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A crossover trial is an efficient trial design when there is no carry-overeffect. To reduce the impact of the biological carry-over effect, a wash-outperiod is often designed. However, the carry-over effect remains an outstandingconcern when a wash-out period is unethical or cannot sufficiently diminish theimpact of the carry-over effect. The latter can occur in comparativeeffectiveness research where the carry-over effect is often non-biological butbehavioral. In this paper, we investigate the crossover design under apotential outcomes framework with and without the carry-over effect. We findthat when the carry-over effect exists and satisfies a sign condition, thebasic estimator underestimates the treatment effect, which does not inflate thetype I error of one-sided tests but negatively impacts the power. This leads toa power trade-off between the crossover design and the parallel-group design,and we derive the condition under which the crossover design does not lead totype I error inflation and is still more powerful than the parallel-groupdesign. We also develop covariate adjustment methods for crossover trials. Weillustrate the performance of cross-over design and covariate adjustment usingsimulations based on resampling data from an HIV prevention trial.

Behavioral Carry-Over Effect and Power Consideration in Crossover Trials