Power for studies with random group sizes

In any study it is essential to select the sample size carefully to ensure adequate power. For many studies this is simple: recruit a desired number of subjects within each group, conduct measurements, and perform the statistical test. In some studies (e.g. observational studies), however, the group membership is unknown at recruitment. In this paper we examine the effect of random group sizes on power. Additionally, we consider the situation when the group proportions are unknown and specified by a prior distribution. The problem that initially motivated this research is presented (power for a 2-by-2 table), as are examples using continuous outcomes. We find that standard estimates of power using expected group sizes can over or underestimate power. SAS macros are available at http://www.phs.wfubmc.edu/public/wambrosi/RandomPower. Copyright (C) 2010 John Wiley & Sons, Ltd.