TY - JOUR
TI - Comparative Poisson trials for comparing multiple new treatments to the control
DO - https://doi.org/doi:10.7282/T3FJ2GHX
PY - 2010
AB - Comparative Poisson Trials often test interventions to prevent rare adverse binomial outcomes. We extend Gail’s “Design A” approach to continues the trial until a predetermined total number of disease cases, D, occur into comparing K>1, treatments to one control. Controlling overall type I error and a post-hoc procedures to identify which treatments are better are addressed. With the Poisson as the underlying distribution, conditioning on D disease cases total, the number in each group is multinomial distributed with parameters that depend on the incidence ratios of treatment to the control arms. Rejection regions based on the 1) numbers of cases that occur in control and/or 2) minimum number of cases among treatment groups are considered to test the global null hypothesis that no treatment is superior to the control. A tool known as the stochastic matrix simplifies size and power computations. Decision rules which are robust to some treatments being inferior to the control are discussed. There is no uniformly most powerful test against all alternatives, but rejection regions should have the Lower Left Quadrant Rule property. The discreteness of multinomial complicates derivation of theoretical results. Still, some identities are proven for comparing K=2 treatments to the control that we believe will extend to K ≥ 3. For K=2, the post-hoc procedure that applies standard binomial tests to each individual treatment vs. control hypothesis when the global hypothesis is rejected is superior to the Bonferroni adjustment; reducing by 7 % to 18 % the follow up disease cases required for the range of settings we studied. We considered unbalanced allocation of follow up time to treatment and control groups. While discreteness of the multinomial distribution prevents analytic solution, a systematic point by point search that computes powers for a range of treatment / control allocation ratios with small increments is applied to find the optimum allocation ratio. In most cases the optimum allocation ratios do not perform substantially better than equal allocation in terms of minimization of the D or expected subject time needed to obtain D for given Type-1 error or power.
KW - Statistics and Biostatistics
KW - Poisson distribution
KW - Multiple comparisons (Statistics)
LA - eng
ER -