Estimating the marginal survival function in the presence of time dependent covariates

Abstract

We propose a new estimator of the marginal (overall) survival function of failure times that is in the class of survival function estimators proposed by Robins (Proceedings of the American Statistical Association—Biopharmaceutical Section, 1993, p. 24). These estimators are appropriate when, in addition to (right-censored) failure times, we also observe covariates for each individual that affect both the hazard of failure and the hazard of being censored. The observed data are re-weighted at each failure time t according to Aalen's linear model of the cumulative hazard for being censored at some time greater than or equal to t given each individual's covariates; then, a product-limit estimator is calculated using the weighted data. When covariates have no effect on censoring times, our estimator reduces to the ordinary Kaplan–Meier estimator. An expression for its asymptotic variance formula is obtained using martingale techniques.