Choice of number of doses for maximum likelihood estimation of the ED50 for quantal dose-response data.

We address the question of how to choose the number of doses when estimating the median effective dose (ED50) of a symmetric dose-response curve by the maximum likelihood method. One criterion for this choice here is the asymptotic mean squared error (determined by the asymptotic variance) of the estimated ED50 of a dose-response relationship with qualitative responses. The choice is based on an analysis of the inverse of the information matrix. We find that in many cases, assuming various symmetric dose-response curves and various design densities, choice of as many doses as possible, i.e., the allocation of one subject per dose, is optimal. The theoretical and numerical results are supported by simulations and by an example concerning choice of design in an adolescence study.