (M3) Rel. Dev. 0.7 5 94 - 8 1.69 9 48.6 30.3 90.1 51.3 Exponential (M4) Rel. Dev. 0. 835 1 - 8 3.6 56 47.8 20.9 98.3 62.0 Sam e best fit , but more fitted parameters than M2 Exponential (M5) Rel. Dev. 0. 9337 - 79.79 3 47.8 12.6 error error Model did not com pute BMD for BMR = 10% Hill Rel. Dev. NA - 79.793 48.5 13.1 error error Chi - square test for fit is not valid . Model did not com pute BMD for BMR = 10% Power Rel. Dev. 0.7 5 62 - 8 1.697 48.6 30.7 88.9 51.2 Polynomial 3° Rel. Dev. NA - 79.793 42.5 1 9.7 error error Chi - square test for fit is not valid . Model did not com pute BMD for BMR = 10% Polynomial 2° Rel. Dev. 0.7367 - 81.680 48.5 19.7 85.9 57.6 **Linear Rel. Dev.**  **0. 93**  **6 6**  **- 8**  **3.662 47.9**  **30.7 95.8**  **61.3** 

### 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= **30.7 mg**  **- hr/L was selected for the analysis.** 

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



### Page **2** of **15** 

# Model output files for BMR **=5%**

====================================================================

**Exponential Model.** (Version: 1.9; Date: 01/29/2013) Input Data File: C :/Bmds/BMDS240/Data/exp_NMP_Saillenfait_BW_Cmax_Setting.(d) Gnuplot Plotting File: Thu Sep 12 14:49:40 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}] M odel 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 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 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 .40995 5.40995 5.95455 5.95455 b 0.00105023 0.00105023 0.026838 0.026838 c -- -- 0.862566 0.862566 d -- 1 -- 1

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

-------- ------- ------- ------- ------- lnalpha 10.4028 11.4716 10.4028 9.88712 rho - 7.27186 - 7.89679 - 7.27186 - 6.97149 a 5.66815 5.65943 5.66815 5.65863 b 0.00107208 0.00161294 0.00107208 0.034696 c -- -- 0 0.947571 d -- 1.16651 -- 2.22275

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



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

----- --- ---------- ------------- 0 24 5.671 0.37 11.9 20 5.623 0.358 24.05 19 5.469 0.252 49.57 25 5.393 0.446 Estimated Values of Interest Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 5.668 0.3307 0.04223 11.9 5.596 0.3464 0.3447 24.05 5.524 0.3632 - 0.6585 49.57 5.375 0.4012 0.2269 3 0 5.659 0.3302 0.1716 11.9 5.603 0.3434 0.2543 24.05 5.533 0.361 - 0.7737 49.57 5.37 0.4062 0.2832 4 0 5.668 0.3307 0.04223 11.9 5.596 0.3464 0.3447 24.05 5.524 0.3632 - 0.6585 49.57 5.375 0.4012 0.2269 5 0 5.659 0.3336 0.1816 11.9 5.62 0.3417 0.04083 24.05 5.5 14 0.3651 - 0.5367 49.57 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 45.82797 4 - 83.65594 3 45.84964 5 - 81.69927 4 45.82797 4 - 83.65594 5 45.89652 6 - 79.79305 Additive constant for all log - likelihoods = - 80. 87. This constant added to the above values gives the log - likelihood i ncluding the term that does not depend on the model parameters.

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



### 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 0.1371 2 0.9337 Test 5a 0.09377 1 0.7594 Test 5b 0.04333 1 0.8351 Test 6a 0. 1371 2 0.9337 Test 6b 2.26e - 012 0 N/A Test 7a - 2.127e - 011 0 N/A Test 7b 0.09377 1 0.75 94 Test 7c 0.1371 2 0.9337 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 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 tha n 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.

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



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

------- ------------ ---------- 2 47.8448 30.1693 3 48.5931 30.2615 4 47.8448 20.9141 5 47.7531 12.5535

