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. Copyright © 2005 John Wiley & Sons, Ltd.