### DDVP Dog ‐ Week 13 ‐ RBC 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 09:02:54 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 -3.337 -3.337 -3.337 -3.337 rho 2.13506 2.13506 2.13506 2.13506 a 2.61954 2.61954 9.345 9.345 b 0.543931 0.543931 0.806855 0.806855 c -- -- 0.0856073 0.0856073 d -- 1 -- 1

Parameter Estimates by Model

Variable Model 2 Model 3 Model 4 Model 5

-------- ------- ------- ------- -------lnalpha -3.13476 -3.13476 -3.3699 -3.3699 rho 2.11969 2.11969 2.16696 2.16696 a 7.90215 7.90215 8.3663 8.3663 b 0.54289 0.54289 0.971055 0.971055 c -- -- 0.147844 0.147844 d -- 1 -- 1

Table of Stats From Input Data

Dose N Obs Mean Obs Std Dev

----- --- ---------- ------------- 0 4 8.9 2.47 0.05 4 7.3 1.86 1 4 4.1 0.42 3 4 1.6 0.42

Estimated Values of Interest

Model Dose Est Mean Est Std Scaled Residual

------- ------ ---------- --------- ---------------- 2 0 7.902 1.865 1.07 0.05 7.691 1.812 -0.4309 1 4.592 1.049 -0.9372 3 1.55 0.332 0.2993 3 0 7.902 1.865 1.07 0.05 7.691 1.812 -0.4309 1 4.592 1.049 -0.9372 3 1.55 0.332 0.2993 4 0 8.366 1.853 0.5762 0.05 8.028 1.772 -0.8223 1 3.937 0.8186 0.399 3 1.624 0.3136 -0.1534 5 0 8.366 1.853 0.5762 0.05 8.028 1.772 -0.8223 1 3.937 0.8186 0.399 3 1.624 0.3136 -0.1534

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 -12.95921 5 35.91841 A2 -4.857717 8 25.71543 A3 -6.674776 6 25.34955R -26.30027 2 56.60055 2 -8.654198 4 25.3084 3 -8.654198 4 25.3084 4 -7.315069 5 24.63014 5 -7.315069 5 24.63014

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 42.89 6 < 0.0001 Test 2 16.2 3 0.00103 Test 3 3.634 2 0.1625 Test 4 3.959 2 0.1381 Test 5a 3.959 2 0.1381 Test 5b 3.197e-014 0 N/A Test 6a 1.281 1 0.2578 Test 6b 2.678 1 0.1017 Test 7a 1.281 1 0.2578 Test 7b 2.678 1 0.1017 Test 7c 2.558e-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 seems to 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 0.194073 0.165103 3 0.194073 0.165103 4 0.128547 0.0946144 5 0.128547 0.09461440 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

09:02 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 3 with 0.95 Confidence Level

09:02 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

09:02 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

09:02 05/21 2014 BMD BMDL Exponential