Page 1 of 61

APPENDIX C: Summaries OF BMD Analyses of 

Studies on LH Surge
Page 2 of 61

TABLE OF CONTENTS

C.1 NHEERL STUDY................................................................................................................................................ 3

C.2 MORSETH ONE MONTH LH STUDY ................................................................................................................ 11

C.3. MORSETH SIX MONTH LH STUDY ................................................................................................................. 27

C.4. MINNEMA ONE MONTH LH STUDY .............................................................................................................. 43

C.5 BMD OUTPUT SUMMARIES – AUC................................................................................................................ 51

C.6. PREDICTED DAILY STEADY STATE SERUM AUC ............................................................................................ 56
Page 3 of 61

C.1 NHEERL STUDY 

Model 

(Constant 

Variance)

BMD BMDL p-value AIC

Exponential 2 58.5 29.6 0.004 515.8

Exponential 3 58.5 29.6 0.004 515.8

Exponential 4 4.23 1.96 0.94 501.3

Exponential 5 4.31 1.96 0.86 503.3

Hill 4.16 1.68 0.87 503.3

Linear 78.4 53.1 0.002 518.1

Polynomial 78.4 53.1 0.002 518.1

Power 78.4 53.1 0.002 518.1

NHEERL Study: BMD OUTPUT for Exponential Model Runs (Constant Variance; 

Best Model Fit)

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

== 

 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/exp_Actualruns_Setting.(d) 

 Gnuplot Plotting File: 

Tue Jul 20 14:07:40 2010

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

== 

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.
Page 4 of 61

 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]))

 rho is set to 0.

 A constant variance model is fit.

 Total number of dose groups = 7

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 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 4.07816 4.07816 4.07816 4.07816

 rho(S) 0 0 0 0

 a 11.0009 11.0009 22.9404 22.9404

 b 0.00794702 0.00794702 0.0449039 0.0449039

 c -- -- 0.352881 0.352881

 d -- 1 -- 1

 (S) = Specified

 Parameter Estimates by Model

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha 4.25603 4.25603 4.08595 4.08581

 rho 0 0 0 0

 a 16.8823 16.8823 21.9754 21.9037

 b 0.0117718 0.0117718 0.219622 0.22213

 c -- -- 0.422997 0.427096

 d -- 1 -- 1.07687
Page 5 of 61

 Table of Stats From Input Data

 Dose N Obs Mean Obs Std Dev

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

 0 16 21.85 7

 1.56 11 18.57 10.8

 3.12 12 16.05 9.3

 6.25 17 11.81 7

 12.5 7 11.88 9

 25 14 8.5 7.6

 75 20 9.6 6.7

 Estimated Values of Interest

 Model Dose Est Mean Est Std Scaled Residual

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

 2 0 16.88 8.398 2.365

 1.56 16.58 8.398 0.7878

 3.12 16.27 8.398 -0.09425

 6.25 15.68 8.398 -1.902

 12.5 14.57 8.398 -0.8482

 25 12.58 8.398 -1.817

 75 6.982 8.398 1.394

 3 0 16.88 8.398 2.365

 1.56 16.58 8.398 0.7878

 3.12 16.27 8.398 -0.09425

 6.25 15.68 8.398 -1.902

 12.5 14.57 8.398 -0.8482

 25 12.58 8.398 -1.817

 75 6.982 8.398 1.394

 4 0 21.98 7.714 -0.06604

 1.56 18.3 7.714 0.1173

 3.12 15.69 7.714 0.1613

 6.25 12.51 7.714 -0.3737

 12.5 10.11 7.714 0.6071

 25 9.348 7.714 -0.4113

 75 9.296 7.714 0.1765

 5 0 21.9 7.713 -0.02886

 1.56 18.47 7.713 0.04191

 3.12 15.75 7.713 0.1316

 6.25 12.38 7.713 -0.303

 12.5 9.978 7.713 0.6526

 25 9.377 7.713 -0.4255

 75 9.355 7.713 0.1421
Page 6 of 61

 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 -246.2909 8 508.5818

 A2 -243.8179 14 515.6358

 A3 -246.2909 8 508.5818

 R -261.9739 2 527.9478

 2 -254.9177 3 515.8354

 3 -254.9177 3 515.8354

 4 -246.6687 4 501.3374

 5 -246.6617 5 503.3234

 Additive constant for all log-likelihoods = -89.14. This constant added to the

 above values gives the log-likelihood including the term that does not

 depend on the model parameters.

 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)
Page 7 of 61

 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 36.31 12 0.0002886

 Test 2 4.946 6 0.5508

 Test 3 4.946 6 0.5508

 Test 4 17.25 5 0.004043

 Test 5a 17.25 5 0.004043

 Test 5b -7.39e-013 0 N/A

 Test 6a 0.7556 4 0.9443

 Test 6b 16.5 1 < 0.0001

 Test 7a 0.7416 3 0.8634

 Test 7b 16.51 2 0.0002597

 Test 7c 0.01397 1 0.9059

 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 greater than .1. A homogeneous

 variance model appears to be appropriate here.

 The p-value for Test 3 is greater than .1. The modeled

 variance appears to be appropriate here.

 The p-value for Test 4 is less than .1. Model 2 may not adequately

 describe the data; you may want to consider another model.

