Date of Award
Doctor of Philosophy
This thesis contains an investigation of the effects of categorical data clustering on three estimators of the common odds ratio and on three tests of the null hypothesis that the odds ratio is 1. The beta binomial distribution is used to model the clustering.;Maximum likelihood theory is developed for the estimation of the odds ratio under beta binomial modelling. The unconditional maximum likelihood estimator is shown to be consistent under clustering and an expression for the dispersion matrix of the parameters is derived. The Mantel-Haenszel estimator of the odds ratio is shown to be consistent under cluster sampling and an expression for it large sample variance is derived.;An adjustment to the Mantel-Haenszel chi-square statistic to account for clustering is derived.;In a simulation study, the three estimators are compared. Three estimators of the intracluster correlation coefficient--the maximum likelihood estimate, the moment estimator and an analysis of variance estimator--are compared by simulation. These estimates are used to adjust the Mantel-Haenszel and the unconditional likelihood ratio test in order to allow for clustering. The Mantel-Haenszel estimator is found to be robust under conditions of low clustering. The ANOVA estimator of the intracluster correlation coefficient is found to be superior to the other estimators and the ANOVA adjusted Mantel-Haenszel test of significance is recommended.
Donald, Alan William, "The Analysis Of Clustered Data In Sets Of 2x2 Contingency Tables" (1985). Digitized Theses. 1407.