Enhancing precision in breast cancer diagnosis using Tailored Ratio-Integrated Variance Estimation using Neyman allocation Implementation(TRIVENI).

In stratified random sampling, precise variance estimation is essential especially when supplementary information is provided. This article presents an innovative Tailored Ratio-Integrated Variance Estimation employing Neyman Allocation Implementation (TRIVENI), which effectively combines ratio-based modifications to improve variance estimation. Despite traditional methods, TRIVENI leverages two auxiliary variables in multiple ways to measure the combined effect on population variance estimations. Applying Neyman allocation, it effectively distributes the sample among strata, ensuring minimal variance and improved precision. The combined use of ratio estimation promotes the application of auxiliary information, hence reducing estimate bias and enhancing accuracy. Theoretical derivations and simulation studies confirm that TRIVENI surpasses traditional estimators, demonstrating improved efficiency in various stratification contexts. The proposed methodology signifies a significant advancement in stratified variance estimation, rendering it a crucial instrument for survey sampling experts and researchers.