Modelling dependent censoring in time-to-event data using boosting copula regression.

Abstract

Survival analysis plays a pivotal role across disciplines, including engineering, economics, and social sciences—not just in biomedical research. In many of these applications, incomplete observations due to censoring are common, arising from limited follow-up periods, study dropouts, or administrative constraints. A standard assumption in such settings is that the censoring mechanism is independent of the survival process. This assumption primarily holds when censoring occurs at the end of the observation period. However, there may be dependence between event and censoring times. For example, if a patient’s health deteriorates and they withdraw due to poor prognosis, the time of censoring depends on their health status, leading to dependent censoring as sicker patients are censored earlier. To address such situations adequately in statistical analyses, we propose a model-based boosting approach using distributional copula regression. Our approach models the joint distribution of survival and censoring times by linking unknown marginal distributions through an unknown parametric copula. All distribution parameters of the resulting joint distribution are estimated simultaneously as functions of potentially different covariates. A key merit of the boosting approach is its data-driven variable selection, which is particularly important for such flexible models. Estimation remains feasible even for high-dimensional data with more covariates than observations, where classical estimation frameworks meet their limits. To investigate the performance of our method, we conduct a comprehensive simulation study, and demonstrate its practical application using a recent observational study analyzing the overall survival of patients with colon cancer. The data has a high proportion of right-censored observations without information on the cause of censoring.