A recursive formula for the Kaplan–Meier estimator with mean constraints and its application to empirical likelihood

The Kaplan–Meier estimator is very popular in analysis of survival data. However, it is not easy to compute the ‘constrained’ Kaplan–Meier. Current computational method uses expectation-maximization algorithm to achieve this, but can be slow at many situations. In this note we give a recursive compu...

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Bibliographic Details
Published in:Computational statistics Vol. 30; no. 4; pp. 1097 - 1109
Main Authors: Zhou, Mai, Yang, Yifan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015
Springer Nature B.V
Subjects:
Algorithms
Computation
Constraints
Economic Theory/Quantitative Economics/Mathematical Methods
Empirical analysis
Estimators
Lagrange multiplier
Mathematical analysis
Mathematics and Statistics
Original Paper
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Random variables
Recursive
Statistics
Empirical likelihood ratio
NPMLE
Right censored data
Wilks test
ISSN:0943-4062, 1613-9658
Online Access:Get full text
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Summary:The Kaplan–Meier estimator is very popular in analysis of survival data. However, it is not easy to compute the ‘constrained’ Kaplan–Meier. Current computational method uses expectation-maximization algorithm to achieve this, but can be slow at many situations. In this note we give a recursive computational algorithm for the ‘constrained’ Kaplan–Meier estimator. The constraint is assumed given in linear estimating equations or mean functions. We also illustrate how this leads to the empirical likelihood ratio test with right censored data. Speed comparison to the EM based algorithm favours the current procedure.
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ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-015-0567-9