DDVP Dog ‐ Week 53 ‐ Brain 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 09:48:22 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 Model 
 Variable 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 0.361646 
 5

 6

 7

 8

 9

 10

 11

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

09:48 05/21 2014

BMDL BMD

 

Exponential
 5

 6

 7

 8

 9

 10

 11

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 3 with 0.95 Confidence Level

09:48 05/21 2014

BMDL BMD

 

Exponential
 5

 6

 7

 8

 9

 10

 11

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

09:48 05/21 2014

BMDL BMD

 

Exponential
 5

 6

 7

 8

 9

 10

 11

 0 0.5 1 1.5 2 2.5 3

Mean Response

dose

Exponential Model 5 with 0.95 Confidence Level

09:48 05/21 2014

BMDL BMD

 

Exponential