title: Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring.
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.
authors.affiliation: Academic Medical Center, Department of Clinical Epidemiology, Biostatistics and Bioinformatics, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands. statistics@inter.nl.net
authors.forename: Ronald B
authors.initials: RB
authors.lastname: Geskus
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000401:mortality*; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015994:Incidence; D008297:Male; D015233:Models, Statistical; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods; D012307:Risk Factors; D016019:Survival Analysis; D015996:Survival Rate; D014481:United States / Q000453:epidemiology