document: 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 -LRB- parametric -RRB- frailty random variable . This hybrid method is much faster than the standard EM method and faster than the standard direct maximum likelihood method -LRB- ML , Newton-Raphson -RRB- 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 theta / sub 0 / be the true value of the frailty variance parameter . Then the asymptotic distribution is normal for theta / sub 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 theta / sub 0 / = 0 . For small samples , simulations suggest that the frailty variance estimates are approximately distributed as an x - -LRB- 100-x -RRB- % mixture , 0 < or = x < or = 50 , between a point mass at zero and a normal random variable on the positive axis even for theta / sub 0 / > 0 . 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
doc_bio_tags: O O O O O O O B I I O O O O O O O O O O O O O O O O O B I I O O O O O O O B I I I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O B O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B I I B I I I
extractive_keyphrases: maximum likelihood estimates cox proportional hazard models busselton health study coronary heart disease data hazard functions simulations frailty variance estimates asymptotic distribution normal random variable
abstractive_keyphrases: hybrid ml-em algorithm data analysis normal distribution semiparametric shared log-normal frailty models