Overdispersion in Wadley's Problem

摘要

Wadley's problem relates to dose-response experiments in which the number of individuals surviving a given dose is recorded but the number originally present in the system is unknown. The situation can be modelled by assuming that the number of individuals initially present is Poisson and that the number of individuals surviving, given the number originally present, is binomial. It then follows that the number of individuals surviving is Poisson with parameter proportional to the probability of survival. In the present study an approach to the modelling of overdispersion in Wadley's problem based on the assumption that the probability of survival is beta distributed is introduced and follows closely the development of the beta-binomial paradigm. The resultant beta-Poisson distribution is reviewed and estimation of the model parameters within the dose-response context is illustrated by means of data drawn from a study on anti-malarial drugs.