### DDVP Dog ‐ Week 52 ‐ RBC ChE

– Males

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 09:58:16 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 -1.87114 -1.87114 -1.87114 -1.87114 rho 1.12058 1.12058 1.12058 1.12058 a 2.43323 2.43323 11.34 11.34 b 0.69011 0.69011 0.948193 0.948193 c -- -- 0.0573192 0.0573192 d -- 1 -- 1Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha -1.77348 -1.87114 -2.20608 -2.20608 rho 1.05211 1.12058 1.19831 1.19831 a 10.1386 2.43323 10.4076 10.4076 b 0.734019 0.69011 1.03775 1.03775 c -- -- 0.0850058 0.0850058 d -- 1 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 4 10.8 1.31 0.05 4 9.5 1.69 1 4 4.3 0.8 3 4 1.3 0.47

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 10.14 1.393 0.9493 0.05 9.773 1.367 -0.3998 1 4.866 0.9471 -1.196 3 1.121 0.4375 0.8179 3 0 0 0 1.#IO 0.05 0 0 1.#IO 1 0 0 1.#IO 3 0 0 1.#IO 4 0 10.41 1.351 0.5811 0.05 9.926 1.313 -0.6492 1 4.258 0.7906 0.1057 3 1.308 0.3898 -0.04134 5 0 10.41 1.351 0.5811 0.05 9.926 1.313 -0.6492 1 4.258 0.7906 0.1057 3 1.308 0.3898 -0.04134

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 InterestModel Log(likelihood) DF AIC

------- ----------------- ---- ------------ A1 -8.148268 5 26.29654 A2 -4.964902 8 25.9298 A3 -5.241243 6 22.48249 R -30.11069 2 64.22139 2 -7.053267 4 22.10653 3 -753.94 4 1515.88 4 -5.582085 5 21.16417 5 -5.582085 5 21.16417

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 50.29 6 < 0.0001 Test 2 6.367 3 0.09507 Test 3 0.5527 2 0.7586 Test 4 3.624 2 0.1633 Test 5a 1497 2 < 0.0001 Test 5b -1494 0 N/A Test 6a 0.6817 1 0.409 Test 6b 2.942 1 0.08628 Test 7a 0.6817 1 0.409 Test 7b 1497 1 < 0.0001 Test 7c -3.499e-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 greater than .1. Model 2 seemsto 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 greater than .1. Model 4 seems to adequately describe the data.

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 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 0.143539 0.116788 3 0.152672 Bad completion 4 0.111526 0.0887295 5 0.111526 0.08872950 2 4 6 8 10 12 14

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 2 with 0.95 Confidence Level

09:58 05/21 2014 BMD BMDL Exponential0 2 4 6 8 10 12 14

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

dose Exponential Model 3 with 0.95 Confidence Level

09:58 05/21 2014 BMD BMDL Exponential0 2 4 6 8 10 12 14

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 4 with 0.95 Confidence Level

09:58 05/21 2014 BMD BMDL Exponential0 2 4 6 8 10 12 14

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 5 with 0.95 Confidence Level

09:58 05/21 2014 BMD BMDL Exponential