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Transition probability estimates for non‐Markov multi‐state models
Author(s) -
Titman Andrew C.
Publication year - 2015
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12349
Subject(s) - estimator , markov chain , univariate , generalization , statistics , markov model , mathematics , markov property , econometrics , computer science , multivariate statistics , mathematical analysis
Summary Non‐parametric estimation of the transition probabilities in multi‐state models is considered for non‐Markov processes. Firstly, a generalization of the estimator of Pepe et al., (1991) (Statistics in Medicine) is given for a class of progressive multi‐state models based on the difference between Kaplan–Meier estimators. Secondly, a general estimator for progressive or non‐progressive models is proposed based upon constructed univariate survival or competing risks processes which retain the Markov property. The properties of the estimators and their associated standard errors are investigated through simulation. The estimators are demonstrated on datasets relating to survival and recurrence in patients with colon cancer and prothrombin levels in liver cirrhosis patients.