Comparative poisson clinical trials of multiple experimental treatments vs a single control using the negative multinomial distribution.

This paper introduces a method which conditions on the number of events that occur in the control group to determine rejection regions and power for comparative Poisson trials with multiple experimental treatment arms that are each compared to one control arm. This leads to the negative multinomial as the statistical distribution used for testing. For one experimental treatment and one control with curtailed sampling, this is equivalent to Gail's (1974) approach. We provide formulas to calculate exact one-sided overall Type I error and pointwise power for tests of treatment superiority and inferiority (vs the control). Tables of trial design parameters for combinations of one-sided overall Type I error = 0.05, 0.01 and pointwise power = 0.90, 0.80 are provided. Curtailment approaches are presented to stop follow-up of experimental treatment arms or to stop the study entirely once the final outcomes for each arm are known.