A Comparative Study of the Estimation Methods on Frailty Mixture Survival Model

Abstract

Frailty mixture survival models are statistical models which allow for a cured fraction and frailty. The cured fraction refers to a proportion of individuals who are expected not to experience the event of interest, while frailty refers to unobserved information amongst the individuals who experience the event of interest. In this study, we extend the frailty mixture survival model by including covariates into the frailty part of the model. We also employed both semiparametric and parametric methods in Gamma frailty mixture model. Using parametric method, the baseline survival function is assumed to follow Weibull distribution, while using semiparametric method, the cummulative baseline hazard function is assumed to be unknown since in some cases a parametric assumtionis diffuclt to justify. Estimation methods based on EM-algorithm and newton-raphson are utilized to obtain the maximum likelihood estimates of the unknown model parameters involved in both the semiparametric and parametric model. The study aims to compare the performance of estimators using these two methods in terms of their accuracy and efficiency measures. Keywords: Cured fraction; Frailty; EM-algorithm; Maximum Likelihood; Semiparametric; Para- metric 2010 Mathematics Subject Classification: 62N02