Selection effects in randomized trials with count data

Selection criteria are specified in clinical trials to define the study population from which the sample will be obtained. It is common for one of these criteria to be based on historical or baseline measurements of the clinical sign or symptom that will serve as the response variable in the trial. The effect of such selection criteria has been studied extensively for normally distributed responses, but less is known about the situation in which the response is a count or a possibly recurrent event. In this paper we examine the bias and relative efficiency of some common methods of analysis for count data in the presence of selection criteria. The investigation is carried out using asymptotic theory pertaining to misspecified models and by simulation. Applications involving data from an epilepsy trial and a study of transient myocardial ischaemia illustrate the effect of ignoring the selection mechanism.