 The p-value for Test 5a is less than .1. Model 3 may not adequately

 describe the data; you may want to consider another model.

 Degrees of freedom for Test 5b are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 The p-value for Test 6a is greater than .1. Model 4 seems
Page 8 of 61

 to adequately describe the data.

 The p-value for Test 6b is less than .05. Model 4 appears

 to fit the data better than Model 2.

 The p-value for Test 7a is greater than .1. Model 5 seems

 to adequately describe the data.

 The p-value for Test 7b is less than .05. Model 5 appears

 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.

 Benchmark Dose Computations:

 Specified Effect = 1.000000

 Risk Type = Estimated standard deviations from control

 Confidence Level = 0.950000

 BMD and BMDL by Model

 Model BMD BMDL

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

 2 58.451 29.553

 3 58.451 29.553

 4 4.26795 1.9583

 5 4.30751 1.962
Page 9 of 61

 5

 10

 15

 20

 25

 0 10 20 30 40 50 60 70

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

14:07 07/20 2010

BMDL BMD

 

Exponential

 5

 10

 15

 20

 25

 0 10 20 30 40 50 60 70

Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

14:07 07/20 2010

BMDL BMD

 

Exponential
Page 10 of 61

 5

 10

 15

 20

 25

 0 10 20 30 40 50 60 70

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

14:07 07/20 2010

BMDL BMD

 

Exponential

 5

 10

 15

 20

 25

 0 10 20 30 40 50 60 70

Mean Response

dose

Exponential Model 5 with 0.95 Confidence Level

14:07 07/20 2010

BMDL BMD

 

Exponential
Page 11 of 61

________________________________________________________________

C.2 MORSETH ONE MONTH LH STUDY 

Model 

(Constant 

Variance) a

BMD BMDL p-value AIC

Exponential 2 152.4 25.6 0.78 819.9

Exponential 3 152.4 25.6 0.78 819.9

Exponential 4 129.6 11.8 0.85 821.2

Exponential 5 Not Computed Not Computed -- --

Hill Not Computed Not Computed -- --

Linear 226.5 126.7 0.54 821.0

Polynomial 215.9 128.8 0.59 820.8

Power 215.9 128.8 0.59 820.8 a

Nonhomogeneous Variance recommended by BMDS output

Model 

(Nonhomogeneous 

Variance)

BMD BMDL p-value AIC

Exponential 2 523.7 174.7 0.017 795.3

Exponential 3 523.7 174.7 0.017 795.3

Exponential 4 Not 

Computed

Not 

Computed

-- --

Exponential 5 Not 

Computed

Not 

Computed

-- --

Hill Not 

Computed

Not 

Computed

-- --

Linear 291.3 197.3 0.006 797.5

Polynomial 291.3 197.3 0.006 797.5

Power 291.3 197.3 0.006 797.5

Morseth One Month LH Study: BMD OUTPUT for Exponential Model Runs

(Constant Variance)
Page 12 of 61

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

== 

 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/exp_Actualruns_Setting.(d) 

 Gnuplot Plotting File: 

Thu Jul 22 13:45:53 2010

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

== 

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]))

 rho is set to 0.

 A constant variance model is fit.

 Total number of dose groups = 5

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 Relative Function Convergence has been set to: 1e-008

 Parameter Convergence has been set to: 1e-008

 MLE solution provided: Exact
Page 13 of 61

 Initial Parameter Values

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha 15.2574 15.2574 15.2574 15.2574

 rho(S) 0 0 0 0

 a 1413.18 1413.18 3165.75 3165.75

 b 0.00610828 0.00610828 0.0210595 0.0210595

 c -- -- 0.244281 0.244281

 d -- 1 -- 1

 (S) = Specified

 Parameter Estimates by Model

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha 15.2794 15.2794 15.2638 15.2609

 rho 0 0 0 0

 a 2764.3 2764.3 2913.32 2803.53

 b 0.00915046 0.00915045 0.0267425 0.0265255

 c -- -- 0.269019 0.28969

 d -- 1 -- 2.20144

 NC = No Convergence

 Table of Stats From Input Data

 Dose N Obs Mean Obs Std Dev

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

 0 10 2650 2389

 2.5 10 3015 3220

 5 10 2717 2542

 40 10 1450 857

 200 10 812 470

 Estimated Values of Interest

 Model Dose Est Mean Est Std Scaled Residual

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

 2 0 2764 2079 -0.1738

 2.5 2702 2079 0.4764
Page 14 of 61

 5 2641 2079 0.1161

 40 1917 2079 -0.7103

 200 443.4 2079 0.5606

 3 0 2764 2079 -0.1738

 2.5 2702 2079 0.4764

 5 2641 2079 0.1161

 40 1917 2079 -0.7103

 200 443.4 2079 0.5606

 4 0 2913 2063 -0.4036

 2.5 2776 2063 0.367

 5 2647 2063 0.1076

 40 1514 2063 -0.09875

 200 793.9 2063 0.0278

 5 0 2804 2060 -0.2357

 2.5 2798 2060 0.3324

 5 2780 2060 -0.09725

 40 1449 2060 0.0007715

 200 812.2 2060 -0.0002382

 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 -406.4352 6 824.8704

 A2 -388.3924 10 796.7849

 A3 -406.4352 6 824.8704

 R -410.3636 2 824.7272

 2 -406.986 3 819.9719

 3 -406.986 3 819.9719
Page 15 of 61

 4 -406.5955 4 821.1911

 5 -406.5231 5 823.0462

 Additive constant for all log-likelihoods = -45.95. This constant added to the

 above values gives the log-likelihood including the term that does not

 depend on the model parameters.