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

0 20 40 60 80 100MeanResponse

dose Exponential Model 2, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

14:53 09/12 2013 BMD BMDL Exponential

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

0 10 20 30 40 50 60 70 80 90MeanResponse

dose Exponential Model 3, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

14:53 09/12 2013 BMD BMDL Exponential

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

0 20 40 60 80 100MeanResponse

dose Exponential Model 4, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

14:53 09/12 2013 BMD BMDL Exponential

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 10 20 30 40 50MeanResponse

dose Exponential Model 5

14:53 09/12 2013 BMD Exponential

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



### Page **6** of **15** ====================================================================

**Hill Model** . (Version: 2.17; Date: 01/28/2013) Input Data File: C:/ Bmds/BMDS240/Data/hil_NMP_Saillenfait_BW_Cmax_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/hil_NMP_Saillenfait_BW_Cmax_Opt.plt Thu Sep 12 15:07:41 2013 ==================================================================== BMDS Mode l 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 restri cted 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 Conver gence has been set to: 1e - 008 Parameter Convergence has been set to: 1e - 008 Default Initial Parameter Values lalpha = - 1.98839 rho = 0 interce pt = 5.671 v = - 0.278 n = 3.77069 k = 19.0795 Asymptotic Correlation Matrix of Parameter Estimates lalpha rho intercept v n k lalpha 1 - 1 - 0.35 - 0.24 - 0.19 0.43 rho - 1 1 0.36 0.24 0.19 - 0.43 intercept - 0.35 0.36 1 - 0.31 - 0.34 - 0.017 v - 0.24 0.24 - 0.31 1 0.94 - 0.92 n - 0.19 0.19 - 0.34 0.94 1 - 0.85 k 0.43 - 0.43 - 0.017 - 0.92 - 0.85 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Es timate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 9.88715 14.1954 - 17.9352 37.7096 rho - 6.97151 8.29351 - 23.2265 9.28347 inte rcept 5.65863 0.071347 5.5188 5.79847 v - 0.358204 0.474051 - 1.28733 0.570918 n 2.44477 4.67247 - 6.7131 11.6 026 k 28.2007 40.5975 - 51.3689 107.77 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 11.9 20 5.62 5.62 0.358 0.342 0.0408 24.05 19 5.47 5.51 0.252 0.365 - 0.537 49.57 25 5.39 5.37 0.446 0.4 0.257 Warning: Likelihood for fitted model larger than the Likelihood for model A3.

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



### Page **7** 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 parameter s 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 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 - 5.35465e - 011 0 NA 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 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 Risk Typ e = Relative deviation Confidence level = 0.95 BMD = 48.4703 BMDL = 13.0919 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 10 20 30 40 50MeanResponse

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

15:07 09/12 2013 BMD BMDL Hill

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



### Page **8** of **15** ====================================================================

**Power Model** . (Version: 2.17; Date : 01/28/2013) Input Data File: C:/Bmds/BMDS240/Data/pow_NMP_Saillenfait_BW_Cmax_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/pow_NMP_Saillenfait_BW_Cmax_Opt.plt Thu Sep 12 15:14:26 2013 ========================================== ========================== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = control + slope * dose^power Dependent variable = Mean Independent variable = Do se 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 iteratio ns = 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 control = 5.671 slope = - 129.432 power = - 1.57384 Asymptotic Correlation Matrix of Parameter Estimates lalpha rho control slope power lalpha 1 - 1 - 0.41 0.43 0.4 rho - 1 1 0.41 - 0.43 - 0.4 control - 0.41 0.41 1 - 0.69 - 0.64 slope 0.43 - 0.43 - 0.69 1 0.99 power 0.4 - 0.4 - 0.64 0.99 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 11.4954 13.3254 - 14.6218 37.6126 rho - 7.91072 7.78441 - 23.1679 7.34643 control 5.65941 0.0692366 5.5237 5.79511 slope - 0.00326494 0.0114188 - 0.0256454 0.01911 55 power 1.14888 0.868344 - 0.553038 2.85081 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 0.33 0.172 11.9 20 5.62 5.6 0.358 0.343 0.257 24.05 19 5.47 5.53 0.252 0.361 - 0.777 49.57 25 5.39 5.37 0.446 0.406 0.283 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

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



### Page **9** of **15** 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 45.848341 5 - 81.696681 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 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 0.096366 1 0.7562 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 The p - value for Te st 4 is greater th an .1. The model chosen seems to adequately describe the data Benchmark Dose Computation Specified effect = 0.05 Risk Type = Relative deviation Confidence level = 0.95 BMD = 48 .6112 BMDL = 30.7309

5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 10 20 30 40 50MeanResponse

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

15:14 09/12 2013 BMD BMDL Power

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



### Page **10** of **15** ====================================================================

**Polynomial Model –**  **3 rd**  **degree.** (Version: 2.17; Date: 01/28/2013) Input Data File: C:/ Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.plt Thu Sep 12 15:20:55 2013 ====================================== ============================== BMDS Mode l Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is:

Y[dose] = beta_0 + be ta_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 = 5.671 beta_1 = 0.00380278 beta_2 = - 0.000806573 beta_3 = 1.24414e - 005 Asymptotic Correlatio n Matrix of Parameter Estimates lalpha rho beta_0 b eta_1 beta_2 beta_3 lalpha 1 - 1 - 0.17 - 0.18 0.35 - 0.41 rho - 1 1 0.17 0.18 - 0.35 0.41 beta_0 - 0.17 0.17 1 - 0.44 0.23 - 0.16 beta_1 - 0.18 0.18 - 0.44 1 - 0.95 0.91 beta_2 0.35 - 0.35 0.23 - 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 9.88711 15.0342 - 19.5793 39.3535 rho - 6.97149 8.77078 - 24.1619 10.2189 beta_0 5.65863 0.0697728 5.52188 5.79539 beta_1 0.00124345 0.020928 - 0.0397746 0.0422615 beta_2 - 0.000452908 0.00139175 - 0 .00318069 0.00227488 beta_3 6.28146e - 006 2.03946e - 005 - 3.36912e - 005 4.62541 e - 005 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 11.9 20 5.62 5.62 0.358 0.342 0.0408 24.05 19 5.47 5.51 0.252 0.365 - 0.537 49.57 25 5.39 5.37 0. 446 0.4 0.257 Warning: Likelihood for fitted model larger th an the Likelihood for model A3.

