Sample Size Determination for a 3-Treatment 3-Period Crossover Trial in Frequency Data

Background: To reduce the number of patients needed or increase the power of hypothesis testing for the parallel groups design, the crossover design has been often employed when one is studying noncurable chronic diseases. This article focuses attention on sample size calculation for testing non-inferiority and equality in frequency data under a 3-treatment 3-period crossover trial. Method: Under a multiplicative mixed effects model, this article provides asymptotic sample size calculation procedures for testing non-inferiority of an experimental treatment to a control treatment, as well as for simultaneously testing either of 2 treatments versus a placebo. To improve the performance of these asymptotic procedures in small-sample cases, this article further suggests a simple ad hoc adjustment. Results: On the basis of Monte Carlo simulation, we demonstrate that the asymptotic test procedures proposed here can perform well with respect to Type I error. We find that the asymptotic sample size calculation procedures can generally perform well with respect to power when the resulting sample size is moderate or large. We further find that using the simple ad hoc adjustment can improve the performance of the proposed sample size calculation procedures, which are derived from large-sample theory, in small-sample cases.