 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 43.94 8 < 0.0001

 Test 2 36.09 4 < 0.0001

 Test 3 36.09 4 < 0.0001

 Test 4 1.102 3 0.7767

 Test 5a 1.102 3 0.7767

 Test 5b -1.819e-011 0 N/A

 Test 6a 0.3207 2 0.8518

 Test 6b 0.7808 1 0.3769

 Test 7a 0.1758 1 0.675

 Test 7b 0.9257 2 0.6295

 Test 7c 0.1449 1 0.7034

 The p-value for Test 1 is less than .05. There appears to be a

 difference between response and/or variances among the dose
Page 16 of 61

 levels, it seems appropriate to model the data.

 The p-value for Test 2 is less than .1. Consider running

 a non-homogeneous variance model.

 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.

 Degrees of freedom for Test 5b are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 The p-value for Test 6a is greater than .1. Model 4 seems

 to adequately describe the data.

 The p-value for Test 6b is greater than .05. Model 4 does

 not seem to fit the data better than Model 2.

 The p-value for Test 7a is greater than .1. Model 5 seems

 to adequately describe the data.

 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.

 Benchmark Dose Computations:

 Specified Effect = 1.000000

 Risk Type = Estimated standard deviations from control

 Confidence Level = 0.950000

 BMD and BMDL by Model

 Model BMD BMDL

 ------- ------------ ----------
Page 17 of 61

 2 152.443 25.6454

 3 152.443 25.6454

 4 129.57 11.8371

 5 0 0 Not computed

 0

 1000

 2000

 3000

 4000

 5000

 0 50 100 150 200

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

13:45 07/22 2010

BMDL BMD

 

Exponential
Page 18 of 61

 0

 1000

 2000

 3000

 4000

 5000

 0 50 100 150 200

Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

13:45 07/22 2010

BMDL BMD

 

Exponential

 0

 1000

 2000

 3000

 4000

 5000

 0 50 100 150 200

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

13:45 07/22 2010

BMDL BMD

 

Exponential
Page 19 of 61

________________________________________________________________

Morseth One Month LH Study: BMD OUTPUT for Exponential Model Runs 

(Nonhomogeneous Variance)

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

== 

 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/exp_Actualruns_Setting.(d) 

 Gnuplot Plotting File: 

Fri Aug 06 09:35:01 2010

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

== 

BMDS Model Run 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~

 0

 1000

 2000

 3000

 4000

 5000

 0 50 100 150 200

Mean Response

dose

Exponential Model 5

13:45 07/22 2010

BMD

Exponential
Page 20 of 61

 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 = 5

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 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 -7.57613 -7.57613 -7.57613 -7.57613

 rho 2.94035 2.94035 2.94035 2.94035

 a 1413.18 1413.18 3165.75 3165.75

 b 0.00610828 0.00610828 0.0210595 0.0210595

 c -- -- 0.244281 0.244281

 d -- 1 -- 1

 Parameter Estimates by Model

 Variable Model 2 Model 3 Model 4 Model 5
Page 21 of 61

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

 lnalpha -7.94834 -7.94834 -7.47498 -7.51913

 rho 2.99971 2.99971 2.91611 2.92104

 a 2583.98 2583.98 3033.27 2862.72

 b 0.00589281 0.00589281 0.035215 0.0290775

 c -- -- 0.273458 0.291831

 d -- 1 -- 2.06427

 NC = No Convergence

 Table of Stats From Input Data

 Dose N Obs Mean Obs Std Dev

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

 0 10 2650 2389

 2.5 10 3015 3220

 5 10 2717 2542

 40 10 1450 857

 200 10 812 470

 Estimated Values of Interest

 Model Dose Est Mean Est Std Scaled Residual

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

 2 0 2584 2466 0.08467

 2.5 2546 2412 0.6146

 5 2509 2359 0.2788

 40 2041 1732 -1.08

 200 795.1 421 0.1266

 3 0 2584 2466 0.08467

 2.5 2546 2412 0.6146

 5 2509 2359 0.2788

 40 2041 1732 -1.08

 200 795.1 421 0.1266

 4 0 3033 2842 -0.4264

 2.5 2848 2592 0.2043

 5 2677 2369 0.05275

 40 1368 890.3 0.2903

 200 831.4 430.6 -0.1425

 5 0 2863 2606 -0.2581

 2.5 2854 2594 0.1967

 5 2825 2556 -0.1339

 40 1353 871.8 0.3532

 200 835.4 431.3 -0.1718
Page 22 of 61

 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 -406.4352 6 824.8704

 A2 -388.3924 10 796.7849

 A3 -388.5412 7 791.0824

 R -410.3636 2 824.7272

 2 -393.6414 4 795.2827

 3 -393.6414 4 795.2827

 4 -389.3963 5 788.7925

 5 -389.0987 6 790.1974

 Additive constant for all log-likelihoods = -45.95. This constant added to the

 above values gives the log-likelihood including the term that does not

 depend on the model parameters.

