A Contingency Table Alternative to Poisson Regression in Comparing the Frequency Distributions of Two Populations

Date of Award

6-2024

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Joshua Naranjo, Ph.D.

Second Advisor

Duy Ngo, Ph.D.

Third Advisor

Yingying Zhang, Ph.D.

Fourth Advisor

Clifton E. Ealy, Ph.D.

Keywords

Binary data, Cochran-Mantel-Haenszel, odds ratio, treatment effect heterogeneity

Abstract

When testing the conditional independence between a binary outcome and a binary treatment indicator, conditioned on a categorical variable with k levels, typically represented by a K × 2 frequency table, researchers often turn to Poisson regression and the Cochran-Mantel-Haenszel (CMH) test. However, a common challenge encountered in these analyses is the presence of treatment effect heterogeneity. Introducing an interaction term between treatment indicators and effect modifiers in log-linear regression offers potential solutions, yet the equidispersion assumption of Poisson regression remains problematic. On the other hand, the CMH test assumes similar treatment effects across all strata, disregarding potential variations among different population characteristics. These limitations can lead to invalid test results or compromised statistical power, undermining the reliability of study findings. We propose an alternative method based on log odds ratios, which accommodates treatment effect heterogeneity while maintaining simplicity. The proposed method controls the type I error rate and achieves better power for a broader range of treatment effects. These improvements over current methods were illustrated by simulation studies. We also demonstrated the proposed method with data from existing literature, showcasing its practical application and advantages in real-world scenarios.

Access Setting

Dissertation-Abstract Only

Restricted to Campus until

6-1-2026

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