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Supplemental material, sj-docx-1-smm-10.1177_09622802231181235 for Economizing comparative poisson clinical trials of multiple experimental treatments by testing against the same control by Joseph A Chiarappa, Donald R Hoover and Alison Pedley in Statistical Methods in Medical Research

Clinical trials that compare one or more experimental treatments to a control treatment in which event incidence (i.e. incidence of disease or an adverse event) is rare often assume that comparative Poisson methodology is appropriate for modeling the number of events that occur in each treatment group. Clinical studies of multiple Poisson parameters may be conducted under one of two designs: (A) wait until a total number of events occur among all treatment groups before stopping the study, or (B) wait until a specified amount of time has passed before terminating the study. Exact tests under these approaches are based on the multinomial distribution.In this dissertation, we consider an alternative approach termed “Design C”, which is to wait until the control group accumulates a pre-specified number of events before stopping the study. The joint distribution of the number of events in the experimental treatment groups at the time of study stoppage, conditional on the number of events observed in the control group, follows a negative multinomial distribution (NMD). The minimum (respectively, maximum) number of events among the experimental treatment arms will be shown to be an appropriate test statistic for determining whether one or more of the experimental treatments is superior (respectively, inferior) to the control at a given one-sided overall Type I error; as such, we first determine the distribution of the order statistics of the NMD. We subsequently provide tables of trial design parameters for select values of one-sided overall Type I error and pointwise power and assuming equal allocation of study subjects to the treatment groups. These studies can be improved by applying curtailed stoppage rules; that is, follow-up of the treatment arms can be discontinued prior to the control group reaching its planned number of events once the ultimate decision is known for each arm. Curtailment has substantial practical implications as reduced follow-up implies reduced study costs and more rapid knowledge of the trial results. We provide simple algorithms to estimate the expected amount of subject follow up (presented in terms of person years) that would be needed until trial termination under both uncurtailed and curtailed stopping rules. Finally, we combine the superiority and inferiority test procedures to provide a two-sided test and briefly consider pairwise comparison of the experimental treatments to each other under the Design C framework.