 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)
Page 23 of 61

 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 43.94 8 < 0.0001

 Test 2 36.09 4 < 0.0001

 Test 3 0.2976 3 0.9605

 Test 4 10.2 3 0.01694

 Test 5a 10.2 3 0.01694

 Test 5b 0 0 N/A

 Test 6a 1.71 2 0.4253

 Test 6b 8.49 1 0.003571

 Test 7a 1.115 1 0.291

 Test 7b 9.085 2 0.01065

 Test 7c 0.5951 1 0.4405

 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 greater than .1. The modeled

 variance appears to be appropriate here.

 The p-value for Test 4 is less than .1. Model 2 may not adequately

 describe the data; you may want to consider another model.

 The p-value for Test 5a is less than .1. Model 3 may not adequately

 describe the data; you may want to consider another model.

 Degrees of freedom for Test 5b are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 The p-value for Test 6a is greater than .1. Model 4 seems
Page 24 of 61

 to adequately describe the data.

 The p-value for Test 6b is less than .05. Model 4 appears

 to fit the data better than Model 2.

 The p-value for Test 7a is greater than .1. Model 5 seems

 to adequately describe the data.

 The p-value for Test 7b is less than .05. Model 5 appears

 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.

 Benchmark Dose Computations:

 Specified Effect = 1.000000

 Risk Type = Estimated standard deviations from control

 Confidence Level = 0.950000

 BMD and BMDL by Model

 Model BMD BMDL

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

 2 523.696 174.68

 3 523.696 174.68

 4 0 0 Not computed

 5 0 0 Not computed
Page 25 of 61

 0

 1000

 2000

 3000

 4000

 5000

 0 100 200 300 400 500

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

09:35 08/06 2010

BMDL BMD

 

Exponential

 0

 1000

 2000

 3000

 4000

 5000

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Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

09:35 08/06 2010

BMDL BMD

 

Exponential
Page 26 of 61

 0

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dose

Exponential Model 4

09:35 08/06 2010

BMD

Exponential

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dose

Exponential Model 5

09:35 08/06 2010

BMD

Exponential
Page 27 of 61

________________________________________________________________

C.3. MORSETH SIX MONTH LH STUDY 

Model 

(Constant 

Variance)

BMD BMDL p-value AIC

Exponential 2 20.3 4.6 0.67 661.7

Exponential 3 20.3 Not Computed 0.67 661.7

Exponential 4 16.7 3.4 0.38 663.7

Exponential 5 3.9 3.7 N/A 664.5

Hill 4.2 3.3 0.58 663.2

Linear 26.2 16.3 0.61 661.9

Polynomial 20.6 12.9 0.05 666.9

Power 25.9 16.3 0.61 661.9

Model 

(Nonhomogeneous 

Variance)

BMD BMDL p-value AIC

Exponential 2 36.2 17.1 0.52 636.1

Exponential 3 36.2 17.1 0.52 636.1

Exponential 4 Not 

Computed

Not 

Computed

-- --

Exponential 5 Not 

Computed

Not 

Computed

-- --

Hill Not 

Computed

Not 

Computed

-- --

Linear 32.6 22.9 0.36 636.9

Polynomial 32.6 22.9 0.36 636.9

Power 32.6 22.9 0.36 636.9

Morseth 6 Month LH Study - Exponential (Constant Variance) Model Results

Warning: optimum may not have been found form model 2 (BMDL). Bad process 

completion in Optimization routine.
Page 28 of 61

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

== 

 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/exp_Actualruns_Setting.(d) 

 Gnuplot Plotting File: 

Thu Jul 29 13:57:08 2010

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

== 

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]))

 rho is set to 0.

 A constant variance model is fit.

 Total number of dose groups = 4

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 Relative Function Convergence has been set to: 1e-008

 Parameter Convergence has been set to: 1e-008

 MLE solution provided: Exact
Page 29 of 61

 Initial Parameter Values

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha 15.3723 15.3723 15.3723 15.3723

 rho(S) 0 0 0 0

 a 1497.19 1497.19 3812.55 3812.55

 b 0.0471466 0.0471466 0.14585 0.14585

 c -- -- 0.21433 0.21433

 d -- 1 -- 1

 (S) = Specified

 Parameter Estimates by Model

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha 15.3924 15.3924 15.3913 15.3746

