A score test for determining sample size in matched case-control studies with categorical exposure

The paper considers the problem of determining the number of matched sets in 1: M matched case-control studies with a categorical exposure having k + 1 categories, k > 1. The basic interest lies in constructing a test statistic to test whether the exposure is associated with the disease. Estimates of the k odds ratios for 1: M matched case-control studies with dichotomous exposure and for 1: 1 matched case-control studies with exposure at several levels are presented in Breslow and Day (1980), but results holding in full generality were not available so far. We propose a score test for testing the hypothesis of no association between disease and the polychotomous exposure. We exploit the power function of this test statistic to calculate the required number of matched sets to detect specific departures from the null hypothesis of no association. We also consider the situation when there is a natural ordering among the levels of the exposure variable. For ordinal exposure variables, we propose a test for detecting trend in disease risk with increasing levels of the exposure variable. Our methods are illustrated with two datasets, one is a real dataset on colorectal cancer in rats and the other a simulated dataset for studying disease-gene association.