A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models

This paper describes a generalised hybrid ML-EM algorithm for the calculation of maximum likelihood estimates in semiparametric shared frailty models, the Cox proportional hazard models with hazard functions multiplied by a (parametric) frailty random variable. This hybrid method is much faster than...

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Vydáno v:	Computational statistics & data analysis Ročník 40; číslo 1; s. 173 - 187
Hlavní autoři:	Vu, Hien T.V., Knuiman, Matthew W.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 28.07.2002 Elsevier Science Elsevier
Edice:	Computational Statistics & Data Analysis
Témata:	Applications Distribution theory Exact sciences and technology Frailty variance estimates Hybrid ML-EM Linear inference, regression Mathematics Medical sciences MLE Newton–Raphson Non-parametric hazards Parametric inference Probability and statistics Sciences and techniques of general use Shared frailties Simulations Statistics Simulations Shared frailties MLE Newton–Raphson EM Frailty variance estimates Hybrid ML-EM Non-parametric hazards ML Biometrics Normal variable Statistical distribution Variance estimation Large sample Gaussian distribution Non parametric estimation Statistical simulation Variance Semiparametric model Hypothesis test Statistical test Medical science Distribution function Simulation model Newton method Random variable Hazard Likelihood function Mixed distribution Asymptotic property Hazard function Covariance analysis Asymptotic behavior Semiparametric method Variance analysis Newton Raphson method Statistical method Statistical regression Cox model Simulation Asymptotic normality Small sample Asymptotic approximation Maximum likelihood EM algorithm Small sample property
ISSN:	0167-9473, 1872-7352
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Shrnutí:	This paper describes a generalised hybrid ML-EM algorithm for the calculation of maximum likelihood estimates in semiparametric shared frailty models, the Cox proportional hazard models with hazard functions multiplied by a (parametric) frailty random variable. This hybrid method is much faster than the standard EM method and faster than the standard direct maximum likelihood method (ML, Newton–Raphson) for large samples. We have previously applied this method to semiparametric shared gamma frailty models, and verified by simulations the asymptotic and small sample statistical properties of the frailty variance estimates. Let θ 0 be the true value of the frailty variance parameter. Then the asymptotic distribution is normal for θ 0>0 while it is a 50–50 mixture between a point mass at zero and a normal random variable on the positive axis for θ 0=0. For small samples, simulations suggest that the frailty variance estimates are approximately distributed as an x−(100− x)% mixture, 0⩽ x⩽50, between a point mass at zero and a normal random variable on the positive axis even for θ 0>0. In this paper, we apply this method and verify by simulations these statistical results for semiparametric shared log-normal frailty models. We also apply the semiparametric shared gamma and log-normal frailty models to Busselton Health Study coronary heart disease data.
ISSN:	0167-9473 1872-7352
DOI:	10.1016/S0167-9473(01)00099-8