Ordered categorical variables arise frequently in cancer clinical trials and other biomedical studies. The statistical procedures for analyzing such data are well known and software for performing the analysis is readily available. The basic idea is to condition on the margins of the contingency table created by the categorical data and thereby obtain a distribution free test that automatically corrects for ties. Despite the popularity of this conditional approach for analyzing ordered categorical data there has been very little work done on power and sample-size considerations at the design phase. A biomedical investigator about to launch a clinical trial for comparing two treatments with ordered categorical outcomes will find it extremely difficult to determine what sample size is needed. Either the investigator must assume that the data are continuous, or else that the data are binary, since these are the only cases for which reliable methods and software are available. Both approaches are inappropriate for ordered categorical data. We propose to fill the void by providing new exact and Monte Carlo methods that provide accurate power and sample-size estimates for conditional tests on ordered categorical data.
