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

==================================================================== 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 09:29:36 2014

====================================================================

BMDS Model Run

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 -0.279863 -0.279863 -0.279863 -0.279863 rho(S) 0 0 0 0 a 5.7745 5.7745 9.45 9.45 b 0.191948 0.191948 0.367024 0.367024 c -- -- 0.253968 0.253968 d -- 1 -- 1

(S) = SpecifiedParameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- ------- lnalpha -0.148951 -0.148951 -0.151103 -0.151103 rho 0 0 0 0 a 8.53828 8.53828 8.56315 8.56314 b 0.194029 0.194029 0.272587 0.272587 c -- -- 0.214578 0.214578 d -- 1 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 4 9 0.86 0.05 4 8 1.25 1 4 7 0.83 3 4 4.8 1.02

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 8.538 0.9282 0.9948 0.05 8.456 0.9282 -0.9822 1 7.032 0.9282 -0.06985 3 4.771 0.9282 0.06334 3 0 8.538 0.9282 0.9948 0.05 8.456 0.9282 -0.9822 1 7.032 0.9282 -0.06985 3 4.771 0.9282 0.06334 4 0 8.563 0.9272 0.9423 0.05 8.472 0.9272 -1.018 1 6.958 0.9272 0.08963 3 4.806 0.9272 -0.01361 5 0 8.563 0.9272 0.9423 0.05 8.472 0.9272 -1.018 1 6.958 0.9272 0.08963 3 4.806 0.9272 -0.01361

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 -5.761098 5 21.5222 A2 -5.321718 8 26.64344 A3 -5.761098 5 21.5222 R -17.2447 2 38.48939 2 -6.808395 3 19.61679 3 -6.808395 3 19.61679 4 -6.791178 4 21.58236 5 -6.791178 4 21.58236

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 23.85 6 0.0005574 Test 2 0.8788 3 0.8306 Test 3 0.8788 3 0.8306 Test 4 2.095 2 0.3509 Test 5a 2.095 2 0.3509 Test 5b -1.776e-015 0 N/A Test 6a 2.06 1 0.1512 Test 6b 0.03443 1 0.8528 Test 7a 2.06 1 0.1512 Test 7b 0.03443 1 0.8528 Test 7c 1.172e-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 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 seemsto adequately describe the data.

The p-value for Test 5a is greater than .1. Model 3 seems to adequately describe the data.

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 greater than .05. Model 5 does not seem 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 0.543015 0.412005 3 0.543015 0.412005 4 0.499608 0.238052 5 0.499608 0.2380523 4 5 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

09:29 05/21 2014 BMD BMDL Exponential3 4 5 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

09:29 05/21 2014 BMD BMDL Exponential3 4 5 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

09:29 05/21 2014 BMD BMDL Exponential3 4 5 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

09:29 05/21 2014 BMD BMDL Exponential