Linear Bayes Estimators of the Potency Curve in Bioassay

摘要

The Bayesian nonparametric approach to estimating the tolerance distribution in quantal bioassay has received some attention. The computational difficulty in evaluating these Bayes estimators has hindered their applications. This paper explores the linear Bayes approach to the bioassay problem. These linear Bayes estimators can be computed easily by using statistical software which has the capability of inverting a matrix. Let us state the quantal bioassay problem as follows: The experimenter intends to test the potency of a stimulus by giving subjects injections of the stimulus at different levels; namely, he chooses L dosage levels, t sub 1,...., t sub L, and treats n sub 1,....,n sub L subjects at these levels respectively. Each subject possesses a fixed tolerance level. If a stimulus exceeds a subject's tolerance level, the subject responds positively. If not, there is no response. Therefore we observe the number of positive responses at each level. These numbers are denoted by k sub 1,...,k sub l. The potency curve F is the distribution of tolerance levels; i.e. F is defined by the probability F(t) of getting a positive response to a dosage at level t for all t. The objective of this article is to make inferences about the potency curve F. Keywords: Ferguson's Dirichlet process.