We compared the Cox model with the Fine-Gray model when assessing the risk of low-trauma re-fractures. The risk of re-fracture was consistently higher when using the Cox model compared with the Fine-Gray model. The Fine-Gray model more accurately assesses the risk of re-fracture when a competing risk is present.
Purpose: Compared with the Kaplan-Meier and Cox model, the Fine-Gray competing risk model was developed to take competing risks into account, which provides a better estimation for the risk of the main outcome of interest when one or more competing risks are presented. To date, it remains underused. This study aims to use a case study to illustrate why and how the Fine-Gray model should be used and interpreted, especially when a competing risk is present.
Methods: Using a cohort of patients who presented to a NSW hospital with a non-trauma-related fracture between 2013/2014 and 2017/2018, the cumulative incidence and rate of re-fracture were estimated by the Kaplan-Meier and the Cox model, and by the Fine-Gray model when deaths present as competing events.
Results: The cumulative incidence of re-fracture at day 1825 (5 years) was 20.7% when using the Kaplan-Meier model and was 17.7% when using the Fine-Gray model. The estimations of cumulative incidence or rate of re-fracture were consistently higher by traditional survival analyses (Kaplan-Meier or Cox) compared with the Fine-Gray model. For patients aged 90 years and older, the re-fracture incidence at year 5 was estimated to be 66% vs. 28% whereas patients with a history of osteoporosis were 44% vs. 31%. Similarly, compared with patients without osteoporosis history, the estimated re-fracture rate for those with osteoporosis was 9.2 times higher by the Cox model but only 2.6 times higher by the Fine-Gray model.
Conclusion: The Fine-Gray model more accurately estimates the cumulative incidence of re-fracture and the effect of covariates on the hazard rate than the Kaplan-Meier and Cox models in the presence of a competing risk. This accuracy improves the larger the rate of a competing event.
Keywords: Competing risks; Fine-Gray; Osteoporotic fracture; Re-fracture; Survival analysis.