Adjustments to the Mantel–Haenszel chi‐square statistic and odds ratio variance estimator when the data are clustered

Abstract

Dependence between observations on a dichotomous variable renders invalid the usual chi-square tests of independence and inflates the variances of parameter estimates. Such a situation occurs, for example, when subjects consist of members of the same family or with repeated observations on the same person. In this paper we describe methods of measuring the extent of correlation (or clustering). We also develop methods of adjusting the Mantel–Haenszel chi-square test statistic and the variance of the Mantel–Haenszel estimate of a common odds ratio in sets of 2 × 2 contingency tables.