Valid overall odds ratio estimators using different stratified sampling schemes

The study presents valid estimators for determining the overall odds ratio between two independent groups within stratified populations, utilizing both simple stratified sampling (SSRS) and stratified ranked set sampling (SRSS) methodologies. Through analytical derivations, we establish the expected values and variances for these estimators. Two distinct types of estimators namely, the naive weighted and the Cochran Mantel-Haenszel-Haenszel approaches are thoroughly examined. Our investigation encompasses an in-depth analysis of the expectation and variance of these estimators, shedding light on their performance characteristics. Through intensive simulation experiments, we discern that estimators based on SRSS exhibit notable advantages over their SSRS counterparts. To validate the efficacy of our proposed estimators, we conduct an empirical assessment utilizing data from the (2009-2010) National Health and Nutrition Examination Survey (NHANES). Through this analysis, we glean insights into the performance of the estimators in a real-world context. In summary, our study contributes valuable insights into the estimation of the overall odds ratio within stratified populations. By comparing SSRS and SRSS methodologies and evaluating different estimation approaches, we provide researchers with robust tools for analyzing odds ratios in diverse settings. Moreover, our empirical validation using NHANES data underscores the practical utility of the proposed estimators in real-world applications.