The Beta-Poisson Distribution in Wadley’s Problem

In dose-response studies, Wadley’s problem occurs when the number of organisms that survive exposure to varying doses of a treatment is observed but the number initially present is unknown. The unknown number of organisms initially treated has traditionally been modelled by a Poisson distribution, resulting in a Poisson distribution for the number of survivors with parameter proportional to the probability of survival. Data in this setting are often overdispersed. This study revisits the beta-Poisson distribution and considers its effectiveness in modelling overdispersed data from a Wadley’s problem setting.