A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models - Vu, Hien T.V.; Knuiman, Matthew W. (Computational statistics & data analysis, 2002)
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.