Sample size determination for alternate periods of use study designs with binary responses

In this article, we consider several study designs that arise in practice, which are variations of standard crossover designs. Often, they may result from modifications made to a standard crossover design due to practical considerations. Characteristic features of the studies we are concerned with are (a) treatments consist of external use of products with little or no possibility of carry over effects, and (b) the periods of use are dictated by the subjects or by some specific event, such as diaper leakage or menstrual flow. We consider a number of such study designs for estimating the difference in the efficacy of two treatments or test products. We provide brief descriptions of studies to motivate the study design, the underlying data structure, and computations of the variances of the usual unbiased estimators of the difference in efficacy, and the sample size formulas. The situations considered here cover a number of popular crossover designs. The objective of our work is to provide guidance to members of a wide audience on how to answer the sample size question for their own nonstandard situations. We conclude the article with a brief report on a simulation study we conducted to investigate the impact of estimation on the sample size determination and consequently on the actual power realized in an effort to promote the "best practice" of checking whether the recommended sample sizes indeed achieve the desired level of power.