Dichotomous Noncancer Data

The benchmark dose (BMD) modeling of dichotomous data is conducted with the U.S. EPA’s Benchmark Dose Software (BMDS; Version 2.6 was used for this document). For these data, the Gamma, Logistic, Log-Logistic, Log-Probit, Multistage, Probit, and Weibull dichotomous models available within the software are fit using a benchmark response (BMR) of 10% extra risk. Alternative BMRs may also be used where appropriate, as outlined in the Benchmark Dose Technical Guidance (U.S. EPA, 2012). In general, the BMR should be near the low end of the observable range of increased risk in the study. BMRs that are too low can result in widely disparate benchmark dose lower confidence limit (BMDL) estimates from different models (high model-dependence). Adequacy of model fit is judged based on the χ² goodness-of-fit p-value (p > 0.1), magnitude of scaled residuals (absolute value < 2.0), and visual inspection of the model fit. Among all models providing adequate fit, the BMDL from the model with the lowest Akaike’s information criterion (AIC) is selected as a potential point of departure (POD), if the BMDLs are sufficiently close (<threefold); if the BMDLs are not sufficiently close (>threefold), model-dependence is indicated, and the model with the lowest reliable BMDL is selected.

Increased Incidence of Forestomach Hyperplasia in Male F344 Rats Exposed to Commercial Crotonaldehyde via Gavage for 13 Weeks (Hazleton Laboratories, 1986b)

The procedure outlined above for dichotomous data was applied to the data for forestomach hyperplasia in male F344 rats exposed to commercial crotonaldehyde (>95% trans-isomer) via gavage in corn oil 5 days/week for 13 weeks (see Table D-3). Table E-1 summarizes the BMD modeling results. All models provided an adequate fit to the data. BMDL values were sufficiently close (differed by <threefold), so the model with the lowest AIC was selected (Log-Probit). Figure E-1 shows the fit of the Log-Probit model to the data, using the BMR of 10% extra risk. Based on adjusted daily doses (ADDs), the BMD₁₀ and BMDL₁₀ for increased incidence of forestomach hyperplasia in male rats were 6 and 3 mg/kg-day, respectively.

BMD Model Output for Figure E-1:

====================================================================  
  Probit Model. (Version: 3.4;  Date: 5/21/2017)  
  Input Data File: C:/Users/jdean04/BMDS2704/Data/lnp_Crotonaldehyde-hazleton male forestomach hyperplasia_Lnp-BMR10-Restrict.(d)   
  Gnuplot Plotting File:  C:/Users/jdean04/BMDS2704/Data/lnp_Crotonaldehyde-hazleton male forestomach hyperplasia_Lnp-BMR10-Restrict.plt 
Wed Nov 20 15:14:54 2019 
 ====================================================================  

 BMDS_Model_Run  
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

   The form of the probability function is:  

   P[response] = Background 
+(1-Background) * CumNorm(Intercept+Slope*Log(Dose)),

   where CumNorm(.) is the cumulative normal distribution function 


   Dependent variable = Effect 
   Independent variable = Dose 
   Slope parameter is restricted as slope >= 1 

   Total number of observations = 6 
   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 



   User has chosen the log transformed model 


	Default Initial (and Specified) Parameter Values  
		background =		0 
		 intercept =     -2.76936 
		     slope =		1 


Asymptotic Correlation Matrix of Parameter Estimates 

( *** The model parameter(s)  -background   
have been estimated at a boundary point, or have been specified by the user, 
and do not appear in the correlation matrix ) 

	intercept        slope 

 intercept	1        -0.96 

     slope	-0.96	     1 



				Parameter Estimates 

							95.0% Wald Confidence
Interval 
       Variable		Estimate	Std. Err.     Lower Conf. Limit   Upper Conf.
Limit 
     background			0		NA 
      intercept		-3.44396
0.889948		-5.18822	-1.69969
		slope	1.24058		0.34207			0.570132
1.91102 

NA - Indicates that this parameter has hit a bound 
     implied by some inequality constraint and thus 
     has no standard error. 



Analysis of Deviance Table 

       Model      Log(likelihood)  # Param's  Deviance  Test d.f.   P-value 
     Full model		-17.2213	6 
   Fitted model		-18.7434	2       3.04412      4          0.5505 
  Reduced model		-32.5964	1       30.7501      5		<.0001 

AIC:41.4867


				Goodness  of  Fit 
								Scaled 
     Dose     Est._Prob.    Expected    Observed     Size       Residual 
  ------------------------------------------------------------------------ 
    0.0000     0.0000		0.000     0.000      10.000	0.000 
    1.8000     0.0033           0.033     0.000      10.000     -0.182 
    4.0000     0.0423		0.423     0.000      10.000     -0.665
    7.1000     0.1557		1.557     3.000      10.000     1.259
   14.0000     0.4325		4.325     3.000      10.000     -0.846
   29.0000     0.7684		7.684     8.000      10.000     0.237

