Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Magdalena Niewiadomska-Bugaj

Second Advisor

Dr. Joshua Naranjo

Third Advisor

Dr. Hyun Bin Kang

Fourth Advisor

Dr. Duy Ngo


Odds ratio, contingency table, small samples, bias correction


This study is focusing on properties of estimators of odds ratio or its logarithm in case of 2x2 tables with small counts. The odds ratio represents the odds that an outcome of interest will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure. Both parameters are often used to quantify the strength of association of two binary variables and are common measurements reported in case-control, cohort, and cross-sectional studies.

Because of their wide applicability, both parameters, odds ratio, and its logarithm, have been intensively studied in the literature. However, most of their desirable properties are based on the asymptotic normality of the estimators which are not necessarily true in case of small sample sizes. In addition, contingency tables with small counts often contain cells with counts that equal zero which makes maximum likelihood estimators of odds ratio and its logarithm undefined. While in many research areas it is possible to collect data of the size needed, there are areas, such as health related multi-center research, where sample size cannot be increased.

We are studying performance of estimators of odds ratio, and its logarithm, for independent 2x2 tables with small counts. Among other applications, our conclusions could also serve as recommendations for comparison of odds ratios in multiple 2x2 tables—a step necessary before performing meta-analysis.


Fifth Advisor: Dr. Clifton Edgar Ealy

Access Setting

Dissertation-Open Access