==================================================================== 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 M_Setting.(d) Gnuplot Plotting File: Wed May 28 08:52:40 2014

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BMDS Model Run - 13 week rat subchronic oral - 13 wk RBC ChE - male

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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 -0.449995 -0.449995 -0.449995 - 0.449995 rho 1.38856 1.38856 1.38856 1.38856 a 950.763 950.763 1425.9 1425.9 b 0.0303067 0.0303067 0.197284 0.197284 c -- -- 0.52565 0.52565 d -- 1 -- 1Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha 21.1723 -5.08112 -0.646221 -0.646219 rho -1.62778 2.14617 1.42776 1.42776 a 1299.58 1228.63 1321.27 1321.27 b 0.135299 0.0305362 0.604089 0.604089 c -- -- 0.59785 0.59785 d -- 1 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 10 1358 145.5 0.1 10 1247 113.9 1.5 10 1014 62.6 15 10 787 103.6

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 1300 115.7 1.597 0.1 1282 117 -0.9496 1.5 1061 136.4 -1.086 15 170.8 603.4 3.23 3 0 1229 162.9 2.512 0.1 1225 162.3 0.4307 1.5 1174 155.1 -3.255 15 777.1 99.63 0.3131 4 0 1321 122.4 0.9493 0.1 1290 120.3 -1.133 1.5 1005 100.6 0.2945 15 790 84.77 -0.1112 5 0 1321 122.4 0.9493 0.1 1290 120.3 -1.133 1.5 1005 100.6 0.2945 15 790 84.77 -0.1112

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^2Likelihoods of Interest

Model Log(likelihood) DF AIC

------- ----------------- ---- ------------ A1 -206.0746 5 422.1493 A2 -202.8208 8 421.6416 A3 -205.2366 6 422.4733 R -239.8279 2 483.6558 2 -228.3096 4 464.6192 3 -218.28 4 444.5599 4 -206.4856 5 422.9712 5 -206.4856 5 422.9712

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 74.01 6 < 0.0001 Test 2 6.508 3 0.08936 Test 3 4.832 2 0.08929 Test 4 46.15 2 < 0.0001 Test 5a 26.09 2 < 0.0001 Test 5b 20.06 0 N/A Test 6a 2.498 1 0.114 Test 6b 43.65 1 < 0.0001 Test 7a 2.498 1 0.114 Test 7b 23.59 1 < 0.0001 Test 7c -2.274e-013 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 less than .1. A non-homogeneousvariance 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 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.

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.

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 0.778721 0.502764 3 3.45035 2.86896 4 0.473278 0.344679 5 0.473278 0.34467970080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 2 with 0.95 Confidence Level08:52 05/28 2014BMDBMDLExponential70080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 3 with 0.95 Confidence Level08:52 05/28 2014BMDBMDLExponential70080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 4 with 0.95 Confidence Level08:52 05/28 2014BMDBMDLExponential70080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 5 with 0.95 Confidence Level08:52 05/28 2014BMDBMDLExponential