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

Frailty mixture survival models are statistical models which allow for acured fraction and frailty. The cured fraction refers to a proportion of individuals whoare expected not to experience the event of interest, while frailty refers to unobservedinformation amongst the individuals who experience the event of interest. In thisstudy, we extend the frailty mixture survival model by including covariates into thefrailty part of the model. We also employed both semiparametric and parametricmethods in Gamma frailty mixture model. Using parametric method, the baselinesurvival function is assumed to follow Weibull distribution, while usingsemiparametric method, the cummulative baseline hazard function is assumed to beunknown since in some cases a parametric assumtionis diffuclt to justify. Estimationmethods based on EM-algorithm and newton-raphson are utilized to obtain themaximum likelihood estimates of the unknown model parameters involved in both thesemiparametric and parametric model. The study aims to compare the performance ofestimators using these two methods in terms of their accuracy and efficiency measures.