A Semiparametric Logistic/Proportional-Mean Residual Life Mixture Model With Auxiliary Covariate

As biological studies become more expensive to conduct,it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured.In the research of some diseases,there usually exists a substantial fraction of long-term survivors who are either cured or immune to the disease.In this paper,we proposed a induced cure rate mean residual life time regression model to accommodate the survival data with a cure fraction and auxiliary covariate,in which the exposure variable is assessed only in a validation set,but a continuous auxiliary covariate for it is ascertained for all subjects in the study cohort.In a mixture formulation,we apply the logistic regression for the indicators of whether patients are susceptible and a proportional mean residual life regression to model the residual survival times of susceptible subjects,using a nonparametric kernel smoothing estimator and generalized estimating equation method for model parametric.Under the frame of logistic/proportional-mean residual life mixture model,we propose to estimate the induced cure rate and relative mean residual life function in the nonvalidation set through kernel smoothing method and then obtain an induced estimating equation.Simulation studies show the practical performance of the proposed method under finite samples,and in addition,we demonstrate the method with a heart disease data from the Study of Left Ventricular Dysfunction(SOLVD).