==================================================================== Exponential Model. (Version: 1.9; Date: 01/29/2013) Input Data File: C:/USEPA/BMDS240/Data/exp_Ray 14wksubC in rats - 49d RBC M_Setting.(d) Gnuplot Plotting File: Sun May 25 17:54:13 2014

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BMDS Model Run - Rat 98d subchronic - 49d Mrat RBC

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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 -2.98213 -2.98213 -2.98213 -2.98213
rho 1.91103 1.91103 1.91103 1.91103
a 803.413 803.413 1254.75 1254.75
b 0.0386515 0.0386515 0.208832 0.208832
c -- -- 0.477424
0.477424 d -- 1 -- 1

Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5-------- ------- ------- ------- ------- lnalpha -6.33806 -6.33806 -4.07553 -4.25438
rho 2.42906 2.42906 2.06272 2.08851
a 1111.36 1111.36 1195.44 1183.41 b 0.0386655 0.0386655 0.493411 0.561031
c -- -- 0.526705 0.532594 d -- 1 -- 1.87706

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 10 1195 163.1
0.1 10 1166 244.3
1.5 10 903 138
15 10 629 109.3

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 1111 210.4 1.257
0.1 1107 209.4 0.89
1.5 1049 196.1 -2.351
15 622.3 104 0.2049
3 0 1111 210.4 1.257
0.1 1107 209.4 0.89
1.5 1049 196.1 -2.351
15 622.3 104 0.2049
4 0 1195 194.6 -0.007155
0.1 1168 190 -0.03663
1.5 899.6 145.1 0.07492
15 630 100.5 -0.03115
5 0 1183 192.9 0.19
0.1 1181 192.5 -0.2454
1.5 898.6 144.7 0.09594
15 630.3 99.91 -0.04048

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 -223.6124 5 457.2247
A2 -220.0339 8 456.0678
A3 -221.0093 6 454.0186
R -245.5007 2 495.0014
2 -226.1592 4 460.3184
3 -226.1592 4 460.3184
4 -221.0528 5 452.1056
5 -221.0093 6 454.0186

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 50.93 6 < 0.0001
Test 2 7.157 3 0.06706
Test 3 1.951 2 0.377
Test 4 10.3 2 0.0058
Test 5a 10.3 2 0.0058 Test 5b -2.217e-012 0 N/A
Test 6a 0.08697 1 0.7681 Test 6b 10.21 1 0.001395 Test 7a -2.842e-013 0 N/A
Test 7b 10.3 2 0.0058
Test 7c 0.08697 1 0.7681

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 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.

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 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 = 0.100000

Risk Type = Relative deviation

Confidence Level = 0.950000

BMD and BMDL by Model

Model BMD BMDL

------- ------------ ---------- 2 2.72492 2.25722
3 2.72493 2.25722
4 0.481039 0.318256
5 0.834692 0.3202585006007008009001000110012001300140002468101214

Mean ResponsedoseExponential Model 2, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL17:54 05/25 2014BMDBMDLExponential5006007008009001000110012001300140002468101214

Mean ResponsedoseExponential Model 3, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL17:54 05/25 2014BMDBMDLExponential5006007008009001000110012001300140002468101214

Mean ResponsedoseExponential Model 4, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL17:54 05/25 2014BMDBMDLExponential5006007008009001000110012001300140002468101214

Mean ResponsedoseExponential Model 5, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL17:54 05/25 2014BMDBMDLExponential