Bayesian Bioassay Design

Abstract

A Bayesian treatment of the quantal bioassay design problem is given. It is assumed that the potency curve is a Dirichlet random distribution $F$ with parameter $\alpha(t) = MF_0(t)$, and that $n_1, \cdots, n_L$ animals are treated at drug levels $t_1, \cdots, t_L$ respectively. The optimal design levels $t_1, \cdots, t_L$ that minimize the Bayes risk for weighted integrated quadratic loss functions are found in the following cases: (i) $L = 1$ and the weight function arbitrary; (ii) uniform prior guess, uniform weight and two animals treated; and (iii) uniform weight and $L$ arbitrary, but $M \rightarrow 0$. These results disprove a conjecture of Antoniak.