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

Samane Nematolahi1, Sahar Nazari2, Zahra Shayan1

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This study introduces a new method for survival probability estimation using Partially Rank-Ordered Set (PROS) sampling. This novel approach improves accuracy compared to traditional simple random sampling in medical studies.

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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.