Testing for Association in Stratified 2x2 Contingency Tables


Eunice Ampah

Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Magdalena Niewiadomska-Bugaj

Second Advisor

Dr. Joshua D. Naranjo

Third Advisor

Dr. Joseph W. McKean

Fourth Advisor

Dr. Jezaniah-Kira S. Tena


Stratified data, CMH, odds ratio, Breslow-DAD, contingency tables, effects


In epidemiology and most medical research, it is common for study results to be summarized in 2x2 contingency tables with classification of an exposure variable to a risk factor and an outcome variable each with two levels. In the presence of confounders, the data can be stratified into several 2x2 contingency tables known as strata. Using odds ratio in each stratum as an effect measure, in this study, we examine the nature of the association between the classification variables across strata.

The Breslow-Day (BD) test is widely used to determine if the odds ratios in the strata are all equal. If its null hypothesis is not rejected then the BD test is followed by the Cochran Mantel-Haenszel (CMH) test to determine if all the odds ratios are equal to one. Sometimes the CMH test is performed first and if the null hypothesis is rejected, then the BD test is performed to see if the rejection was caused by the fact that the odds ratios were not all equal or because they were equal but different from one.

We are proposing and studying several procedures testing if there is a treatment effect in at least one stratum without requiring running a second test. We show that, when the design in each stratum is balanced and the odds ratios are equal across strata, then, statistic T*1 is as powerful as the Cochran Mantel-Haenszel test of conditional independence across strata under both small and large sample configurations. On the contrary, when the design in each stratum is unbalanced, then T*1 performs best under large sample size settings with equal odds ratio across strata as compared to the Cochran Mantel-Haenszel.

Furthermore, we demonstrate that when one of the odds ratio is at least different in at least one stratum, then given a balanced design for both small and large sample size setup, our proposed tests T2, T3 and T4 are more powerful than the Breslow-Day test.

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