DDVP Dog ‐ Week 52 ‐ RBC ChE – Females

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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 09:18:35 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 -3.25242 -3.25242 -3.25242 -3.25242 

 rho 2.26077 2.26077 2.26077 2.26077 

 a 2.92145 2.92145 9.345 9.345 

 b 0.51536 0.51536 0.75236 0.75236 

 c -- -- 0.0963082 

0.0963082 

 d -- 1 -- 1 

 Parameter Estimates by Model 

 Variable Model 2 Model 3 Model 4 Model 5 

 -------- ------- ------- ------- ------- 
 lnalpha -3.55297 -3.55297 -3.5817 -3.5817 

 rho 2.31837 2.31837 2.31313 2.31313 

 a 8.28299 8.28299 8.52887 8.52887 

 b 0.513075 0.513075 0.721068 0.721068 

 c -- -- 0.109516 0.109516 

 d -- 1 -- 1 

 Table of Stats From Input Data 

 Dose N Obs Mean Obs Std Dev 

 ----- --- ---------- ------------- 

 0 4 8.9 2.14 

 0.05 4 7.8 2.43 

 1 4 4.7 0.97 

 3 4 1.8 0.4 

 Estimated Values of Interest 

 Model Dose Est Mean Est Std Scaled Residual 

 ------- ------ ---------- --------- ---------------- 

 2 0 8.283 1.963 0.6288 

 0.05 8.073 1.905 -0.2868 

 1 4.959 1.083 -0.4777 

 3 1.777 0.3296 0.139 

 3 0 8.283 1.963 0.6288 

 0.05 8.073 1.905 -0.2868 

 1 4.959 1.083 -0.4777 

 3 1.777 0.3296 0.139 

 4 0 8.529 1.99 0.373 

 0.05 8.26 1.918 -0.4797 

 1 4.627 0.9811 0.149 

 3 1.807 0.3307 -0.04305 

 5 0 8.529 1.99 0.373 

 0.05 8.26 1.918 -0.4797 

 1 4.627 0.9811 0.149 

 3 1.807 0.3307 -0.04305 

 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 -14.20615 5 38.41231 

 A2 -8.506332 8 33.01266 

 A3 -8.75637 6 29.51274 
 R -26.32188 2 56.64377 

 2 -9.15332 4 26.30664 

 3 -9.15332 4 26.30664 

 4 -8.855035 5 27.71007 

 5 -8.855035 5 27.71007 

 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 35.63 6 < 0.0001 

 Test 2 11.4 3 0.00975 

 Test 3 0.5001 2 0.7788 

 Test 4 0.7939 2 0.6724 

 Test 5a 0.7939 2 0.6724 

 Test 5b -9.734e-013 0 N/A 

 Test 6a 0.1973 1 0.6569 

 Test 6b 0.5966 1 0.4399 

 Test 7a 0.1973 1 0.6569 

 Test 7b 0.5966 1 0.4399 

 Test 7c -1.776e-014 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 0.205351 0.177675 

 3 0.205351 0.177675 

 4 0.165199 0.113926 

 5 0.165199 0.113926 
 2

 4

 6

 8

 10

 12

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

09:18 05/21 2014

BMDL BMD

 

Exponential
 2

 4

 6

 8

 10

 12

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

09:18 05/21 2014

BMDL BMD

 

Exponential
 2

 4

 6

 8

 10

 12

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

09:18 05/21 2014

BMDL BMD

 

Exponential
 2

 4

 6

 8

 10

 12

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 5 with 0.95 Confidence Level

09:18 05/21 2014

BMDL BMD

 

Exponential