The effects of treatment noncompliance on power in a 2 x 2 factorial design

Clinical trials testing interventions that are available to the public and thus to potential participants must consider the impact of noncompliance on the power of the planned study to detect treatment differences. In long-term trials noncompliance may be assumed to vary over time. Increases in power of the F-test to detect differences in the proportion of participants responding to treatment in a 2 x 2 factorial design are observed when a simple, discrete, time-varying noncompliance model is compared to an assumption of immediate noncompliance. This increase holds in the presence of interaction and can become more substantial as trial duration lengthens or alpha level decreases.