Estimation of the Absolute Risk of Cardiovascular Disease and Other Events: Issues With the Use of Multiple Fine-Gray Subdistribution Hazard Models.

BACKGROUND

The Fine-Gray subdistribution hazard model is frequently used in the cardiovascular literature to estimate subject-specific probabilities of the occurrence of an event of interest over time in the presence of competing risks. A little-known limitation of this approach is that, for some subjects and for some time points, the sum of the subject-specific probabilities for the different event types (eg, cardiovascular and noncardiovascular death) can exceed one.

METHODS

We used data on 8238 patients hospitalized with congestive heart failure in Ontario, Canada. We fit 2 Fine-Gray subdistribution hazards models, one for cardiovascular death and one for noncardiovascular death and estimated the probability of death due to each cause within 5 years of hospital admission. We also fit 2 cause-specific hazard models for the 2 event types and combined the estimated cause-specific hazard functions to obtain subject-specific estimates of the probabilities of each of the 2 event types occurring within 5 years.

RESULTS

When adding the probabilities of 5-year cardiovascular death and 5-year noncardiovascular death obtained from the Fine-Gray subdistribution hazard models, 8.6% of subjects had an estimated probability of 5-year all-cause mortality that exceeded 1 (100%). This problem was avoided by fitting 2 cause-specific hazard models, one for each outcome type, and combining the estimated cause-specific hazard functions to obtain subject-specific estimates of the risk of cardiovascular and noncardiovascular death.

CONCLUSIONS

The Fine-Gray subdistribution hazard model may be problematic to use for a comprehensive assessment of absolute risks of multiple outcomes, while the combination of 2 cause-specific hazard models shows better statistical behaviour. Cause-specific modeling should not be discarded in competing risk situations.