Date of Award

6-2025

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Joshua Naranjo, Ph.D.

Second Advisor

Hyun Bin Kang, Ph.D.

Third Advisor

Kevin Lee, Ph.D.

Fourth Advisor

Yuanlong Liu, Ph.D.

Abstract

In medical and social sciences fields, data are measured in terms of discrete categories. The primary question of interest involves the relationship between a set of factors and a set of response variables under studies. Moreover, the distribution of the response variables may be influenced by another set of variables called confounders. The data from such studies are summarized in 3-way tables. The hypothesis we are interested in can be expressed in terms of "no partial association" between the sub-populations and the response levels.

The methods for testing the association or independence in a 2x2 contingency table have been developed, such as Pearson’s chi-square test and likelihood ratio test. For a series of stratified 2x2 tables and stratified RxC tables, the CMH (Cochran–Mantel–Haenszel) test and the generalized CMH test are used for testing the association respectively. However, before applying both of the CMH type tests, there is an assumption of homogeneity of odds ratios cross all the strata.

The decomposition of a chi-square statistic allows writing the statistic as the sum of independent chi-square statistics. Therefore, by taking the partitions of a RxC contingency table, there are going to be (R x 1)(C x 1) 2 x 2 contingency tables. This can be applied to R x C x K contingency tables. Without the assumption of homogeneous odds ratio, the new methods are based on the decompositions of the R x C x K contingency table, such as the sum of the chi-square test, the sum of the CMH test, and the maximum of the CMH test. By applying the similar process, the sum and the maximum log odds ratio tests are also proper to test the association in stratified contingency tables.

Access Setting

Dissertation-Open Access

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