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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| Veröffentlicht in: | Computational statistics Jg. 30; H. 4; S. 1097 - 1109 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Springer Berlin Heidelberg
01.12.2015
Springer Nature B.V |
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| ISSN: | 0943-4062, 1613-9658 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Yang, Yifan Zhou, Mai |
| Author_xml | – sequence: 1 givenname: Mai surname: Zhou fullname: Zhou, Mai organization: Department of Statistics, University of Kentucky – sequence: 2 givenname: Yifan surname: Yang fullname: Yang, Yifan email: yifan.yang@uky.edu organization: Department of Statistics, University of Kentucky |
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| Cites_doi | 10.1080/01621459.1958.10501452 10.1093/biomet/69.3.521 10.1201/9781420036152 10.1093/biomet/75.2.237 10.1198/106186005X59270 10.1016/S0378-3758(98)00156-6 10.1080/10629360600890998 10.1016/0167-7152(94)00210-Y 10.1016/j.jmva.2007.02.007 10.1214/aos/1031594729 10.1080/01621459.1975.10480315 |
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| DOI | 10.1007/s00180-015-0567-9 |
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| References | Pan, Zhou (CR8) 1999; 75 CR9 CR12 Li (CR3) 1995; 25 Miller, Halpern (CR4) 1982; 69 Owen (CR7) 2001 Kaplan, Meier (CR2) 1958; 53 Owen (CR6) 1988; 75 Zhou, Li (CR13) 2008; 99 Chen, Zhou (CR1) 2007; 77 Zhou (CR11) 2005; 14 Murphy, van der Vaart (CR5) 1997; 25 Thomas, Grunkemeier (CR10) 1975; 70 567_CR9 M Zhou (567_CR13) 2008; 99 SA Murphy (567_CR5) 1997; 25 AB Owen (567_CR7) 2001 AB Owen (567_CR6) 1988; 75 EL Kaplan (567_CR2) 1958; 53 K Chen (567_CR1) 2007; 77 G Li (567_CR3) 1995; 25 DR Thomas (567_CR10) 1975; 70 R Miller (567_CR4) 1982; 69 XR Pan (567_CR8) 1999; 75 567_CR12 M Zhou (567_CR11) 2005; 14 |
| References_xml | – volume: 53 start-page: 457 issue: 282 year: 1958 end-page: 481 ident: CR2 article-title: Nonparametric estimation from incomplete observations publication-title: J Am Stat Assoc doi: 10.1080/01621459.1958.10501452 – volume: 69 start-page: 521 issue: 3 year: 1982 end-page: 531 ident: CR4 article-title: Regression with censored data publication-title: Biometrika doi: 10.1093/biomet/69.3.521 – year: 2001 ident: CR7 publication-title: Empirical likelihood doi: 10.1201/9781420036152 – volume: 75 start-page: 237 issue: 2 year: 1988 end-page: 249 ident: CR6 article-title: Empirical likelihood ratio confidence intervals for a single functional publication-title: Biometrika doi: 10.1093/biomet/75.2.237 – ident: CR12 – volume: 14 start-page: 643 issue: 3 year: 2005 end-page: 656 ident: CR11 article-title: Empirical likelihood ratio with arbitrarily censored/truncated data by em algorithm publication-title: J Comput Gr Stat doi: 10.1198/106186005X59270 – volume: 75 start-page: 379 issue: 2 year: 1999 end-page: 392 ident: CR8 article-title: Using one-parameter sub-family of distributions in empirical likelihood ratio with censored data publication-title: J Stat Plan Inference doi: 10.1016/S0378-3758(98)00156-6 – ident: CR9 – volume: 77 start-page: 1033 issue: 12 year: 2007 end-page: 1042 ident: CR1 article-title: Computation of the empirical likelihood ratio from censored data publication-title: J Stat Comput Simul doi: 10.1080/10629360600890998 – volume: 25 start-page: 95 issue: 2 year: 1995 end-page: 104 ident: CR3 article-title: On nonparametric likelihood ratio estimation of survival probabilities for censored data publication-title: Stat Probab Lett doi: 10.1016/0167-7152(94)00210-Y – volume: 99 start-page: 649 issue: 4 year: 2008 end-page: 664 ident: CR13 article-title: Empirical likelihood analysis of the Buckley–James estimator publication-title: J Multivar Anal doi: 10.1016/j.jmva.2007.02.007 – volume: 25 start-page: 1471 year: 1997 end-page: 1509 ident: CR5 article-title: Semiparametric likelihood ratio inference publication-title: The Annals of Statistics doi: 10.1214/aos/1031594729 – volume: 70 start-page: 865 issue: 352 year: 1975 end-page: 871 ident: CR10 article-title: Confidence interval estimation of survival probabilities for censored data publication-title: J Am Stat Assoc doi: 10.1080/01621459.1975.10480315 – volume: 77 start-page: 1033 issue: 12 year: 2007 ident: 567_CR1 publication-title: J Stat Comput Simul doi: 10.1080/10629360600890998 – volume-title: Empirical likelihood year: 2001 ident: 567_CR7 doi: 10.1201/9781420036152 – volume: 53 start-page: 457 issue: 282 year: 1958 ident: 567_CR2 publication-title: J Am Stat Assoc doi: 10.1080/01621459.1958.10501452 – volume: 25 start-page: 1471 year: 1997 ident: 567_CR5 publication-title: The Annals of Statistics doi: 10.1214/aos/1031594729 – ident: 567_CR12 – volume: 99 start-page: 649 issue: 4 year: 2008 ident: 567_CR13 publication-title: J Multivar Anal doi: 10.1016/j.jmva.2007.02.007 – volume: 25 start-page: 95 issue: 2 year: 1995 ident: 567_CR3 publication-title: Stat Probab Lett doi: 10.1016/0167-7152(94)00210-Y – volume: 69 start-page: 521 issue: 3 year: 1982 ident: 567_CR4 publication-title: Biometrika doi: 10.1093/biomet/69.3.521 – volume: 75 start-page: 237 issue: 2 year: 1988 ident: 567_CR6 publication-title: Biometrika doi: 10.1093/biomet/75.2.237 – ident: 567_CR9 – volume: 14 start-page: 643 issue: 3 year: 2005 ident: 567_CR11 publication-title: J Comput Gr Stat doi: 10.1198/106186005X59270 – volume: 70 start-page: 865 issue: 352 year: 1975 ident: 567_CR10 publication-title: J Am Stat Assoc doi: 10.1080/01621459.1975.10480315 – volume: 75 start-page: 379 issue: 2 year: 1999 ident: 567_CR8 publication-title: J Stat Plan Inference doi: 10.1016/S0378-3758(98)00156-6 |
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| SubjectTerms | 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 |
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| Title | A recursive formula for the Kaplan–Meier estimator with mean constraints and its application to empirical likelihood |
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