(Honors Thesis under the direction of Dr. Gary G. Koch)

Abstract: In clinical and biological research, comparisons of treatment effects often involve rare events observed over unequal exposure times, making crude event counts misleading. This study focuses on exposure-adjusted incidence densities as a principled approach for comparing event rates while accounting for varying time at risk and stratification factors such as demographic or geographic characteristics. Under a Poisson framework, we present and connect several methods for estimating stratified incidence density ratios, including the Mantel–Haenszel test, Fieller’s method, stratified conditional Poisson regression, and standard Poisson regression. Using melanoma and rotavirus datasets, we demonstrate how these methods perform under different data conditions, including varying sample sizes and event frequencies. Results show consistent inference across methods when assumptions are met, while highlighting differences in applicability depending on homogeneity across strata and sample size. In particular, Fieller’s method and conditional Poisson regression provide valid inference in small-sample settings, whereas standard Poisson regression is more suitable for larger datasets. Overall, this work emphasizes the importance of adjusting for both exposure and stratification, and provides practical guidance on selecting appropriate statistical methods for estimating incidence density ratios in applied research settings.