Power to detect clinically relevant carry-over in a series of cross-over studies

The potential for carry-over effects is an important consideration in the design of any cross-over study, and can cause an investigator to abandon the design altogether. In cross-over studies, carry-over is the lingering effect of a treatment into the subsequent period. Carry-over effects are differences in the extent of the carry-over between the treatments under consideration. It is well known that the test for carry-over effects in individual studies has low power. Empirical evidence of carry-over effects, or the absence of carry-over effects, could be useful for investigators considering the design. Here we develop methods for expressing the power to detect carry-over as a function of the power to detect a clinically relevant treatment effect. Our results suggest that for two-treatment, two-period cross-over studies the power to detect clinically relevant carry-over effects is often less than 15 per cent, and the number of studies needed to differentiate this effect from the type I error rate of 10 per cent is prohibitive. For the three-treatment three-period cross-over design, the power to detect carry-over effects was larger than for the two-period study, but still approached the type I error rate in a number of cases. Unequivocal conclusions about the absence of carry-over effects based on collections of hypothesis tests appear unlikely. Similar findings are presented for bioequivalence studies. For bioequivalence studies, small carry-over effects (e.g. 12.5 per cent of the treatment effect) can seriously inflate the type I error rate, particularly when the power to detect equivalence is high.