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Semiparametric Estimation of Random Effects Using the Cox Model Based on the EM Algorithm

John P. Klein
Biometrics
Vol. 48, No. 3 (Sep., 1992), pp. 795-806
DOI: 10.2307/2532345
Stable URL: http://www.jstor.org/stable/2532345
Page Count: 12
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Semiparametric Estimation of Random Effects Using the Cox Model Based on the EM Algorithm
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Abstract

Consider a survival experiment where individuals within a certain subset of the population share a common, unobservable, random frailty. Such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households. Suppose that if the frailty, ω, is known, the Cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate. Assuming that the random frailties follow a gamma distribution, estimates of the fixed and random effects are obtained by using an EM algorithm based on a profile likelihood construction. The method developed is applied to the Framingham Heart Study to examine the risks of smoking and cholesterol levels, adjusting for potential random effects.

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