A generalisation of the Mantel—Haenszel test to bivariate failure time data

Abstract

This paper presents a class of Mantel & Haenszel(1959) type statistics for testing independence between pairs of failure times. This class is extended to include a weight function in order to enhance test power. Large sample distributions of these statistics are given under the null hypothesis of independence. The paper also presents a simplified test, the covariance test, which is asymptotically equivalent to the Mantel-Haenszel-type test. In order to account for heterogeneity among subjects, both tests are generalised to include subject-specific covariates. In a simulation study, the weighted Mantel-Haenszel and covariance tests are shown to lead to an increase in power for detecting dependence, compared to unweighted tests and to a score test (Commenges & Andersen, 1995) that is based on a random effects model. An example is used to illustrate the methodology.