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Proportional hazards model with random effects
Author(s) -
Vaida Florin,
Xu Ronghui
Publication year - 2000
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/1097-0258(20001230)19:24<3309::aid-sim825>3.0.co;2-9
Subject(s) - random effects model , mathematics , markov chain monte carlo , statistics , multivariate statistics , monte carlo method , medicine , meta analysis
We propose a general proportional hazards model with random effects for handling clustered survival data. This generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk, in a way similar to the modelling of random effects in linear, generalized linear and non‐linear mixed models. The distribution of the random effects is generally assumed to be multivariate normal, but other (preferably symmetrical) distributions are also possible. Maximum likelihood estimates of the regression parameters, the variance components and the baseline hazard function are obtained via the EM algorithm. The E‐step of the algorithm involves computation of the conditional expectations of functions of the random effects, for which we use Markov chain Monte Carlo (MCMC) methods. Approximate variances of the estimates are computed by Louis' formula, and posterior expectations and variances of the individual random effects can be obtained as a by‐product of the estimation. The inference procedure is exemplified on two data sets. Copyright © 2000 John Wiley & Sons, Ltd.