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. 

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 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 0.987842 
 c -- -- 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 0.100868 
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Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

08:50 05/21 2014

BMDL BMD

 

Exponential
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Mean Response

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Exponential Model 3 with 0.95 Confidence Level

08:50 05/21 2014

BMDL BMD

 

Exponential
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Mean Response

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Exponential Model 4 with 0.95 Confidence Level

08:50 05/21 2014

BMDL BMD

 

Exponential
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Mean Response

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Exponential Model 5 with 0.95 Confidence Level

08:50 05/21 2014

BMDL BMD

 

Exponential