 rho 0 0 0 0

 a 3458.46 3458.46 3544.45 3483.5

 b 0.0498021 0.0498021 0.0805078 0.262698

 c -- -- 0.16111 0.246304

 d -- 1 -- 18

 Table of Stats From Input Data

 Dose N Obs Mean Obs Std Dev

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

 0 10 3336 3138

 1.8 10 3631 2732

 3.65 10 2500 1897

 29.4 10 858 416

 Estimated Values of Interest

 Model Dose Est Mean Est Std Scaled Residual

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

 2 0 3458 2200 -0.176

 1.8 3162 2200 0.6743

 3.65 2884 2200 -0.5514

 29.4 799.8 2200 0.08362

 3 0 3458 2200 -0.176
Page 30 of 61

 1.8 3162 2200 0.6743

 3.65 2884 2200 -0.5514

 29.4 799.8 2200 0.08362

 4 0 3544 2199 -0.2998

 1.8 3143 2199 0.7014

 3.65 2787 2199 -0.4133

 29.4 849.9 2199 0.01171

 5 0 3484 2180 -0.2139

 1.8 3483 2180 0.2139

 3.65 2500 2180 -9.656e-007

 29.4 858 2180 2.459e-007

 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 -327.446 5 664.892

 A2 -313.3212 8 642.6425

 A3 -327.446 5 664.892

 R -331.828 2 667.6559

 2 -327.8484 3 661.6967

 3 -327.8484 3 661.6967

 4 -327.826 4 663.652

 5 -327.4918 5 664.9836

 Additive constant for all log-likelihoods = -36.76. This constant added to the

 above values gives the log-likelihood including the term that does not

 depend on the model parameters.
Page 31 of 61

 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 37.01 6 < 0.0001

 Test 2 28.25 3 < 0.0001

 Test 3 28.25 3 < 0.0001

 Test 4 0.8047 2 0.6687

 Test 5a 0.8047 2 0.6687

 Test 5b -1.137e-013 0 N/A

 Test 6a 0.7599 1 0.3833

 Test 6b 0.04476 1 0.8325

 Test 7a 0.09163 0 N/A

 Test 7b 0.7131 2 0.7001

 Test 7c 0.6683 1 0.4136

 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. Consider running

 a non-homogeneous variance model.

 The p-value for Test 3 is less than .1. You may want to

 consider a different variance model.
Page 32 of 61

 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.

 Degrees of freedom for Test 5b are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 The p-value for Test 6a is greater than .1. Model 4 seems

 to adequately describe the data.

 The p-value for Test 6b is greater than .05. Model 4 does

 not seem to fit the data better than Model 2.

 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.

 Benchmark Dose Computations:

 Specified Effect = 1.000000

 Risk Type = Estimated standard deviations from control

 Confidence Level = 0.950000

 BMD and BMDL by Model

 Model BMD BMDL

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

 2 20.2989 4.57536

 3 20.2989 Bad completion

 4 16.7073 3.43496

 5 3.92994 3.66097
Page 33 of 61

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dose

Exponential Model 2 with 0.95 Confidence Level

13:57 07/29 2010

BMDL BMD

 

Exponential

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Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

13:57 07/29 2010

BMDL BMD

 

Exponential
Page 34 of 61

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Exponential Model 4 with 0.95 Confidence Level

13:57 07/29 2010

BMDL BMD

 

Exponential

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dose

Exponential Model 5 with 0.95 Confidence Level

13:57 07/29 2010

BMDL BMD

 

Exponential
Page 35 of 61

Morseth 6 Month LH Study - Exponential (Nonhomogeneous Variance) Model 

Results

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

== 

 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/exp_Actualruns_Setting.(d) 

 Gnuplot Plotting File: 

Thu Jul 29 14:00:34 2010

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

== 

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 = 250

 Relative Function Convergence has been set to: 1e-008

 Parameter Convergence has been set to: 1e-008
Page 36 of 61

 MLE solution provided: Exact

 Initial Parameter Values

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha -6.65625 -6.65625 -6.65625 -6.65625

 rho 2.77485 2.77485 2.77485 2.77485

 a 1497.19 1497.19 3812.55 3812.55

 b 0.0471466 0.0471466 0.14585 0.14585

 c -- -- 0.21433 0.21433

 d -- 1 -- 1

 Parameter Estimates by Model

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha -7.30123 -7.30123 -7.07367 -6.96831

 rho 2.84795 2.84795 2.81591 2.80183

 a 3418.7 3418.7 3725.66 3553.63

 b 0.0471113 0.0471113 0.124728 0.213467

 c -- -- 0.210352 0.241407

 d -- 1 -- 2.9234

 NC = No Convergence

 Table of Stats From Input Data

 Dose N Obs Mean Obs Std Dev

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

 0 10 3336 3138

 1.8 10 3631 2732

 3.65 10 2500 1897

 29.4 10 858 416

 Estimated Values of Interest

 Model Dose Est Mean Est Std Scaled Residual

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

 2 0 3419 2797 -0.0935
Page 37 of 61

 1.8 3141 2479 0.6254

 3.65 2879 2190 -0.5468

 29.4 855.7 389.2 0.01852

 3 0 3419 2797 -0.0935

 1.8 3141 2479 0.6254

 3.65 2879 2190 -0.5468

 29.4 855.7 389.2 0.01852

 4 0 3726 3105 -0.3968

 1.8 3134 2434 0.6456

 3.65 2650 1922 -0.2464

 29.4 858.9 393.4 -0.007039

 5 0 3554 2891 -0.2381

 1.8 3394 2711 0.2765

 3.65 2522 1789 -0.03959

 29.4 857.9 394.8 0.001045

 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 -327.446 5 664.892

 A2 -313.3212 8 642.6425

 A3 -313.4172 6 638.8345

 R -331.828 2 667.6559

 2 -314.0727 4 636.1453

 3 -314.0727 4 636.1453

 4 -313.7385 5 637.477

 5 -313.4172 6 638.8345
Page 38 of 61

 Additive constant for all log-likelihoods = -36.76. This constant added to the

 above values gives the log-likelihood including the term that does not

 depend on the model parameters.

