### DDVP Dog ‐ Week 53 ‐ Brain ChE ‐ Females

==================================================================== 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 09:48:22 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])) rho is set to 0. A constant variance model is fit.

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 0.016599 0.016599 0.016599 0.016599 rho(S) 0 0 0 0 a 6.82735 6.82735 9.45 9.45 b 0.126461 0.126461 0.257422 0.257422 c -- -- 0.31746 0.31746 d -- 1 -- 1

(S) = Specified

Parameter Estimates by ModelVariable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha 0.0586711 0.0498116 0.0586712 0.0468717 rho 0 0 0 0 a 8.81087 8.75022 8.81087 8.75 b 0.124837 0.150749 0.124837 0.846488 c -- -- 0 0.685714 d -- 1.22428 -- 5.96991

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 4 8.5 1.73 0.05 4 9 0.94 1 4 7.9 1.06 3 4 6 0.65

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 8.811 1.03 -0.6038 0.05 8.756 1.03 0.4738 1 7.777 1.03 0.2392 3 6.059 1.03 -0.1138 3 0 8.75 1.025 -0.4881 0.05 8.728 1.025 0.5302 1 7.928 1.025 -0.05555 3 5.993 1.025 0.01401 4 0 8.811 1.03 -0.6038 0.05 8.756 1.03 0.4738 1 7.777 1.03 0.2392 3 6.059 1.03 -0.1138 5 0 8.75 1.024 -0.4884 0.05 8.75 1.024 0.4884 1 7.9 1.024 -4.34e-007 3 6 1.024 1.852e-007

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 -8.132792 5 26.26558 A2 -6.153471 8 28.30694 A3 -8.132792 5 26.26558 R -14.69534 2 33.39068 2 -8.469369 3 22.93874 3 -8.398492 4 24.79698 4 -8.469369 3 22.93874 5 -8.374973 5 26.74995

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 17.08 6 0.00898 Test 2 3.959 3 0.266 Test 3 3.959 3 0.266 Test 4 0.6732 2 0.7142 Test 5a 0.5314 1 0.466 Test 5b 0.1418 1 0.7065 Test 6a 0.6732 2 0.7142 Test 6b -1.137e-013 0 N/A Test 7a 0.4844 0 N/A Test 7b 0.04704 1 0.8283 Test 7c 0.1888 2 0.9099

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. A homogeneous variance model appears to be appropriate here.

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 greater than .1. Model 3 seems to adequately describe the data.

The p-value for Test 5b is greater than .05. Model 3 does not seem 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.

Degrees of freedom for Test 6b are less than or equal to 0. The Chi-Square test for fit is not valid.

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

The p-value for Test 7b is greater than .05. Model 5 does not seem to fit the data better than Model 3.

The p-value for Test 7c is greater than .05. Model 5 does not seem to fit the data better than Model 4.

Benchmark Dose Computations:

Specified Effect = 0.100000

Risk Type = Relative deviation

Confidence Level = 0.950000

BMD and BMDL by Model

Model BMD BMDL

------- ------------ ---------- 2 0.843984 0.582755 3 1.0555 0.588232 4 0.843983 0.348065 5 1.00591 0.3616465 6 7 8 9 10 11

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 2 with 0.95 Confidence Level

09:48 05/21 2014 BMD BMDL Exponential5 6 7 8 9 10 11

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 3 with 0.95 Confidence Level

09:48 05/21 2014 BMD BMDL

Exponential5 6 7 8 9 10 11

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 4 with 0.95 Confidence Level

09:48 05/21 2014 BMD BMDL Exponential5 6 7 8 9 10 11

0 0.5 1 1.5 2 2.5 3Mean Response

dose Exponential Model 5 with 0.95 Confidence Level

09:48 05/21 2014 BMD BMDL Exponential