Weighted NPMLE for the Subdistribution of a Competing Risk

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Anna Bellach, Michael R Kosorok, Ludger Rüschendorf, Jason P Fine

Direct regression modeling of the subdistribution has become popular for analyzing data with multiple, competing event types. All general approaches so far are based on non-likelihood based procedures and target covariate effects on the subdistribution. We introduce a novel weighted likelihood function that allows for a direct extension of the Fine-Gray model to a broad class of semiparametric regression models. The model accommodates time-dependent covariate effects on the subdistribution hazard. To motivate the proposed likelihood method, we derive standard nonparametric estimators and discuss a new interpretation based on pseudo risk sets. We establish consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. In comprehensive simulation studies we demonstrate the solid performance of the weighted NPMLE in the presence of independent right censoring. We provide an application to a very large bone marrow transplant dataset, thereby illustrating its practical utility.

Original languageEnglish
JournalJournal of the American Statistical Association
Issue number525
Pages (from-to)259-270
Number of pages12
Publication statusPublished - 2019

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