Robust prediction of the cumulative incidence function under non-proportional subdistribution hazards

Prediction of a cause-specific cumulative incidence function (CIF) for data containing competing risks is of primary interest to clinicians when making treatment decisions for patients given their prognostic characteristics. The Fine–Gray regression model is widely used to incorporate multiple prognostic factors, yet it is not applicable when the assumption of proportional subdistribution hazards (PSH) does not hold. In this study we investigate the properties of the partial-likelihood estimator from the Fine–Gray model under non-proportionality and propose a robust risk prediction procedure that is not sensitive to the assumption and is more favourable in practice because it bypasses the complicated modelling of time-varying covariate effects. We evaluate the prediction performance of our procedure in simulations and demonstrate an application in predicting the absolute risk of locoregional recurrence for breast cancer patients, given a set of prognostic factors in which not all of them satisfy the PSH assumption. The Canadian Journal of Statistics xx: 1–15; 2016 © 2016 Statistical Society of Canada Resume L'estimation de la fonction d'incidence cumulative (FIC) pour des risques concurrents importe aux cliniciens lorsqu'ils prennent des decisions avec leurs patients selon les caracteristiques de leur pronostic. Le modele de regression de Fine-Gray est largement utilise pour tenir compte des facteurs pronostiques meme s'il devient inapplicable lorsque l'hypothese de proportionnalite des risques de chaque sous-distribution (PRSD) est inadequate. Les auteurs etudient les proprietes de l'estimateur au maximum de vraisemblance partielle du modele de Fine-Gray dans le cas de non-proportionalite et proposent une procedure de prevision des risques robuste qui est insensible aux problemes de PRSD et qui elimine l’etape de modelisation des covariables dynamiques sur le plan temporel. Ils evaluent la performance de leur procedure pour la prevision a l'aide de simulations et presentent une application ou le risque absolu de recurrence loco-regionale du cancer du sein est predit chez des patientes en tenant compte de leurs facteurs pronostiques qui ne satisfont pas tous l'hypothese de PRSD. La revue canadienne de statistique xx: 1–15; 2016 © 2016 Societe statistique du Canada

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