Efficient median estimation for stratified multi-population data: health services, medical workforce, and medical education

This paper addresses the problem of robust median estimation in stratified two-phase sampling for the analysis of medical data, where population heterogeneity, skewness, and outliers commonly reduce estimator efficiency. In order to address these difficulties, we suggest an improved type of transformation based estimators aimed at making the estimations of central tendencies of medical measurements more stable and precise. The method is a strong mixture of central tendency measures and transformations, the Winsorized mean, Hodges Lehmann estimator, trimmed mean, and Gini mean difference to enhance the efficacy and preserving the extreme values resistance. With a first order Taylor series expansion, we get expressions of bias and mean squared error and optimal conditions of efficiency are obtained. The extensive Monte Carlo raises using gamma, lognormal, exponential, and Cauchy distributions, inspired by the common distributions in medical exposure data, and studies of actual medical data-sets all indicate that the proposed estimators have lower mean squared errors and higher percent relative efficiencies than previous ratio, difference estimators, and exponential estimators. These results highlight the practicality of transformation based techniques for obtaining reliable median estimates in medical research and applied sciences.