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 Exponential Model. (Version: 1.9; Date: 01/29/2013) 

 Input Data File: C:/USEPA/BMDS240/Data/exp_Ray 14wksubC in rats - 49d RBC 

F_Setting.(d) 

 Gnuplot Plotting File: 

 Sun May 25 18:44:34 2014 

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 BMDS Model Run - 14-weekrat subchronic - 49d RBC - F 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 

 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 = 500 

 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 -9.23222 -9.23222 -9.23222 -9.23222 

 rho 2.77278 2.77278 2.77278 2.77278 

 a 883.974 883.974 1332.45 1332.45 

 b 0.0293556 0.0293556 0.196282 0.196282 

 c -- -- 0.528922 

0.528922 

 d -- 1 -- 1 

 Parameter Estimates by Model 

 Variable Model 2 Model 3 Model 4 Model 5 

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

 lnalpha -15.8632 -18.1029 -10.7812 -10.7812 
 rho 3.76844 4.104 2.99811 2.99811 

 a 1136.48 1119.34 1219.82 1219.82 

 b 0.0290037 0.0633046 0.541102 0.541102 

 c -- -- 0.606671 0.606671 

 d -- 17.0491 -- 1 

 Table of Stats From Input Data 

 Dose N Obs Mean Obs Std Dev 

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

 0 9 1269 246.9 

 0.1 10 1148 125.9 

 1.5 10 956 145.8 

 15 10 740 95.4 

 Estimated Values of Interest 

 Model Dose Est Mean Est Std Scaled Residual 

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

 2 0 1136 205.5 1.935 

 0.1 1133 204.3 0.2293 

 1.5 1088 189.3 -2.207 

 15 735.6 90.51 0.1551 

 3 0 1119 211.6 2.122 

 0.1 1119 211.6 0.4283 

 1.5 1119 211.6 -2.441 

 15 740 90.5 -4.415e-007 

 4 0 1220 192.9 0.7648 

 0.1 1195 187 -0.7872 

 1.5 953.1 133.3 0.06851 

 15 740.2 91.24 -0.0059 

 5 0 1220 192.9 0.7648 

 0.1 1195 187 -0.7872 

 1.5 953.1 133.3 0.06851 

 15 740.2 91.24 -0.0059 

 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 -215.4855 5 440.9711 

 A2 -210.7284 8 437.4569 

 A3 -211.9577 6 435.9155 
 R -234.9383 2 473.8767 

 2 -218.1116 4 444.2231 

 3 -219.8378 5 449.6757 

 4 -213.2307 5 436.4614 

 5 -213.2307 5 436.4614 

 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 48.42 6 < 0.0001 

 Test 2 9.514 3 0.02318 

 Test 3 2.459 2 0.2925 

 Test 4 12.31 2 0.002125 

 Test 5a 15.76 1 < 0.0001 

 Test 5b -3.453 1 N/A 

 Test 6a 2.546 1 0.1106 

 Test 6b 9.762 1 0.001782 

 Test 7a 2.546 1 0.1106 

 Test 7b 13.21 0 N/A 

 Test 7c 7.958e-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 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. 
 The p-value for Test 5b is less than .05. Model 3 appears 

 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. 

 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 greater than .1. Model 5 seems 

 to adequately describe the data. 

 Degrees of freedom for Test 7b are less than or equal to 0. 

 The Chi-Square test for fit is not valid. 

 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 3.63266 2.99039 

 3 13.8433 2.68977 

 4 0.542138 0.343598 

 5 0.542138 0.343598 
 600

 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 10 12 14

Mean Response

dose

Exponential Model 2, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

18:44 05/25 2014

BMDL BMD

Exponential

 600 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 

Mean Response

dose

Exponential Model 3, with BMR of 0.1 Rel. Dev. for the BMD an

18:44 05/25 2014

BMDL 

Exponential

 600 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 10 12 14

Mean Response

dose

Exponential Model 4, with BMR of 0.1 Rel. Dev. for the BMD and 0.95 Lower Confidence Level for BMDL

18:44 05/25 2014

BMDL BMD

Exponential

 600 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 

Mean Response

dose

Exponential Model 5, with BMR of 0.1 Rel. Dev. for the BMD an

18:44 05/25 2014

BMDL BMD

Exponential