Increasing the power of randomized trials comparing different treatment durations

When the optimal treatment duration is uncertain, a randomized trial may allocate patients to receive active treatment for different durations. We use an example where patients receive treatment for 0, 24, or 52 weeks. In this trial, patients in the 24-weeks and 52-weeks arms receive the same treatment during the first 24 weeks. This overlap allows for more powerful analyses than conventional pair-wise comparisons of arms. When the outcome is the time-to-event, the power for the 0-weeks versus 24-weeks comparison can be increased by including patients in the 52-weeks arm as patients in the 24-weeks arm for the first 24 weeks and censoring at 24 weeks. Furthermore, differences observed between the 24-weeks and 52-weeks arms during the first 24 weeks can only reflect noise. Hence, the comparison of these two arms should be restricted to only patients who remain on the study at 24 weeks and include only the events after 24 weeks. Through simulation, we show that modified analyses accounting for these considerations increase study power substantially. Moreover, if patients were allocated equally to the arms, then events or discontinuations during the first 24 weeks will reduce the number of patients available for the 24-weeks versus 52-weeks comparison, and hence the power of this analysis will be lower than that for the 0-weeks versus 24-weeks comparison. We present a sample size calculation procedure for equalizing the power of these two analyses. Typically, this allocation requires much larger sample sizes in the 24-weeks and 52-weeks arms than in the 0-week arm.