On an extension of the promotion time cure model

We consider the problem of estimating distribution time-to-event data that is subject to censoring and for which event interest might never occur, is, some subjects are cured. To model this kind in presence covariates, one leading semiparametric models promotion time cure (Stochastic Models Tumor Latency Their Biostatistical Applications (1996) World Scientific), adapts Cox cured subjects. Estimating conditional results a complicated constrained optimization problem, inference difficult as no closed-formula variance available. propose new model, inspired by leads simple estimation procedure presents closed formula variance. In paper, we show (i) contains special case with an exponential link, hence have simpler way estimate latter than what done so far literature; (ii) case, both estimators equal partial likelihood estimator under usual model; (iii) certain asymptotic properties when correct it misspecified; (iv) error LASSO type order log(nd)/n high-dimensional covariates dimension d sample size n. also study practical behaviour our means simulations, apply method breast cancer set.