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



### Page **11** of **15** Model Descript ions 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 45.896524 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 15.2144 6 0.01865 Test 2 6.58391 3 0.08641 Test 3 5.86329 2 0.05331 Test 4 - 4.84164e - 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 a ppropriate 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 B enchmark Dose Computation S p ecified effect = 0.05 Risk Type = Relative deviation C onfidence level = 0.95 BMD = 42.4735 BMDL = 19.7354 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 10 20 30 40 50MeanResponse

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

15:20 09/12 2013 BMD BMDL Polynomial

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



### Page **12** of **15** ====================================================================

**P olynomial Model**  **– 2**  **nd Order**  . (Ver sion: 2.17; Date: 01/28/2013) Input Data File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/ply_NMP_Saillenfait_BW_Cmax_Opt.plt Thu Sep 12 15:31: 05 2013 ====================================== ============================== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is: Y[dose] = beta_0 + be ta_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 g roups = 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 = 5.68636 beta_1 = - 0.00953107 beta_2 = 7.10263e - 005 Asympt otic Correlatio n Matrix of Parameter Estimates lalpha rho beta_ 0 beta_1 beta_2 lalpha 1 - 1 - 0.26 0.49 - 0.53 rho - 1 1 0.26 - 0.49 0.52 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 0.52 0.59 - 0.97 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 11.3774 13.6414 - 15.3592 38.1139 rho - 7.84161 7.96162 - 23.4461 7.76288 beta_0 5.66132 0.0685418 5.52698 5.79566 beta_1 - 0.00486813 0.00853414 - 0.0215947 0.0118585 beta_2 - 1.99964e - 005 0.000168622 - 0.000350489 0.000310497 Table of Data a nd Estimated Values of Interest Dose N Obs Me an Est Mean Obs Std Dev Est Std Dev Scaled Res.

------ --- -------- -------- ------ ----- ----------- ---------- 0 24 5.67 5.66 0.37 0.33 0.144 11.9 20 5.62 5.6 0.358 0.344 0.291 24.05 19 5.47 5.53 0.252 0.361 - 0.769 49.57 25 5.39 5.37 0.446 0.406 0.273

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



### 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 45.840013 5 - 81.68 0026 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 i o) 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 0.113021 1 0.7367 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 conside r 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 Comput ation S pecified effect = 0.05 Risk Type = Relative deviation Con fidence level = 0.95 BMD = 48.4891 BMDL = 19.737 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 10 20 30 40 50MeanResponse

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

15:31 09/12 2013 BMD BMDL Polynomial

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



### 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_BW_Cmax_Opt.(d) Gnuplot Plotting File: C:/Bmds/BMDS240/Data/lin_NMP_Saillenfait_BW_Cmax_Opt.plt Thu Sep 12 15:36:49 2013 ====================================== ============================== BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The form of the response function is:

Y[dose] = beta _0 + beta_1*dose + be ta_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 = 5.66456 beta_1 = - 0.0058728 Asymptotic Correlatio n Matri x of Parameter Estimates lalpha rho beta_0 beta_1 lalpha 1 - 1 0.077 - 0.11 rho - 1 1 - 0.077 0.11 beta_0 0.077 - 0.077 1 - 0.72 beta_1 - 0.11 0.11 - 0.72 1

Parameter Estimates

95.0% Wald Confidence Interval Variable Estima te Std. Err. Lower Conf. Limit Upper Conf. Limit lalpha 10.5323 11.5553 - 12.1157 33.1803 rho - 7.3476 6.75178 - 20.5809 5.88566 beta_ 0 5.6673 0.0554004 5.55871 5.77588 beta_1 - 0.00591414 0.00209746 - 0.0100251 - 0.00180319 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 0.0549 11.9 20 5. 62 5.6 0.358 0.346 0.337 24.05 19 5.47 5.53 0.252 0.363 - 0.673 49.57 25 5.39 5.37 0.446 0.402 0.235

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



### Page **15** of **15** Model Descriptions for likelihoods calcu late d 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 a ny 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 45.831033 4 - 83.662065 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) 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 0.130982 2 0.936 6 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 appear s 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 = 47.9131 BMDL = 30.6591 5.2 5.3 5.4 5.5 5.6 5.7 5.8

0 10 20 30 40 50MeanResponse

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

15:36 09/12 2013 BMD BMDL Linear