Journal of Biopharmaceutical Statistics, 22: 351–367, 2012 Copyright © Taylor & Francis Group, LLC ISSN: 1054-3406 print/1520-5711 online DOI: 10.1080/10543406.2010.539082 SAMPLE SIZE DETERMINATION FOR ALTERNATE PERIODS OF USE STUDY DESIGNS WITH BINARY RESPONSES Jorge G. Morel 1 and Nagaraj K. Neerchal 2 1 The Procter and Gamble Company, Cincinnati, Ohio, USA 2 Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland, USA 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. Key Words: Crossover designs; Diaper studies; Exchangeable correlation; Menstrual studies; Power; Repeated measures. 1. INTRODUCTION A large number of study designs in practice fall short of the strict definition of a crossover design. While they share the characteristics of crossover designs that the treatments are applied to individuals in a sequential order, there may either be repeated measurements or possibly concurrent multiple applications of the treatments to the same subject within each period of application. We refer to such study designs as alternate periods of use (APU) study designs, and we consider the associated sample size and power determination problem. In crossover studies, each subject receives two or more treatments. The treatments are given to the subjects sequentially according to a preestablished order. Subjects receive Received December 31, 2009; Accepted October 31, 2010 Address correspondence to Jorge G. Morel, The Procter and Gamble Company, 6280 Center Hill Avenue, Cincinnati, OH 45224, USA; E-mail: morel.jg@pg.com 351