 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 37.01 6 < 0.0001

 Test 2 28.25 3 < 0.0001

 Test 3 0.192 2 0.9084

 Test 4 1.311 2 0.5192

 Test 5a 1.311 2 0.5192

 Test 5b -1.137e-013 0 N/A

 Test 6a 0.6425 1 0.4228

 Test 6b 0.6683 1 0.4136

 Test 7a -1.137e-013 0 N/A

 Test 7b 1.311 2 0.5192

 Test 7c 0.6425 1 0.4228

 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
Page 39 of 61

 variance model appears to be appropriate.

 The p-value for Test 3 is greater than .1. The modeled

 variance appears to be appropriate here.

 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.

 Degrees of freedom for Test 5b are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 The p-value for Test 6a is greater than .1. Model 4 seems

 to adequately describe the data.

 The p-value for Test 6b is greater than .05. Model 4 does

 not seem to fit the data better than Model 2.

 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.

 Benchmark Dose Computations:

 Specified Effect = 1.000000

 Risk Type = Estimated standard deviations from control

 Confidence Level = 0.950000

 BMD and BMDL by Model

 Model BMD BMDL

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

 2 36.1811 17.0918

 3 36.1811 17.0918

 4 0 0 Not computed
Page 40 of 61

 5 0 0 Not computed

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Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

14:00 07/29 2010

BMDL BMD

 

Exponential
Page 41 of 61

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dose

Exponential Model 3 with 0.95 Confidence Level

14:00 07/29 2010

BMDL BMD

 

Exponential
Page 42 of 61

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Exponential Model 4

14:00 07/29 2010

BMD

Exponential
Page 43 of 61

________________________________________________________________

C.4. MINNEMA ONE MONTH LH STUDY 

Model 

(Constant 

Variance)

BMD BMDL p-value AIC

Exponential 2 653.3 245.1 0.40 274.6

Exponential 3 653.3 245.1 0.40 274.6

Exponential 4 Not Computed Not Computed -- --

Exponential 5 Not Computed Not Computed -- --

Hill Not Computed Not Computed -- --

Linear 500.8 240.7 0.38 274.7

Polynomial 500.8 239.9 0.38 274.7

Power 500.8 240.7 0.38 274.7

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dose

Exponential Model 5

14:00 07/29 2010

BMD

Exponential
Page 44 of 61

Minnema One Month LH Study - Exponential (Constant Variance) Model Results

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

== 

 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/exp_Actualruns_Setting.(d) 

 Gnuplot Plotting File: 

Fri Jul 23 08:35:00 2010

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

== 

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]))

 rho is set to 0.

 A constant variance model is fit.

 Total number of dose groups = 5

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 Relative Function Convergence has been set to: 1e-008
Page 45 of 61

 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 1.65681 1.65681 1.65681 1.65681

 rho(S) 0 0 0 0

 a 3.0427 3.0427 4.305 4.305

 b 0.00143069 0.00143069 0.0127345 0.0127345

 c -- -- 0.588463 0.588463

 d -- 1 -- 1

 (S) = Specified

 Parameter Estimates by Model

 Variable Model 2 Model 3 Model 4 Model 5

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

 lnalpha 1.68618 1.68618 1.65872 1.65872

 rho 0 0 0 0

 a 3.55899 3.55899 4.04195 4.04195

 b 0.00161956 0.00161956 0.128035 0.128035

 c -- -- 0.669638 0.669638

 d -- 1 -- 1

 NC = No Convergence

 Table of Stats From Input Data

 Dose N Obs Mean Obs Std Dev

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

 0 20 4.1 2.52

 2.5 20 3.51 2.41

 5 20 3.53 2.57

 40 20 2.66 1.71

 200 20 2.75 2.43

 Estimated Values of Interest
Page 46 of 61

 Model Dose Est Mean Est Std Scaled Residual

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

 2 0 3.559 2.324 1.041

 2.5 3.545 2.324 -0.06662

 5 3.53 2.324 -0.0005584

 40 3.336 2.324 -1.301

 200 2.574 2.324 0.3382

 3 0 3.559 2.324 1.041

 2.5 3.545 2.324 -0.06662

 5 3.53 2.324 -0.0005584

 40 3.336 2.324 -1.301

 200 2.574 2.324 0.3382

 4 0 4.042 2.292 0.1133

 2.5 3.676 2.292 -0.3243

 5 3.411 2.292 0.233

 40 2.715 2.292 -0.1066

 200 2.707 2.292 0.08461

 5 0 4.042 2.292 0.1133

 2.5 3.676 2.292 -0.3243

 5 3.411 2.292 0.233

 40 2.715 2.292 -0.1066

 200 2.707 2.292 0.08461

 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 -132.8405 6 277.6809
Page 47 of 61

 A2 -130.8789 10 281.7577

 A3 -132.8405 6 277.6809

 R -135.53 2 275.0599

 2 -134.3092 3 274.6183

 3 -134.3092 3 274.6183

 4 -132.9359 4 273.8719

 5 -132.9359 4 273.8719

 Additive constant for all log-likelihoods = -91.89. This constant added to the

 above values gives the log-likelihood including the term that does not

 depend on the model parameters.

