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Ronald B. Geskus, PhD

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Censoring and truncation: inverse probability weighted estimators of survival

  • FDM-Seminar
Wann 09.12.2011
von 11:15 bis 12:45
Wo Eckerstr.1, Raum 404
Kontakttelefon 0761-2037701
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R.B. Geskus, PhD
biostatistician, Amsterdam Health Service/Academic Medical Center

The hazard has been the basis for non- and semiparametric estimation of survival with (right) censored and (left) truncated data, as reflected in the dominant use of the Kaplan-Meier estimator and the Cox proportional hazards model. We show that the Kaplan-Meier has an equivalent representation as an inverse probability weighted empirical cumulative distribution function (ipw-ecdf), which has an immediate extension to the competing risks setting. The weights in this ipw-ecdf form suggest an estimator of the subdistribution hazard in the situation of competing risks. The resulting nonparametric product-limit estimator is also equivalent to the standard nonparametric estimator for the cause specific cumulative incidence function. Furthermore, by using the proper filtration, a martingale property is derived for the weighted counting process that corresponds to the subdistribution. Using this martingale property, several results and proofs from standard survival analysis are easily extended to the competing risks setting. As an example, we briefly discuss asymptotics in the proportional subdistribution hazards model.



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