Statistical analysis of K 2 x 2 tables: a comparative study of estimators/test statistics for association and homogeneity.

In order to control for confounding variables, epidemiologists often obtain data in the form of a 2 x 2 table. One variable is usually the disease status, while the other variable represents a dichotomous exposure variable that is suspected of being a risk factor. If a confounding variable is present, the data are often stratified into several 2 x 2 tables. The objectives of the analysis are to test for the association between the suspected risk factor and the disease and to estimate the strength of this relationship. Before estimating a common odds ratio, it is important to check whether the odds ratios are homogeneous. This paper presents the results of a Monte Carlo study that was performed to determine the size and power of a number of tests of association and homogeneity when the data are sparse. We also evaluated the performance of three estimators of the common odds ratio. For the Monte Carlo studies, equal numbers of cases and controls were used in a wide variety of sparse data situations. On the basis of these studies, we recommend the Breslow-Day test for nonsparse data, and the T4 and T5 statistics for sparse data to test for homogeneity. The Mantel-Haenszel test of association is recommended for sparse and nonsparse data sets. With sparse data, none of the odds ratio estimators are entirely satisfactory.