==================================================================== 

 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 M_Setting.(d) 

 Gnuplot Plotting File: 

 Wed May 28 08:52:40 2014 

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 BMDS Model Run - 13 week rat subchronic oral - 13 wk RBC ChE - male 

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

 

 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 -0.449995 -0.449995 -0.449995 -

0.449995 

 rho 1.38856 1.38856 1.38856 

1.38856 

 a 950.763 950.763 1425.9 

1425.9 

 b 0.0303067 0.0303067 0.197284 

0.197284 

 c -- -- 0.52565 

0.52565 

 d -- 1 -- 

1 
 Parameter Estimates by Model 

 Variable Model 2 Model 3 Model 4 Model 5 

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

 lnalpha 21.1723 -5.08112 -0.646221 -0.646219 

 rho -1.62778 2.14617 1.42776 

1.42776 

 a 1299.58 1228.63 1321.27 

1321.27 

 b 0.135299 0.0305362 0.604089 

0.604089 

 c -- -- 0.59785 

0.59785 

 d -- 1 -- 1 

 Table of Stats From Input Data 

 Dose N Obs Mean Obs Std Dev 

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

 0 10 1358 145.5 

 0.1 10 1247 113.9 

 1.5 10 1014 62.6 

 15 10 787 103.6 

 Estimated Values of Interest 

 Model Dose Est Mean Est Std Scaled Residual 

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

 2 0 1300 115.7 1.597 

 0.1 1282 117 -0.9496 

 1.5 1061 136.4 -1.086 

 15 170.8 603.4 3.23 

 3 0 1229 162.9 2.512 

 0.1 1225 162.3 0.4307 

 1.5 1174 155.1 -3.255 

 15 777.1 99.63 0.3131 

 4 0 1321 122.4 0.9493 

 0.1 1290 120.3 -1.133 

 1.5 1005 100.6 0.2945 

 15 790 84.77 -0.1112 

 5 0 1321 122.4 0.9493 

 0.1 1290 120.3 -1.133 

 1.5 1005 100.6 0.2945 

 15 790 84.77 -0.1112 

 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 -206.0746 5 422.1493 

 A2 -202.8208 8 421.6416 

 A3 -205.2366 6 422.4733 

 R -239.8279 2 483.6558 

 2 -228.3096 4 464.6192 

 3 -218.28 4 444.5599 

 4 -206.4856 5 422.9712 

 5 -206.4856 5 422.9712 

 Additive constant for all log-likelihoods = -36.76. 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 74.01 6 < 0.0001 

 Test 2 6.508 3 0.08936 

 Test 3 4.832 2 0.08929 

 Test 4 46.15 2 < 0.0001 

 Test 5a 26.09 2 < 0.0001 

 Test 5b 20.06 0 N/A 

 Test 6a 2.498 1 0.114 

 Test 6b 43.65 1 < 0.0001 

 Test 7a 2.498 1 0.114 

 Test 7b 23.59 1 < 0.0001 

 Test 7c -2.274e-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 less than .1. You may want to 

 consider a different variance model. 

 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 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. 

 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 0.778721 0.502764 

 3 3.45035 2.86896 

 4 0.473278 0.344679 

 5 0.473278 0.344679 
 700

 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 10 12 14

Mean Response

dose

Exponential Model 2 with 0.95 Confidence Level

08:52 05/28 2014

BMDL BMD

Exponential

 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 

Mean Response

dose

Exponential Model 3 with 0.95 Con

08:52 05/28 2014

BMDL BMD

Exponential

 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 10 12 14

Mean Response

dose

Exponential Model 4 with 0.95 Confidence Level

08:52 05/28 2014

BMDL BMD

Exponential

 700 800 900

 1000 1100 1200 1300 1400 1500

 0 2 4 6 8 

Mean Response

dose

Exponential Model 5 with 0.95 Con

08:52 05/28 2014

BMDL BMD

Exponential