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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

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.

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

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    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. Somnath Datta & Glen A. Satten, 2002. "Estimation of Integrated Transition Hazards and Stage Occupation Probabilities for Non-Markov Systems Under Dependent Censoring," Biometrics, The International Biometric Society, vol. 58(4), pages 792-802, December.
    2. 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.
    3. Richard J. Cook & Jerald F. Lawless, 2020. "Failure time studies with intermittent observation and losses to follow‐up," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1035-1063, December.
    4. Brent A. Johnson & Anastasios A. Tsiatis, 2004. "Estimating Mean Response as a Function of Treatment Duration in an Observational Study, Where Duration May Be Informatively Censored," Biometrics, The International Biometric Society, vol. 60(2), pages 315-323, June.
    5. 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.
    6. 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.
    7. 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.
    8. Pablo Gonzalez Ginestet & Ales Kotalik & David M. Vock & Julian Wolfson & Erin E. Gabriel, 2021. "Stacked inverse probability of censoring weighted bagging: A case study in the InfCareHIV Register," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 51-65, January.
    9. 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.
    10. 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.
    11. 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.

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