 Chi^2 = 2.83      d.f. = 4			P-value = 0.5865


   Benchmark Dose Computation 

Specified effect =	0.1 

Risk Type        =      Extra risk 

Confidence level =  	0.95 

	     BMD =	5.71482 

	    BMDL =	3.46158 

	    BMDU =	8.4939 

Increased Incidence of Forestomach Hyperplasia in Female F344 Rats Exposed to Commercial Crotonaldehyde via Gavage for 13 Weeks (Hazleton Laboratories, 1986b)

The procedure outlined above for dichotomous data was applied to the data for forestomach hyperplasia in female F344 rats exposed to crotonaldehyde via gavage in corn oil 5 days/week for 13 weeks (see Table D-3). Table E-2 summarizes the BMD modeling results. All models provided adequate statistical fit to the data; however, based on visual inspection, scaled residuals, relatively poor statistical fit, and an outlier result relative to the other models, the Multistage 1-degree model was not considered an adequate fit to the data. Remaining BMDLs differed by <threefold, so the model with the lowest AIC was selected (Multistage 2-degree; Multistage 3- to 5-degree models converged to Multistage 2-degree). Figure E-2 shows the fit of the Multistage 2-degree model to the data, using the BMR of 10% extra risk. Based on ADDs, the BMD₁₀ and BMDL₁₀ for increased incidence of forestomach hyperplasia in female rats were 7 and 4 mg/kg-day, respectively.

BMD Model Output for Figure E-2:

====================================================================  
      Multistage Model. (Version: 3.4;  Date: 05/02/2014)  
     Input Data File: C:/Users/jdean04/BMDS2704/Data/mst_Crotonaldehyde-hazleton female forestomach hyperplasia_Mst3-BMR10-Restrict.(d)   
     Gnuplot Plotting File:  C:/Users/jdean04/BMDS2704/Data/mst_Crotonaldehyde-hazleton female forestomach hyperplasia_Mst3-BMR10-Restrict.plt 
        Wed Nov 20 15:45:42 2019 
 ====================================================================  
 
 BMDS_Model_Run  
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
  
   The form of the probability function is:  
 
   P[response] = background + (1-background)*[1-EXP( 
                 -beta1*dose^1-beta2*dose^2-beta3*dose^3)] 
 
   The parameter betas are restricted to be positive 
 
 
   Dependent variable = Effect 
   Independent variable = Dose 
 
 Total number of observations = 6 
 Total number of records with missing values = 0 
 Total number of parameters in model = 4 
 Total number of specified parameters = 0 
 Degree of polynomial = 3 
 
 
 Maximum number of iterations = 500 
 Relative Function Convergence has been set to: 1e-008 
 Parameter Convergence has been set to: 1e-008 
 
 
 
                  Default Initial Parameter Values   
                     Background =            0 
                        Beta(1) =     0.015664 
                        Beta(2) =    0.0014296 
                        Beta(3) =            0 
 
 
           Asymptotic Correlation Matrix of Parameter Estimates 
 
           ( *** The model parameter(s)  -Background    -Beta(1)    -Beta(3)    
                 have been estimated at a boundary point, or have been specified by the user, 
                 and do not appear in the correlation matrix ) 
 
                Beta(2) 
 
   Beta(2)            1 
 
 
 
                                 Parameter Estimates 
 
                                                         95.0% Wald Confidence Interval 
       Variable         Estimate        Std. Err.     Lower Conf. Limit   Upper Conf. Limit 
     Background                0               NA 
        Beta(1)                0               NA 
        Beta(2)       0.00205175      0.000612406         0.000851457          0.00325204 
        Beta(3)                0               NA 
 
NA - Indicates that this parameter has hit a bound 
     implied by some inequality constraint and thus 
     has no standard error. 
 
 
 
                        Analysis of Deviance Table 
 
       Model      Log(likelihood)  # Param's  Deviance  Test d.f.   P-value 
     Full model         -14.985         6 
   Fitted model        -15.4997         1       1.02949      5          0.9602 
  Reduced model        -31.3594         1       32.7488      5         <.0001 
 
           AIC:         32.9994 
 
 
                                  Goodness  of  Fit  
                                                                 Scaled 
     Dose     Est._Prob.    Expected    Observed     Size       Residual 
  ------------------------------------------------------------------------ 
    0.0000     0.0000         0.000     0.000      10.000        0.000 
    1.8000     0.0066         0.066     0.000      10.000       -0.258 
    4.0000     0.0323         0.323     0.000      10.000       -0.578 
    7.1000     0.0983         0.983     1.000      10.000        0.018 
   14.0000     0.3311         3.311     4.000      10.000        0.463 
   29.0000     0.8219         8.219     8.000      10.000       -0.181 
 
 Chi^2 = 0.65      d.f. = 5        P-value = 0.9857 
 
 
   Benchmark Dose Computation 
 
Specified effect =            0.1 
 
Risk Type        =      Extra risk  
 
Confidence level =           0.95 
 
             BMD =          7.166 
 
            BMDL =         3.8462 
 
            BMDU =        11.1204 
 
Taken together, (3.8462 , 11.1204) is a 90     % two-sided confidence 
interval for the BMD 

Table E-3 summarizes the BMD best-fit modeling results for the modeled endpoints.