Estimation and Asymptotic Theory for Transition Probabilities in Markov Renewal Multi-State Models

In this paper we discuss estimation of transition probabilities for semi–Markov multi–state models. Non–parametric and semi–parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional delta...

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Bibliographic Details
Published in:The international journal of biostatistics Vol. 8; no. 1; pp. 23 - 61
Main Authors: Spitoni, Cristian, Verduijn, Marion, Putter, Hein
Format: Journal Article
Language:English
Published: Germany De Gruyter 07.08.2012
Walter de Gruyter GmbH
Subjects:
Adult
Biostatistics - methods
functional delta–method
Humans
Markov Chains
Middle Aged
Models, Statistical
semi–markov processes
Statistics, Nonparametric
Survival Analysis
ISSN:1557-4679, 2194-573X, 1557-4679
Online Access:Get full text
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Summary:In this paper we discuss estimation of transition probabilities for semi–Markov multi–state models. Non–parametric and semi–parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional delta method and the use of resampling is proposed to derive confidence bands for the transition probabilities. The last part of the paper concerns the presentation of the main ideas of the R implementation of the proposed estimators, and data from a renal replacement study are used to illustrate the behavior of the estimators proposed.
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ISSN:1557-4679
2194-573X
1557-4679
DOI:10.1515/1557-4679.1375