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The Probability Distribution of the Kaplan-Meier Product-Limit Estimator and its Application to Bias and Interval Estimation
Qin, Yuxin
Qin, Yuxin
Abstract
Kaplan and Meier’s 1958 paper developed a nonparametric estimator of the survivor function from a right-censored data set. We devise two algorithms for determining the support values and calculating the support size for the Kaplan–Meier Product–Limit Estimator (KMPLE). We also derived a generalized formula to calculate the associated probability mass function for all sample sizes. The probability mass function is then applied to confirm the bias in the KMPLE as well as calculating the actual coverage functions for different confidence intervals. Finally, we investigated the concept of competing risks in a right-censored data set.
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2023-05-01
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5/8/2028
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Mathematics