Risk Analysis in Cohort Studies with Heterogeneous Strata. A Global χ2-Test for Dose-Response Relationship, Generalizing the Mantel-Haenszel Procedure

Abstract

In cohort studies the Mantel-Haenszel estimator ORMH is computed from sample data and is used as a point estimator of relative risk. Test-based confidence intervals are estimated with the help of the asymptotic chi-squared distributed MH-statistic chi 2MHS. The Mantel-extension-chi-squared is used as a test statistic for a dose-response relationship. Both test statistics--the Mantel-Haenszel-chi as well as the Mantel-extension-chi--assume homogeneity of risk across strata, which is rarely present. Also an extended nonparametric statistic, proposed by Terpstra, which is based on the Mann-Whitney-statistics assumes homogeneity of risk across strata. We have earlier defined four risk measures RRkj (k = 1,2,...,4) in the population and considered their estimates and the corresponding asymptotic distributions. In order to overcome the homogeneity assumption we use the delta-method to get "test-based" confidence intervals. Because the four risk measures RRkj are presented as functions of four weights gik we give, consequently, the asymptotic variances of these risk estimators also as functions of the weights gik in a closed form. Approximations to these variances are given. For testing a dose-response relationship we propose a new class of chi 2(1)-distributed global measures Gk and the corresponding global chi 2-test. In contrast to the Mantel-extension-chi homogeneity of risk across strata must not be assumed. These global test statistics are of the Wald type for composite hypotheses.(ABSTRACT TRUNCATED AT 250 WORDS)