==================================================================== Exponential Model. (Version: 1.9; Date: 01/29/2013) Input Data File: C:/USEPA/BMDS240/Data/exp_Ray 14wksubC in rats - 49d RBC F_Setting.(d) Gnuplot Plotting File: Sun May 25 18:44:34 2014

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BMDS Model Run - 14-weekrat subchronic - 49d RBC - F

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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 -9.23222 -9.23222 -9.23222 -9.23222
rho 2.77278 2.77278 2.77278 2.77278
a 883.974 883.974 1332.45 1332.45
b 0.0293556 0.0293556 0.196282 0.196282
c -- -- 0.528922
0.528922
d -- 1 -- 1

Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha -15.8632 -18.1029 -10.7812 -10.7812rho 3.76844 4.104 2.99811 2.99811
a 1136.48 1119.34 1219.82 1219.82
b 0.0290037 0.0633046 0.541102 0.541102
c -- -- 0.606671 0.606671
d -- 17.0491 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 9 1269 246.9
0.1 10 1148 125.9
1.5 10 956 145.8
15 10 740 95.4

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 1136 205.5 1.935
0.1 1133 204.3 0.2293
1.5 1088 189.3 -2.207
15 735.6 90.51 0.1551
3 0 1119 211.6 2.122
0.1 1119 211.6 0.4283
1.5 1119 211.6 -2.441
15 740 90.5 -4.415e-007
4 0 1220 192.9 0.7648
0.1 1195 187 -0.7872
1.5 953.1 133.3 0.06851
15 740.2 91.24 -0.0059
5 0 1220 192.9 0.7648
0.1 1195 187 -0.7872
1.5 953.1 133.3 0.06851
15 740.2 91.24 -0.0059

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 -215.4855 5 440.9711
A2 -210.7284 8 437.4569
A3 -211.9577 6 435.9155R -234.9383 2 473.8767
2 -218.1116 4 444.2231
3 -219.8378 5 449.6757
4 -213.2307 5 436.4614
5 -213.2307 5 436.4614

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 48.42 6 < 0.0001
Test 2 9.514 3 0.02318
Test 3 2.459 2 0.2925
Test 4 12.31 2 0.002125
Test 5a 15.76 1 < 0.0001 Test 5b -3.453 1 N/A
Test 6a 2.546 1 0.1106
Test 6b 9.762 1 0.001782
Test 7a 2.546 1 0.1106 Test 7b 13.21 0 N/A Test 7c 7.958e-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-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.The p-value for Test 5b is less than .05. Model 3 appears 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.

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.

Degrees of freedom for Test 7b are less than or equal to 0. The Chi-Square test for fit is not valid.

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 3.63266 2.99039
3 13.8433 2.68977
4 0.542138 0.343598
5 0.542138 0.34359860070080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 2, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL18:44 05/25 2014BMDBMDLExponential60070080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 3, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL18:44 05/25 2014BMDBMDLExponential60070080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 4, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL18:44 05/25 2014BMDBMDLExponential60070080090010001100120013001400150002468101214

Mean ResponsedoseExponential Model 5, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL18:44 05/25 2014BMDBMDLExponential