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A review of the use of time‐varying covariates in the Fine‐Gray subdistribution hazard competing risk regression model


In survival analysis, time‐varying covariates are covariates whose value can change during follow‐up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time‐varying covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time‐dependent covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time‐varying covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time‐dependent covariates in the Cox model is that one cannot estimate the survival function or the effect of covariates on the survival function. In the presence of competing risks, the inclusion of internal time‐varying covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time‐varying covariates difficult or impossible. We conducted a review of the use of time‐varying covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time‐varying covariate. Several inappropriately described a time‐varying covariate as having an association with the risk of the outcome.



Austin PC, Latouche A, Fine JP. Stat Med. 2020; 39(2):103-13. Epub 2019 Oct 29.

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