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We provide a systematic treatment of $D$-optimal design for binary regressionand quantal response models in toxicology studies. For the two-parameter case,we provide an analytical equation (WC equation) for computing the $D$-optimaldesign quickly and when analytical solution is not available, we apply particleswarm optimization to solve for the $D$-optimal design. Examples with variouslink functions are given as well as the sensitivity functions. We extend thetwo-parameter case to three-parameter case by providing a neat formula for thedeterminant of the information matrix. We also suggest practitioners to workwith the neat formula to derive optimal designs for three-parameter binaryregression models.

D-optimal Approximate Design for Binary Regression and Quantal Response in Toxicology Studies