Estimating the marginal survival function in the presence of time dependent covariates
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.
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Volume (Year): 54 (2001)
Issue (Month): 4 (October)
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- Zhou, Mai, 1999. "Regression analysis with censored data: Extensions of Koul-Susarla-Van Ryzin approach," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 229-236, February.
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