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 Exponential Model. (Version: 1.7; Date: 12/10/2009) 

 Input Data File: E:/Travel Drive/DDVP 2013 relook/BMD runs/exp_Ray 14wksubC in 

rats - 98d RBC F_Setting.(d) 

 Gnuplot Plotting File: 

 Wed May 28 08:27:34 2014 

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 BMDS Model Run - 13 wk rat subchronic oral - RBC ChE 13 wk timepoint - females 

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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 10.4561 10.4561 10.4561 10.4561 

 rho -0.231556 -0.231556 -0.231556 -0.231556 

 a 989.399 989.399 1387.05 1387.05 

 b 0.0211873 0.0211873 0.178924 0.178924 

 c -- -- 0.600109 0.600109 

 d -- 1 -- 1 

 Parameter Estimates by Model 

 Variable Model 2 Model 3 Model 4 Model 5 

 -------- ------- ------- ------- ------- 
 lnalpha -12.9671 -12.9671 6.19442 6.19442 

 rho 3.23055 3.23055 0.378775 0.378775 

 a 1188.8 1188.8 1283.36 1283.36 

 b 0.0211091 0.0211091 0.826498 0.826498 

 c -- -- 0.682991 0.682991 

 d -- 1 -- 1 

 Table of Stats From Input Data 

 Dose N Obs Mean Obs Std Dev 

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

 0 9 1321 82.3 

 0.1 10 1212 81.4 

 1.5 10 1002 81.5 

 15 10 874 86.8 

 Estimated Values of Interest 

 Model Dose Est Mean Est Std Scaled Residual 

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

 2 0 1189 141.7 2.799 

 0.1 1186 141.2 0.5756 

 1.5 1152 134.6 -3.517 

 15 866.2 84.97 0.292 

 3 0 1189 141.7 2.799 

 0.1 1186 141.2 0.5756 

 1.5 1152 134.6 -3.517 

 15 866.2 84.97 0.292 

 4 0 1283 85.86 1.315 

 0.1 1251 85.45 -1.447 

 1.5 994.3 81.81 0.2983 

 15 876.5 79.88 -0.09989 

 5 0 1283 85.86 1.315 

 0.1 1251 85.45 -1.447 

 1.5 994.3 81.81 0.2983 

 15 876.5 79.88 -0.09989 

 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 -189.7483 5 389.4967 

 A2 -189.7188 8 395.4375 

 A3 -189.7308 6 391.4616 

 R -224.2014 2 452.4028 

 2 -207.0351 4 422.0702 

 3 -207.0351 4 422.0702 

 4 -191.9016 5 393.8033 

 5 -191.9016 5 393.8033 

 Additive constant for all log-likelihoods = -35.84. 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 68.97 6 < 0.0001 

 Test 2 0.05915 3 0.9962 

 Test 3 0.02412 2 0.988 

 Test 4 34.61 2 < 0.0001 

 Test 5a 34.61 2 < 0.0001 

 Test 5b -3.524e-012 0 N/A 

 Test 6a 4.342 1 0.03719 

 Test 6b 30.27 1 < 0.0001 

 Test 7a 4.342 1 0.03719 

 Test 7b 30.27 1 < 0.0001 

 Test 7c -5.684e-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 greater than .1. Consider 

 running a homogeneous model. 

 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 less than .1. Model 2 may not adequately 

 describe the data; you may want to consider another model. 

 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 less than .05. Model 4 appears 

 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 4.99124 4.05236 

 3 4.99124 4.05236 

 4 0.45855 0.294963 

 5 0.45855 0.294963 
 800

 900

 1000 1100 1200 1300 1400

 0 2 4 6 8 10 12 14

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

08:31 05/28 2014

BMDL BMD

Exponential

 800 900

 1000 1100 1200 1300 1400

 0 2 4 6 

Mean Response

dose

Exponential Model 3 with 0

08:31 05/28 2014

BMDL BMD

Exponential

 800 900

 1000 1100 1200 1300 1400

 0 2 4 6 8 10 12 14

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

08:32 05/28 2014

BMDL BMD

Exponential

 800 900

 1000 1100 1200 1300 1400

 0 2 4 6 8 

Mean Response

dose

Exponential Model 5 with 0

08:32 05/28 2014

BMDL BMD

Exponential