Penalised semi-parametric copula method for semi-competing risks data: application to hip fracture in elderly

Hip fracture is a severe complication in the elderly. The affected people are at a higher risk of second fracture and death occurrence, and the best treatment for hip fractures is still being debated. Aside from the treatment, many factors, such as comorbidity conditions, may be associated with second fracture and death occurrence. This study aims to identify effective treatments and important covariates and estimate their effects on the progression of second fracture and death occurrence in hip fracture elderly patients using the semi-competing risks framework, because death dependently censors a second fracture but not vice versa. Due to the complex semi-competing risks data, performing variable selection simultaneously for second fracture and death occurrence is difficult. We propose a penalised semi-parametric copula method for semi-competing risks data. Specifically, we use separate Cox semi-parametric models for both margins and employ a copula to model the two margins' dependence. We develop a coordinate-wise optimisation algorithm that takes into account the data structure and copula function's complexities. Simulations show that the proposed method outperforms the traditional penalised marginal method. We apply the proposed method to a population-based cohort study of hip fracture elderly patients, providing new insights into their treatment and clinical management.