Landmark Proportional Subdistribution Hazards Models for Dynamic Prediction of Cumulative Incidence Functions

Abstract: An individualized risk prediction model that dynamically updates the probability of a clinical event from a specific cause is valuable for physicians to be able to optimize personalized treatment strategies in real-time by incorporating all available information collected over the follow-up. However, this is more complex and challenging when competing risks are present, because it requires simultaneously updating the overall survival and the cumulative incidence functions (CIFs) while adjusting for the time-dependent covariates and time-varying covariate effects. In this study, we developed a landmark proportional subdistribution hazards (PSH) model and a more comprehensive supermodel by extending the landmark method to the Fine-Gray model. The performance of our models was assessed via simulations and through analysis of data from a multicenter clinical trial for breast cancer patients. Our proposed models have appealing advantages over other dynamic prediction models for data with competing risks. First, our models are robust against violations of the PSH assumption and can directly predict the conditional CIFs bypassing the estimation of overall survival and greatly simplify the prediction procedure. Second, our landmark PSH supermodel enables researchers to make predictions at a set of landmark points in one step. Third, the proposed models can easily incorporate various types of time-dependent information using existing standard software without computational burden.