Economizing comparative Poisson clinical trials of multiple experimental treatments by testing against the same control

Comparative Poisson trials of an experimental treatment versus a control typically condition on the total number of events that occur across both arms (Design A). Inference is based on the binomial distribution. Recently, an approach termed Design C to compare K experimental treatments to the same control was introduced. Under Design C without curtailment, the trial continues until a prespecified number of events occur in the control arm, leading to inference based on the negative multinomial distribution. The question remains of how advantageous it is to conduct one Design C trial comparing K experimental treatment arms to the same control arm as opposed to conducting K separate Design A trials each comparing one experimental treatment arm to a different control arm. This paper, therefore, compares the expected number of subjects to enroll for the two designs under uncurtailed and curtailed settings. The designs are evaluated when the null hypothesis and various assumptions for the alternative hypothesis hold. We simulate a variety of combinations for the Type 1 error, power, and ratio of the incidence rate of events in the experimental treatment to control arms. Design C frequently offers significant savings in terms of sample size relative to Design A.