MORE POWERFUL RANDOMIZATION-BASED P-VALUES IN DOUBLE-BLIND TRIALS WITH NONCOMPLIANCE

Standard randomization-based tests of sharp null hypotheses in randomi zed clinical trials, that is, intent-to-treat analyses, are valid with out extraneous assumptions, but generally can be appropriately powerfu l only with alternative hypotheses that involve treatment assignment h aving an effect on outcome. In the context of clinical trials with non -compliance, other alternative hypotheses can be more natural. In part icular, when a trial is double-blind, it is often reasonable for the a lternative hypothesis to exclude any effect of treatment assignment on outcome for a unit unless the assignment affected which treatment tha t unit actually received. Bayesian analysis under this alternative 'ex clusion' hypothesis leads to new estimates of the effect of receipt of treatment, and to a new randomization-based procedure that has freque ntist validity yet can be substantially more powerful than the standar d intent-to-treat procedure. The key idea is to obtain a p-value using a posterior predictive check distribution, which includes a model for non-compliance behaviour, although only under the standard sharp null hypothesis of no effect of assignment (or receipt) of treatment on ou tcome. It is important to note that these new procedures are distinctl y different from 'as treated' and 'per protocol' analyses, which are n ot only badly biased in general, but generally have very low power. (C ) 1998 John Wiley & Sons, Ltd.