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

(mg/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 Type

Risk 

Type

PValue AIC

BMD

(BMR= 

5%)

BMDL

(BMR= 

5%)

BMD

(BMR= 

10%)

BMDL

(BMR= 

10%)

Comments

Exponential (M2) Rel. Dev. 0.9337 -83.656 47.8 30.2 98.3 62.0

Exponential (M3) Rel. Dev. 0.7594 -81.699 48.6 30.3 90.1 51.3

Exponential (M4) Rel. Dev. 0.8351 -83.656 47.8 20.9 98.3 62.0

Same best fit, 

but more fitted 

parameters 

than M2

Exponential (M5) Rel. Dev. 0.9337 -79.793 47.8 12.6 error error

Model did not 

compute 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 

compute BMD 

for BMR = 10%

Power Rel. Dev. 0.7562 -81.697 48.6 30.7 88.9 51.2

Polynomial 3° Rel. Dev. NA -79.793 42.5 19.7 error error

Chi-square test 

for fit is not 

valid.

Model did not 

compute BMD 

for BMR = 10%

Polynomial 2° Rel. Dev. 0.7367 -81.680 48.5 19.7 85.9 57.6

Linear Rel. Dev. 0.9366 -83.662 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}]

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

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

 sign = +1 for increasing trend in data;

 sign = -1 for decreasing trend.

 Model 2 is nested within Models 3 and 4.

 Model 3 is nested within Model 5.

 Model 4 is nested within Model 5.

 Dependent variable = Mean

 Independent variable = Dose

 Data are assumed to be distributed: normally

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

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

 Total number of dose groups = 4

 Total number of records with missing values = 0

 Maximum number of iterations = 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 5.514 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 including 

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 0.7594

 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 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. 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 than 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 Effect = 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 80 100

Mean Response

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

BMDL BMD

 

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 90

Mean Response

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

BMDL BMD

 

Exponential

 5.1

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 5.9

 0 20 40 60 80 100

Mean Response

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

BMDL BMD

 

Exponential

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 10 20 30 40 50

Mean Response

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 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 has been set to: 1e-008

 Parameter Convergence has been set to: 1e-008

 Default Initial Parameter Values 

 lalpha = -1.98839

 rho = 0

 intercept = 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 Estimate 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

 intercept 5.65863 0.071347 5.5188 5.79847

 v -0.358204 0.474051 -1.28733 0.570918

 n 2.44477 4.67247 -6.7131 11.6026

 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 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 -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 Type = 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 50

Mean Response

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

BMDL BMD

 

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 = 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 = -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 0.0191155

 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 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 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 50

Mean Response

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

BMDL BMD

 

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 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 = 5.671

 beta_1 = 0.00380278

 beta_2 = -0.000806573

 beta_3 = 1.24414e-005

 Asymptotic Correlation Matrix of Parameter Estimates

 lalpha rho beta_0 beta_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 4.62541e-005

 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 11 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 45.896524 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 than .05. There appears to be a difference between response and/or variances among the dose 

levelsIt 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 Type = Relative deviation 

Confidence 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 50

Mean Response

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

BMDL BMD

 

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

Page 12 of 15

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

 Polynomial Model – 2

nd Order. (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 15:31:05 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 = 5.68636

 beta_1 = -0.00953107

 beta_2 = 7.10263e-005

 Asymptotic Correlation 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 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 0.144

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 -81.680026

 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 0.113021 1 0.7367

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 Computation

Specified effect = 0.05

Risk Type = Relative deviation 

Confidence 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 50

Mean Response

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

BMDL BMD

 

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

Page 14 of 15

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

 Linear Model (Polynomial Model, 1st 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 + 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 = 5.66456

 beta_1 = -0.0058728

 Asymptotic Correlation Matrix 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 Estimate 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 and 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 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 45.831033 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 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 0.130982 2 0.9366

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 Computation

Specified effect = 0.05

Risk Type = Relative deviation 

Confidence 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 50

Mean Response

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

BMDL BMD

 

Linear