==================================================================== Exponential Model. (Version: 1.7; Date: 12/10/2009) Input Data File: E:/Travel Drive/DDVP 2013 relook/BMD runs/exp_Ray 14wksubC in rats - 98d RBC F_Setting.(d) Gnuplot Plotting File: Wed May 28 08:27:34 2014

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BMDS Model Run - 13 wk rat subchronic oral - RBC ChE 13 wk timepoint - females

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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 = 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 10.4561 10.4561 10.4561 10.4561 rho -0.231556 -0.231556 -0.231556 -0.231556 a 989.399 989.399 1387.05 1387.05 b 0.0211873 0.0211873 0.178924 0.178924 c -- -- 0.600109 0.600109 d -- 1 -- 1

Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- -------lnalpha -12.9671 -12.9671 6.19442 6.19442 rho 3.23055 3.23055 0.378775 0.378775 a 1188.8 1188.8 1283.36 1283.36 b 0.0211091 0.0211091 0.826498 0.826498 c -- -- 0.682991 0.682991 d -- 1 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 9 1321 82.3 0.1 10 1212 81.4 1.5 10 1002 81.5 15 10 874 86.8

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 1189 141.7 2.799 0.1 1186 141.2 0.5756 1.5 1152 134.6 -3.517 15 866.2 84.97 0.292 3 0 1189 141.7 2.799 0.1 1186 141.2 0.5756 1.5 1152 134.6 -3.517 15 866.2 84.97 0.292 4 0 1283 85.86 1.315 0.1 1251 85.45 -1.447 1.5 994.3 81.81 0.2983 15 876.5 79.88 -0.09989 5 0 1283 85.86 1.315 0.1 1251 85.45 -1.447 1.5 994.3 81.81 0.2983 15 876.5 79.88 -0.09989

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 -189.7483 5 389.4967 A2 -189.7188 8 395.4375 A3 -189.7308 6 391.4616 R -224.2014 2 452.4028 2 -207.0351 4 422.0702 3 -207.0351 4 422.0702 4 -191.9016 5 393.8033 5 -191.9016 5 393.8033

Additive constant for all log-likelihoods = -35.84. 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 68.97 6 < 0.0001 Test 2 0.05915 3 0.9962 Test 3 0.02412 2 0.988 Test 4 34.61 2 < 0.0001 Test 5a 34.61 2 < 0.0001 Test 5b -3.524e-012 0 N/A Test 6a 4.342 1 0.03719 Test 6b 30.27 1 < 0.0001 Test 7a 4.342 1 0.03719 Test 7b 30.27 1 < 0.0001 Test 7c -5.684e-014 0 N/A

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. Consider running a homogeneous model.

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 less than .1. Model 4 may not adequately describe the data; you may want to consider another model.

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 less than .1. Model 5 may not adequately describe the data; you may want to consider another model.

The p-value for Test 7b is less than .05. Model 5 appears 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 = 0.100000

Risk Type = Relative deviation

Confidence Level = 0.950000

BMD and BMDL by Model

Model BMD BMDL

------- ------------ ---------- 2 4.99124 4.05236 3 4.99124 4.05236 4 0.45855 0.294963 5 0.45855 0.2949638009001000110012001300140002468101214

Mean ResponsedoseExponential Model 2 with 0.95 Confidence Level08:31 05/28 2014BMDBMDLExponential8009001000110012001300140002468101214

Mean ResponsedoseExponential Model 3 with 0.95 Confidence Level08:31 05/28 2014BMDBMDLExponential8009001000110012001300140002468101214

Mean ResponsedoseExponential Model 4 with 0.95 Confidence Level08:32 05/28 2014BMDBMDLExponential8009001000110012001300140002468101214

Mean ResponsedoseExponential Model 5 with 0.95 Confidence Level08:32 05/28 2014BMDBMDLExponential