==================================================================== Multistage Model. (Version: 3.3; Date: 02/28/2013) Input Data File: C:/tmp/1-Study2013-Endpoint-Multi3-10Pct-4d.(d) Gnuplot Plotting File: C:/tmp/1-Study2013-Endpoint-Multi3-10Pct-4d.plt Fri Sep 06 12:33:48 2013 ==================================================================== 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 = Response Independent variable = Dose Total number of observations = 4 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 = 0.00189185 Beta(1) = 3.51519e-005 Beta(2) = 0 Beta(3) = 8.00751e-013 Asymptotic Correlation Matrix of Parameter Estimates ( *** The model parameter(s) -Background -Beta(2) have been estimated at a boundary point, or have been specified by the user, and do not appear in the correlation matrix ) Beta(1) Beta(3) Beta(1) 1 -0.92 Beta(3) -0.92 1 Parameter Estimates 95.0% Wald Confidence Interval Variable Estimate Std. Err. Lower Conf. Limit Upper Conf. Limit Background 0 * * * Beta(1) 3.70534e-005 * * * Beta(2) 0 * * * Beta(3) 7.72094e-013 * * * * - Indicates that this value is not calculated. Analysis of Deviance Table Model Log(likelihood) # Param's Deviance Test d.f. P-value Full model -61.4008 4 Fitted model -61.4097 2 0.0176826 2 0.9912 Reduced model -89.5738 1 56.3459 3 <.0001 AIC: 126.819 Goodness of Fit Scaled Dose Est._Prob. Expected Observed Size Residual ------------------------------------------------------------------------ 0.0000 0.0000 0.000 0.000 50 0.000 1000.0000 0.0371 1.856 2.000 50 0.108 3000.0000 0.1237 6.183 6.000 50 -0.079 8000.0000 0.4993 24.965 25.000 50 0.010 Chi^2 = 0.02 d.f. = 2 P-value = 0.9911 Benchmark Dose Computation Specified effect = 0.1 Risk Type = Extra risk Confidence level = 0.95 BMD = 2512.85 BMDL = 1492.15 BMDU = 3755.36 Taken together, (1492.15, 3755.36) is a 90 % two-sided confidence interval for the BMD