### DDVP Dog ‐ Week 13 ‐ RBC ChE ‐ Males

!!! Warning: optimum may not have been found for Model 3 !!! !!! Bad completion code in maximum likelihood optimization routine !!! !!! Try choosing different initial values !!!

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

==================================================================== Exponential Model. (Version: 1.7; Date: 12/10/2009) Input Data File: C:/Users/jliccion/Desktop/BMDS230/Data/exp_TestContinuous1_Setting.(d) Gnuplot Plotting File: Wed May 21 08:50:32 2014

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BMDS Model Run

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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 -2.49317 -2.49317 -2.49317 -2.49317 rho 1.26471 1.26471 1.26471 1.26471 a 2.18125 2.18125 11.025 11.025 b 0.725302 0.725302 0.987842 0.987842c -- -- 0.0498866 0.0498866 d -- 1 -- 1

Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha -2.81358 -2.49317 -2.89959 -2.89959 rho 1.48629 1.26471 1.50238 1.50238 a 9.58653 2.18125 9.75821 9.75821 b 0.737282 0.725302 0.886149 0.886149 c -- -- 0.0456694 0.0456694 d -- 1 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 4 10.5 1.03 0.05 4 8.6 1.24 1 4 4.3 0.88 3 4 1.1 0.28

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 9.587 1.314 1.39 0.05 9.24 1.278 -1.001 1 4.586 0.7596 -0.7538 3 1.05 0.2539 0.3961 3 0 0 0 1.#IO 0.05 0 0 1.#IO 1 0 0 1.#IO 3 0 0 1.#IO 4 0 9.758 1.299 1.142 0.05 9.355 1.258 -1.199 1 4.285 0.6999 0.04382 3 1.098 0.2517 0.0154 5 0 9.758 1.299 1.142 0.05 9.355 1.258 -1.199 1 4.285 0.6999 0.04382 3 1.098 0.2517 0.0154

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 -4.518196 5 19.03639 A2 -1.074028 8 18.14806 A3 -1.460796 6 14.92159 R -29.1745 2 62.349 2 -3.491692 4 14.98338 3 -1383.73 4 2775.46 4 -3.019846 5 16.03969 5 -3.019846 5 16.03969

Additive constant for all log-likelihoods = -14.7. 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 56.2 6 < 0.0001 Test 2 6.888 3 0.07554 Test 3 0.7735 2 0.6792 Test 4 4.062 2 0.1312 Test 5a 2765 2 < 0.0001 Test 5b -2760 0 N/A Test 6a 3.118 1 0.07743 Test 6b 0.9437 1 0.3313 Test 7a 3.118 1 0.07743 Test 7b 2761 1 < 0.0001 Test 7c 8.882e-016 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 greater than .1. Model 2 seems to adequately describe the data.

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 greater than .05. Model 4 does not seem 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 0.142904 0.126238 3 0.145264 Bad completion 4 0.124913 0.100868 5 0.124913 0.1008680 2 4 6 8 10 12

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 2 with 0.95 Confidence Level

08:50 05/21 2014 BMD BMDL Exponential0 2 4 6 8 10 12

-1 -0.5 0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 3 with 0.95 Confidence Level

08:50 05/21 2014 BMD BMDL Exponential0 2 4 6 8 10 12

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 4 with 0.95 Confidence Level

08:50 05/21 2014 BMD BMDL Exponential0 2 4 6 8 10 12

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 5 with 0.95 Confidence Level

08:50 05/21 2014 BMD BMDL Exponential