Fine-Gray subdistribution hazard models to simultaneously estimate the absolute risk of different event types: Cumulative total failure probability may exceed 1

Peter C. Austin*, Ewout W. Steyerberg, Hein Putter

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

33 Citations (Scopus)


The Fine-Gray subdistribution hazard model has become the default method to estimate the incidence of outcomes over time in the presence of competing risks. This model is attractive because it directly relates covariates to the cumulative incidence function (CIF) of the event of interest. An alternative is to combine the different cause-specific hazard functions to obtain the different CIFs. A limitation of the subdistribution hazard approach is that the sum of the cause-specific CIFs can exceed 1 (100%) for some covariate patterns. Using data on 9479 patients hospitalized with acute myocardial infarction, we estimated the cumulative incidence of both cardiovascular death and non-cardiovascular death for each patient. We found that when using subdistribution hazard models, approximately 5% of subjects had an estimated risk of 5-year all-cause death (obtained by combining the two cause-specific CIFs obtained from subdistribution hazard models) that exceeded 1. This phenomenon was avoided by using the two cause-specific hazard models. We provide a proof that the sum of predictions exceeds 1 is a fundamental problem with the Fine-Gray subdistribution hazard model. We further explored this issue using simulations based on two different types of data-generating process, one based on subdistribution hazard models and other based on cause-specific hazard models. We conclude that care should be taken when using the Fine-Gray subdistribution hazard model in situations with wide risk distributions or a high cumulative incidence, and if one is interested in the risk of failure from each of the different event types.

Original languageEnglish
Pages (from-to)4200-4212
Number of pages13
JournalStatistics in Medicine
Issue number19
Publication statusPublished - 9 May 2021

Bibliographical note

Funding Information:
Canadian Institutes of Health Research, PJT 166161; Heart and Stroke Foundation of Canada, Mid‐Career Investigator Award; Ontario Ministry of Health and Long‐Term Care Funding information

Funding Information:
This study was supported by ICES, which is funded by an annual grant from the Ontario Ministry of Health and Long‐Term Care (MOHLTC). The opinions, results and conclusions reported in this article are those of the authors and are independent from the funding sources. No endorsement by ICES or the Ontario MOHLTC is intended or should be inferred. This research was supported by operating grant from the Canadian Institutes of Health Research (CIHR) (PJT 166161). Dr. Austin is supported in part by a Mid‐Career Investigator award from the Heart and Stroke Foundation of Ontario. We thank Daniele Giardiello for providing comments on an earlier version of this article.

Publisher Copyright:
© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.


Dive into the research topics of 'Fine-Gray subdistribution hazard models to simultaneously estimate the absolute risk of different event types: Cumulative total failure probability may exceed 1'. Together they form a unique fingerprint.

Cite this