Abstract
In this thesis, we first introduce four different approaches in case-control studies with the association of confounding and interaction effect and then compare their sample sizes based on normal approximation for a specified power at a certain significance level. These approaches are: (1) an unmatched design with an unstratified analysis; (2) an unmatched design with a stratified analysis; (3) a matched design with an unstratified analysis; (4) a matched design with a stratified analysis. We also develop the analysis for case-control studies with two exposure variables using maximum likelihood method. Calculation of sample size required to detect the interaction effect between two exposure variables in the presence of a confounding variable.