# Attirbutable risk from competing risks

There are a number of ways to estimate attributable risk fractions from Cox regression and logistic regression. Does anyone know how to estimate attributable risk from a competing risks regression using subdistribution hazard ratios, with 95% confidence intervals?

This page provides quick summary of the Fine-Gray subdistribution hazard approach to competing risks, with a link to further information. As @AdamO put it on that page:

The intepretation of this subdistributional hazard function is the instantaneous risk of death from cause 1 given you are either still alive, or you've already died of something else. In effect, it averages across these two possibilities in such a way that a high risk of dying previously from other causes lowers your hazard for that specific failure.

According to the vignette on competing risks provided with the R survival package, this approach to modeling competing risks:

can be done as a two stage process: the first stage creates a special data set while the second fits a weighted coxph or survfit model to the data.

The special data set is a collection of data sets, one for each endpoint, formulated to meet the requirements of the Fine-Gray analysis. That package has a finegray() function to produce the data sets from the original survival data. Cox regressions with weights assigned by the finegray() function then provide the basis for hazard ratios, confidence intervals, and so forth for each endpoint. There is also a cmprsk package for such analyses.

Before you proceed, however, make sure that you understand the limitations of this approach. As the competing risks vignette puts it on page 24:

A weakness of the Fine-Gray approach is that since the two endpoints are modeled separately, the results do not have to be consistent.

And on page 25:

The primary strength of the Fine-Gray model with respect to the Cox model approach is that if lifetime risk is a primary question, then the model has given us a simple and digestible answer to that question ... . This simplicity is not without a price, however, and these authors are not proponents of the approach. There are five issues.

Of which the first and perhaps most important is:

1. The attempt to capture a complex process as a single value is grasping for a simplicity that does not exist for many (perhaps most) data sets. The necessary assumptions in a multivariate Cox model of proportional hazards, linearity of continuous variables, and no interactions are strong ones. For the FG model these need to hold for a combined process — the mixture of transition rates to each endpoint — which turns out to be a more difficult barrier.
• Thank you but attributable risk cannot be calculated directly from cmprsk package – bvowe Oct 2 '19 at 17:55
• @bvowe it might help for you to edit your question to provide more details and an example of the type of attributable risk calculation that you wish to perform for a Fine-Gray analysis. Do you mean risk of each type of event as a function of some type of exposure, or some relative risk of the two types of events? – EdM Oct 2 '19 at 18:14
• thanks for your note i am hoping to estimate the percentage of the outcome that is attributable to a specific risk factor in the context of the competing risks models – bvowe Oct 2 '19 at 19:41
• @bvowe I don't use cmprsk and only included it as it seemed potentially useful. The survival package method for Fine-Gray produces separate datasets for each competing outcome, suitable for Cox regressions. So any method "to estimate attributable risk fractions from Cox regression" would seem to apply to that competing-risks approach. See pages 19-20 of the vignette linked in my answer for an example of such Cox regressions based on Fine-Gray analysis of a data set having 2 competing risks. – EdM Oct 2 '19 at 19:52