 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 9.302 8 0.3174

 Test 2 3.923 4 0.4165

 Test 3 3.923 4 0.4165

 Test 4 2.937 3 0.4014

 Test 5a 2.937 3 0.4014

 Test 5b 0 0 N/A

 Test 6a 0.191 2 0.9089

 Test 6b 2.746 1 0.09747

 Test 7a 0.191 2 0.9089

 Test 7b 2.746 1 0.09747
Page 48 of 61

 Test 7c 2.274e-013 0 N/A

 The p-value for Test 1 is greater than .05. There may not be a

 diffence between responses and/or variances among the dose levels

 Modelling the data with a dose/response curve may not be appropriate.

 The p-value for Test 2 is greater than .1. A homogeneous

 variance model appears to be appropriate here.

 The p-value for Test 3 is greater than .1. The modeled

 variance appears to be appropriate here.

 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.

 Degrees of freedom for Test 5b are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 The p-value for Test 6a is greater than .1. Model 4 seems

 to adequately describe the data.

 The p-value for Test 6b is greater than .05. Model 4 does

 not seem to fit the data better than Model 2.

 The p-value for Test 7a is greater than .1. Model 5 seems

 to adequately describe the data.

 The p-value for Test 7b is greater than .05. Model 5 does

 not seem to fit the data better than Model 3.

 Degrees of freedom for Test 7c are less than or equal to 0.

 The Chi-Square test for fit is not valid.

 Benchmark Dose Computations:

 Specified Effect = 1.000000

 Risk Type = Estimated standard deviations from control

 Confidence Level = 0.950000
Page 49 of 61

 BMD and BMDL by Model

 Model BMD BMDL

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

 2 653.287 245.122

 3 653.287 245.122

 4 0 0 Not computed

 5 0 0 Not computed

 1

 1.5

 2

 2.5

 3

 3.5

 4

 4.5

 5

 5.5

 0 100 200 300 400 500 600

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

08:35 07/23 2010

BMDL BMD

 

Exponential
Page 50 of 61

 1

 1.5

 2

 2.5

 3

 3.5

 4

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 5

 5.5

 0 100 200 300 400 500 600

Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

08:35 07/23 2010

BMDL BMD

 

Exponential

 1.5

 2

 2.5

 3

 3.5

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 0 50 100 150 200

Mean Response

dose

Exponential Model 4

08:35 07/23 2010

BMD

Exponential
Page 51 of 61

C.5 BMD OUTPUT SUMMARIES – AUC

1. AUC for Steady State Serum Levels of Total Triazine Equivalents

Model 

(Constant 

Variance)

BMD BMDL p-value AIC

Exponential 2 6.73 3.66 0.25 407.8

Exponential 3 6.73 3.66 0.25 407.8

Exponential 4 2.19 0.82 0.89 405.1

Exponential 5 2.19 0.82 0.89 405.1

Hill 2.08 0.65 0.92 404.9

Linear 9.91 7.00 0.10 410.1

Polynomial 9.91 7.00 0.10 410.1

Power 9.91 7.00 0.10 410.1

 1.5

 2

 2.5

 3

 3.5

 4

 4.5

 5

 5.5

 0 50 100 150 200

Mean Response

dose

Exponential Model 5

08:35 07/23 2010

BMD

Exponential
Page 52 of 61

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

== 

 Hill Model. (Version: 2.15; Date: 10/28/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/hil_Actualruns_Opt.(d) 

 Gnuplot Plotting File: C:/Usepa/BMDS212/Data/hil_Actualruns_Opt.plt

Fri Jul 30 12:15:38 2010

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

== 

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

 rho is set to 0

 Power parameter restricted to be greater than 1

 A constant variance model is fit

 Total number of dose groups = 6

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 Relative Function Convergence has been set to: 1e-008

 Parameter Convergence has been set to: 1e-008

 Default Initial Parameter Values 

 alpha = 68.6432

 rho = 0 Specified

 intercept = 21.848

 v = -13.348

 n = 1.1704

 k = 1.67918

 Asymptotic Correlation Matrix of Parameter Estimates
Page 53 of 61

 ( *** The model parameter(s) -rho -n 

 have been estimated at a boundary point, or have been specified by the user,

 and do not appear in the correlation matrix )

 alpha intercept v k

 alpha 1 2.4e-009 1.1e-008 -2.1e-008

intercept 2.4e-009 1 -0.37 -0.52

 v 1.1e-008 -0.37 1 -0.48

 k -2.1e-008 -0.52 -0.48 1

 Parameter Estimates

 95.0% Wald Confidence Interval

 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit

 alpha 63.7164 10.2688 43.5899 83.843

 intercept 21.819 1.88733 18.1199 25.5181

 v -14.7403 3.24361 -21.0977 -8.38296

 n 1 NA

 k 1.76071 1.38154 -0.947057 4.46847

NA - Indicates that this parameter has hit a bound

 implied by some inequality constraint and thus

 has no standard error.

 Table of Data and Estimated Values of Interest

Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res.

