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

Page 1 of 15

BMD Analysis (AUC)

Iris Camacho

Paul Schlosser

Saillenfait et al. 2003, fetal body weights

Internal Dose, AUC 

(mg-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 

Type

PValue AIC

BMD

(BMR= 

5%)

BMDL

(BMR= 

5%)

BMD

(BMR= 

10%)

BMDL

(BMR= 

10%)

Comments

Exponential (M2) Rel. Dev. 0.9361 -83.661 384 242 788 497

Exponential (M3) Rel. Dev. 0.7571 -81.697 389 242 728 411

Exponential (M4) Rel. Dev. 0.9361 -83.661 384 166 788 497

Same best fit, 

but more fitted 

parameters 

than M2

Exponential (M5) Rel. Dev. 0.7571 -79.793 382 99 error error

Model did not 

compute 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 

compute BMD 

for BMR = 10%

Power Rel. Dev. 0.7539 -81.695 390 246 784 466

Polynomial 3° Rel. Dev. 0.7254 -79.793 336 156 error error

Chi-square test 

for fit is not 

valid.

Model did not 

compute BMD 

for BMR = 10%

Polynomial 2° Rel. Dev. 0.7362 -81.680 388 156 697 462

Linear Rel. Dev. 0.9386 -83.666 384 246 768 491

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=246 mg-hr/L was selected for the analysis.

Model output files for BMR=5%
Version: 09/12/13 BMCL AUC—Fetal BW—Saillenfait et al.(2003)

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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.

 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 5.41074 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

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

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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 5.514 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 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 AUC—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 0.132 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 0.7571

 Test 7c 0.132 2 0.9361

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 AUC—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

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

 2 383.715 241.79

 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 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Exponential

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Exponential

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Exponential

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

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

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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 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 = 3.74441

 k = 151.058

 Asymptotic Correlation Matrix of Parameter Estimates

 lalpha rho intercept 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 Likelihood for model A3.

Model Descriptions for likelihoods calculated
Version: 09/12/13 BMCL AUC—Fetal BW—Saillenfait et al.(2003)

Page 7 of 15

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 -5.51097e-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 = 388.251

 BMDL = 103.239

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Hill
Version: 09/12/13 BMCL AUC—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.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 Correlation Matrix of Parameter Estimates

 lalpha rho control 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 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

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

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 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 45.847392 5 -81.694784

 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 0.0982629 1 0.7539

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 = 389.506 

 BMDL = 246.217 

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Power
Version: 09/12/13 BMCL AUC—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_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 + 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 = 0.000455788

 beta_2 = -1.25962e-005

 beta_3 = 2.43847e-008

 Asymptotic Correlation Matrix of Parameter Estimates

 lalpha rho beta_0 beta_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 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
Version: 09/12/13 BMCL AUC—Fetal BW—Saillenfait et al.(2003)

Page 11 of 15

Warning: Likelihood for fitted model larger than 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(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 -5.48823e-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 

level. 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 = 336.067

 BMDL = 156.263

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Polynomial
Version: 09/12/13 BMCL AUC—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_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 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 0.53

 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 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 0.142

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
Version: 09/12/13 BMCL AUC—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 45.839777 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 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 0.113493 1 0.7362

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 = 388.382

 BMDL = 155.967

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Polynomial
Version: 09/12/13 BMCL AUC—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_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 Convergence has been set to: 1e-008

 Default Initial Parameter Values 

 lalpha = -1.98839

 rho = 0

 beta_0 = 5.66365

 beta_1 = -0.000731332

 Asymptotic Correlation Matrix of Parameter Estimates

 lalpha rho beta_0 beta_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 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 0.0655

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 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 0.126732 2 0.9386

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 = 384.305

 BMDL = 245.743

 5.2

 5.3

 5.4

 5.5

 5.6

 5.7

 5.8

 0 50 100 150 200 250 300 350 400

Mean Response

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

BMDL BMD

 

Linear