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