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

 0 16 21.8 21.8 7 7.98 0.0145

0.4545 11 18.6 18.8 10.8 7.98 -0.0933

1.331 12 16 15.5 9.3 7.98 0.248

3.024 17 11.8 12.5 7 7.98 -0.358

6.406 7 11.9 10.3 9 7.98 0.538

13.17 14 8.5 8.82 7.6 7.98 -0.149
Page 54 of 61

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)} = Sigma^2

 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 -198.190188 7 410.380377

 A2 -196.288688 12 416.577376

 A3 -198.190188 7 410.380377

 fitted -198.446043 4 404.892085

 R -209.919649 2 423.839298

 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 27.2619 10 0.002367

 Test 2 3.803 5 0.5781

 Test 3 3.803 5 0.5781

 Test 4 0.511709 3 0.9163
Page 55 of 61

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 greater than .1. A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1. The modeled variance appears 

to be appropriate here

The p-value for Test 4 is greater than .1. The model chosen seems 

to adequately describe the data

 Benchmark Dose Computation

Specified effect = 1

Risk Type = Estimated standard deviations from the control mean 

Confidence level = 0.95

 BMD = 2.07966

 BMDL = 0.64721
Page 56 of 61

C.6. PREDICTED DAILY STEADY STATE SERUM AUC

Model 

(Constant 

Variance)

BMD BMDL p-value AIC

Exponential 2 161.7 88.0 0.25 407.8

Exponential 3 161.7 88.0 0.25 407.8

Exponential 4 52.5 19.8 0.87 405.1

Exponential 5 52.5 19.8 0.87 405.1

Hill 49.9 15.6 0.92 404.9

Linear 238.2 168.2 0.10 410.1

Polynomial 238.2 168.2 0.10 410.1

Power 238.2 168.2 0.10 410.1

 5

 10

 15

 20

 25

 0 2 4 6 8 10 12

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:15 07/30 2010

BMDL BMD

 

Hill
Page 57 of 61

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

== 

 Hill Model. (Version: 2.15; Date: 10/28/2009) 

 Input Data File: C:/Usepa/BMDS212/Data/hil_Actualruns_Opt.(d) 

 Gnuplot Plotting File: C:/Usepa/BMDS212/Data/hil_Actualruns_Opt.plt

Fri Jul 30 12:45:13 2010

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

== 

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

 rho is set to 0

 Power parameter restricted to be greater than 1

 A constant variance model is fit

 Total number of dose groups = 6

 Total number of records with missing values = 0

 Maximum number of iterations = 250

 Relative Function Convergence has been set to: 1e-008

 Parameter Convergence has been set to: 1e-008

 Default Initial Parameter Values 

 alpha = 68.6432

 rho = 0 Specified

 intercept = 21.848

 v = -13.348

 n = 1.17066

 k = 40.3586

 Asymptotic Correlation Matrix of Parameter Estimates

 ( *** The model parameter(s) -rho -n 
Page 58 of 61

 have been estimated at a boundary point, or have been specified by the user,

 and do not appear in the correlation matrix )

 alpha intercept v k

 alpha 1 8.8e-010 9.7e-009 -1.9e-008

intercept 8.8e-010 1 -0.37 -0.52

 v 9.7e-009 -0.37 1 -0.48

 k -1.9e-008 -0.52 -0.48 1

 Parameter Estimates

 95.0% Wald Confidence Interval

 Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit

 alpha 63.7164 10.2688 43.5899 83.8429

 intercept 21.8193 1.88737 18.1201 25.5185

 v -14.7416 3.24394 -21.0996 -8.38356

 n 1 NA

 k 42.3243 33.205 -22.7563 107.405

NA - Indicates that this parameter has hit a bound

 implied by some inequality constraint and thus

 has no standard error.

 Table of Data and Estimated Values of Interest

Dose N Obs Mean Est Mean Obs Std Dev Est Std Dev Scaled Res.

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

 0 16 21.8 21.8 7 7.98 0.0144

10.93 11 18.6 18.8 10.8 7.98 -0.093

31.99 12 16 15.5 9.3 7.98 0.248

72.68 17 11.8 12.5 7 7.98 -0.358

153.9 7 11.9 10.3 9 7.98 0.538

316.4 14 8.5 8.82 7.6 7.98 -0.149

Model Descriptions for likelihoods calculated
Page 59 of 61

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)} = Sigma^2

 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 -198.190188 7 410.380377

 A2 -196.288688 12 416.577376

 A3 -198.190188 7 410.380377

 fitted -198.446021 4 404.892043

 R -209.919649 2 423.839298

 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 27.2619 10 0.002367

 Test 2 3.803 5 0.5781

 Test 3 3.803 5 0.5781

 Test 4 0.511666 3 0.9163

The p-value for Test 1 is less than .05. There appears to be a
Page 60 of 61

difference between response and/or variances among the dose levels

It seems appropriate to model the data

The p-value for Test 2 is greater than .1. A homogeneous variance 

model appears to be appropriate here

The p-value for Test 3 is greater than .1. The modeled variance appears 

to be appropriate here

The p-value for Test 4 is greater than .1. The model chosen seems 

to adequately describe the data

 Benchmark Dose Computation

Specified effect = 1

Risk Type = Estimated standard deviations from the control mean 

Confidence level = 0.95

 BMD = 49.9819

 BMDL = 15.5588
Page 61 of 61

 5

 10

 15

 20

 25

 0 50 100 150 200 250 300

Mean Response

dose

Hill Model with 0.95 Confidence Level

12:45 07/30 2010

BMDL BMD

 

Hill