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


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  • Satten, Glen A.
  • Datta, Somnath
  • Robins, James
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 54 (2001)
    Issue (Month): 4 (October)
    Pages: 397-403

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    Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:397-403

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    Keywords: Aalen's linear hazard model Informative censoring Non-parametric estimation Right censoring Survival analysis;


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    Cited by:
    1. Subramanian, Sundarraman & Bandyopadhyay, Dipankar, 2010. "Doubly robust semiparametric estimation for the missing censoring indicator model," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 621-630, April.
    2. Datta, Somnath & Satten, Glen A., 2001. "Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 403-411, December.
    3. Shen, Pao-sheng, 2010. "Semiparametric estimation of survival function when data are subject to dependent censoring and left truncation," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 161-168, February.
    4. Fan, Jie & Datta, Somnath, 2011. "Fitting marginal accelerated failure time models to clustered survival data with potentially informative cluster size," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3295-3303, December.
    5. Tchetgen Tchetgen, Eric J. & Robins, James, 2012. "On parametrization, robustness and sensitivity analysis in a marginal structural Cox proportional hazards model for point exposure," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 907-915.


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