Cause-Specific Cumulative Incidence Estimation and the Fine and Gray Model under Both Left Truncation and Right Censoring. Geskus, R. B. Biometrics, 67(1):39-49, 2011. doi abstract bibtex Summary The standard estimator for the cause-specific cumulative incidence function in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is a weighted empirical cumulative distribution function and the other a product-limit estimator. This equivalence suggests an alternative view of the analysis of time-to-event data with left truncation and right censoring: individuals who are still at risk or experienced an earlier competing event receive weights from the censoring and truncation mechanisms. As a consequence, inference on the cumulative scale can be performed using weighted versions of standard procedures. This holds for estimation of the cause-specific cumulative incidence function as well as for estimation of the regression parameters in the Fine and Gray proportional subdistribution hazards model. We show that, with the appropriate filtration, a martingale property holds that allows deriving asymptotic results for the proportional subdistribution hazards model in the same way as for the standard Cox proportional hazards model. Estimation of the cause-specific cumulative incidence function and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time-dependent weights. We show the implementation in the R statistical package. The proportional subdistribution hazards model is used to investigate the effect of calendar period as a deterministic external time varying covariate, which can be seen as a special case of left truncation, on AIDS related and non-AIDS related cumulative mortality.
@article{ges11cau,
title = {Cause-Specific Cumulative Incidence Estimation and the {{Fine}} and {{Gray}} Model under Both Left Truncation and Right Censoring},
volume = {67},
abstract = {Summary The standard estimator for the cause-specific cumulative incidence function in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is a weighted empirical cumulative distribution function and the other a product-limit estimator. This equivalence suggests an alternative view of the analysis of time-to-event data with left truncation and right censoring: individuals who are still at risk or experienced an earlier competing event receive weights from the censoring and truncation mechanisms. As a consequence, inference on the cumulative scale can be performed using weighted versions of standard procedures. This holds for estimation of the cause-specific cumulative incidence function as well as for estimation of the regression parameters in the Fine and Gray proportional subdistribution hazards model. We show that, with the appropriate filtration, a martingale property holds that allows deriving asymptotic results for the proportional subdistribution hazards model in the same way as for the standard Cox proportional hazards model. Estimation of the cause-specific cumulative incidence function and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time-dependent weights. We show the implementation in the R statistical package. The proportional subdistribution hazards model is used to investigate the effect of calendar period as a deterministic external time varying covariate, which can be seen as a special case of left truncation, on AIDS related and non-AIDS related cumulative mortality.},
number = {1},
journal = {Biometrics},
doi = {10.1111/j.1541-0420.2010.01420.x},
author = {Geskus, Ronald B.},
year = {2011},
keywords = {survival-analysis,competing-risks,subdistribution-hazard,inverse-probability-weight},
pages = {39-49},
citeulike-article-id = {13265927},
citeulike-linkout-0 = {http://dx.doi.org/10.1111/j.1541-0420.2010.01420.x},
posted-at = {2014-07-14 14:10:07},
priority = {0}
}
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