The Markov process as a general method for nonparametric analysis of right-censored medical data

Argye Hillis, Maureen Maguire, Barbara S Hawkins, M. Marvin Newhouse

Research output: Contribution to journalArticle

Abstract

The product limit method of Kaplan and Meier for estimating survival functions and the logrank test of Mantel are widely employed for analysis of longitudinal medical data. Developed for analysis of one-time events such as death, survival analysis is also commonly adapted to more complex states such as loss of vision or cancer remission by restricting analysis to first occurrences. The nonparametric discrete time nonhomogeneous Markov process is proposed as a better model for any applications of the latter type. This simple stochastic model allows for an arbitrary number of possible states and for transitions in any direction. Maximum likelihood estimators are easily computed for the stochastic model and are identical to the product-limit estimates in the special case represented by the Kaplan-Meier model. The logrank test extends to evaluation of differences between populations with respect to any specified transition.

Original languageEnglish (US)
Pages (from-to)595-604
Number of pages10
JournalJournal of Chronic Diseases
Volume39
Issue number8
DOIs
StatePublished - 1986

Fingerprint

Markov Chains
Kaplan-Meier Estimate
Survival Analysis
Population
Neoplasms
Direction compound

ASJC Scopus subject areas

  • Epidemiology

Cite this

The Markov process as a general method for nonparametric analysis of right-censored medical data. / Hillis, Argye; Maguire, Maureen; Hawkins, Barbara S; Newhouse, M. Marvin.

In: Journal of Chronic Diseases, Vol. 39, No. 8, 1986, p. 595-604.

Research output: Contribution to journalArticle

Hillis, Argye ; Maguire, Maureen ; Hawkins, Barbara S ; Newhouse, M. Marvin. / The Markov process as a general method for nonparametric analysis of right-censored medical data. In: Journal of Chronic Diseases. 1986 ; Vol. 39, No. 8. pp. 595-604.
@article{829c6af7683c4887a96ffbe2d524efb2,
title = "The Markov process as a general method for nonparametric analysis of right-censored medical data",
abstract = "The product limit method of Kaplan and Meier for estimating survival functions and the logrank test of Mantel are widely employed for analysis of longitudinal medical data. Developed for analysis of one-time events such as death, survival analysis is also commonly adapted to more complex states such as loss of vision or cancer remission by restricting analysis to first occurrences. The nonparametric discrete time nonhomogeneous Markov process is proposed as a better model for any applications of the latter type. This simple stochastic model allows for an arbitrary number of possible states and for transitions in any direction. Maximum likelihood estimators are easily computed for the stochastic model and are identical to the product-limit estimates in the special case represented by the Kaplan-Meier model. The logrank test extends to evaluation of differences between populations with respect to any specified transition.",
author = "Argye Hillis and Maureen Maguire and Hawkins, {Barbara S} and Newhouse, {M. Marvin}",
year = "1986",
doi = "10.1016/0021-9681(86)90184-0",
language = "English (US)",
volume = "39",
pages = "595--604",
journal = "Journal of Clinical Epidemiology",
issn = "0895-4356",
publisher = "Elsevier USA",
number = "8",

}

TY - JOUR

T1 - The Markov process as a general method for nonparametric analysis of right-censored medical data

AU - Hillis, Argye

AU - Maguire, Maureen

AU - Hawkins, Barbara S

AU - Newhouse, M. Marvin

PY - 1986

Y1 - 1986

N2 - The product limit method of Kaplan and Meier for estimating survival functions and the logrank test of Mantel are widely employed for analysis of longitudinal medical data. Developed for analysis of one-time events such as death, survival analysis is also commonly adapted to more complex states such as loss of vision or cancer remission by restricting analysis to first occurrences. The nonparametric discrete time nonhomogeneous Markov process is proposed as a better model for any applications of the latter type. This simple stochastic model allows for an arbitrary number of possible states and for transitions in any direction. Maximum likelihood estimators are easily computed for the stochastic model and are identical to the product-limit estimates in the special case represented by the Kaplan-Meier model. The logrank test extends to evaluation of differences between populations with respect to any specified transition.

AB - The product limit method of Kaplan and Meier for estimating survival functions and the logrank test of Mantel are widely employed for analysis of longitudinal medical data. Developed for analysis of one-time events such as death, survival analysis is also commonly adapted to more complex states such as loss of vision or cancer remission by restricting analysis to first occurrences. The nonparametric discrete time nonhomogeneous Markov process is proposed as a better model for any applications of the latter type. This simple stochastic model allows for an arbitrary number of possible states and for transitions in any direction. Maximum likelihood estimators are easily computed for the stochastic model and are identical to the product-limit estimates in the special case represented by the Kaplan-Meier model. The logrank test extends to evaluation of differences between populations with respect to any specified transition.

UR - http://www.scopus.com/inward/record.url?scp=0022504884&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022504884&partnerID=8YFLogxK

U2 - 10.1016/0021-9681(86)90184-0

DO - 10.1016/0021-9681(86)90184-0

M3 - Article

C2 - 3525597

AN - SCOPUS:0022504884

VL - 39

SP - 595

EP - 604

JO - Journal of Clinical Epidemiology

JF - Journal of Clinical Epidemiology

SN - 0895-4356

IS - 8

ER -