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


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


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.

Suggested Citation

  • Satten, Glen A. & Datta, Somnath & Robins, James, 2001. "Estimating the marginal survival function in the presence of time dependent covariates," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 397-403, October.
  • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:397-403

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    References listed on IDEAS

    1. 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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    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. 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.
    3. 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.
    4. 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.
    5. Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-40, May.
    6. 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.
    7. Maja Pohar Perme & Janez Stare & Jacques Estève, 2012. "On Estimation in Relative Survival," Biometrics, The International Biometric Society, vol. 68(1), pages 113-120, March.


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