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.
Description
Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. - PubMed - NCBI
%0 Journal Article
%1 Geskus:2011:Biometrics:20377575
%A Geskus, R B
%D 2011
%J Biometrics
%K CompetingRisks SurvivalAnalysis statistics
%N 1
%P 39-49
%R 10.1111/j.1541-0420.2010.01420.x
%T Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring
%U https://www.ncbi.nlm.nih.gov/pubmed/20377575
%V 67
%X 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{Geskus:2011:Biometrics:20377575,
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.},
added-at = {2019-10-27T09:43:52.000+0100},
author = {Geskus, R B},
biburl = {https://www.bibsonomy.org/bibtex/28291bdb575a9a77326b70f559c129878/jkd},
description = {Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. - PubMed - NCBI},
doi = {10.1111/j.1541-0420.2010.01420.x},
interhash = {667f9aaeffeee19337b4a3550509a6e7},
intrahash = {8291bdb575a9a77326b70f559c129878},
journal = {Biometrics},
keywords = {CompetingRisks SurvivalAnalysis statistics},
month = mar,
number = 1,
pages = {39-49},
pmid = {20377575},
timestamp = {2019-10-27T09:43:52.000+0100},
title = {Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring},
url = {https://www.ncbi.nlm.nih.gov/pubmed/20377575},
volume = 67,
year = 2011
}