This article is concerned with computing the total sample size required for a two-sample comparison when the sizes of the two groups to be compared cannot be fixed in advance. This is frequently encountered when group membership depends on a variable which is observable only after the subject is enrolled to the study, such as a genetic or a biological marker. The most common way of circumventing this problem is assuming a fixed number for the prevalence of the condition that will determine the group membership and compute the required sample size conditionally. In this article this practice is formalized by placing a prior distribution on the prevalence which results in an analytically tractable formula for the unconditional sample size. In particular a sample size inflation factor, a number that can be multiplied with conditional sample size, is presented. An example is given from the planning of a clinical trial investigating the prognostic role of molecular markers in gastrointestinal stromal cancer.
Gonen, Mithat, "Computing the Total Sample Size When Group Sizes Are Not Fixed" (August 2005). Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series. Working Paper 4.