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Bayesian path specific frailty models for multi‐state survival data with applications
Author(s) -
de Castro Mário,
Chen MingHui,
Zhang Yuanye
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.12298
Subject(s) - bayesian probability , gibbs sampling , computer science , posterior probability , path (computing) , data mining , data set , bone marrow transplant , bayesian inference , econometrics , statistics , algorithm , bone marrow transplantation , mathematics , artificial intelligence , medicine , transplantation , surgery , programming language
Summary Multi‐state models can be viewed as generalizations of both the standard and competing risks models for survival data. Models for multi‐state data have been the theme of many recent published works. Motivated by bone marrow transplant data, we propose a Bayesian model using the gap times between two successive events in a path of events experienced by a subject. Path specific frailties are introduced to capture the dependence structure of the gap times in the paths with two or more states. Under improper prior distributions for the parameters, we establish propriety of the posterior distribution. An efficient Gibbs sampling algorithm is developed for drawing samples from the posterior distribution. An extensive simulation study is carried out to examine the empirical performance of the proposed approach. A bone marrow transplant data set is analyzed in detail to further demonstrate the proposed methodology.