Alternative criteria for optimal designs of limiting dilution assays

It is well known that criteria for optimal non-linear designs usually depend on the unknown value of parameters. An approximate Bayesian approach imposes a prior on these values and optimizes the expectation of the criterion over this distribution. While this method produces designs that perform well on average, the design may perform badly in some parts of the parameter space, and if the true parameter appears to fall in one of these regions, then the good average performance will be little compensation. Several alternative criteria are introduced in the context of deriving designs for limiting dilution assays. These include constrained optimization of a familiar criterion, a minimax criterion and designs to optimize prespecified centiles of the variance under the prior distribution. The latter are shown to offer a useful compromise between good overall performance and possible poor performance.