Dynamic prediction models for data with competing risks

Prediction of cause-specific cumulative incidence function (CIF) is of primary interest to clinical researchers when conducting statistical analysis involving competing risks. The predicted CIFs need to be dynamically updated by incorporating the time-dependent information measured during follow-up. However, dynamic prediction of the conditional CIFs requires simultaneously updating the overall survival and the CIF while adjusting for the time-dependent covariates and the time-varying covariate effects which is complex and challenging. In this study, we extended the landmark Cox models to data with competing risks, because the landmark Cox models provide a simple way to incorporate various types of time-dependent information for data without competing risks. The resulting new models are called landmark proportional subdistribution hazards (PSH) models. In this study, we first investigated the properties of the Fine-Gray model under non-PSH and proposed a robust risk prediction procedure which is not sensitive to the PSH assumption. Then, we developed a landmark PSH model and a more comprehensive landmark PSH supermodel. The performance of our models was assessed via simulations and through analysis of data from a multicenter clinical trial for breast cancer patients. As compared with other dynamic predictive models, our proposed models exhibited three advantages. 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 users to make predictions with a set of landmark points in one step. Third, the proposed models can simply incorporate various types of time-varying information. Finally, our models are not computationally intensive and can be easily implemented with existing statistical software. Public Health Significance: Prognostic models for predicting the absolute risk of a patient in having a disease are very useful in performing risk stratification and making treatment decisions. Since the patient’s prognosis can change over time, it is necessary to update the risk prediction accordingly. The dynamic prediction models developed in this study can provide more accurate prognoses over the course of disease progression and will be helpful to physicians in adopting personalized treatment regimes