A penalized likelihood approach for mixture cure models.

Cure models have been developed to analyze failure time data with a cured fraction. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. Mixture cure models assume that the studied population is a mixture of susceptible individuals, who may experience the event of interest, and non-susceptible individuals that will never experience it. Important issues in mixture cure models are estimation of the baseline survival function for susceptibles and estimation of the variance of the regression parameters. The aim of this paper is to propose a penalized likelihood approach, which allows for flexible modeling of the hazard function for susceptible individuals using M-splines. This approach also permits direct computation of the variance of parameters using the inverse of the Hessian matrix. Properties and limitations of the proposed method are discussed and an illustration from a cancer study is presented.