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.