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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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 40; no. 1; pp. 173 - 187
Main Authors: Vu, Hien T.V., Knuiman, Matthew W.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 28.07.2002
Elsevier Science
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
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
Online Access:Get full text
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Summary: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