Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Statistics

Background:

• Survival analysis is crucial in medical research, often employing methods like Kaplan-Meier estimation.
• Traditional methods assume simple random sampling, which may not be feasible or efficient in all scenarios.
• Partially Rank-Ordered Set (PROS) sampling offers an alternative when exact measurements are costly, utilizing ranked observations.

Purpose of the Study:

• To develop and evaluate a novel nonparametric estimation methodology for survival probability under random censoring using PROS sampling.
• To adapt the Kaplan-Meier estimator for rank-based sampling designs where data are not identically distributed.
• To assess the performance of the proposed estimator against traditional methods in simulation and real-world data.

Main Methods:

• Derivation of the asymptotic distribution of the Kaplan-Meier estimator under a PROS sampling design.
• Implementation of the proposed methodology for nonparametric survival probability estimation.
• Conducting simulation studies to compare the performance of the novel estimator with estimators from simple random samples.
• Application of the developed methods to a real dataset from a hematological disorder study.

Main Results:

• The proposed estimator derived under PROS sampling demonstrates superior performance compared to its counterpart under simple random sampling (SRS).
• Simulation studies confirm the efficiency and robustness of the novel estimation method.
• The methodology is successfully applied to a real-world hematological disorder dataset, showing practical utility.

Conclusions:

• The novel methodology provides a more accurate and efficient approach to survival probability estimation in situations involving PROS sampling.
• This research extends the applicability of survival analysis techniques to complex sampling designs common in medical and other scientific fields.
• The findings suggest that rank-based sampling designs, when appropriately handled, can yield improved results over simple random sampling for survival estimation.