Enhancing long-term survival prediction with two short-term events: Landmarking with a flexible varying coefficient model.

Patients with cardiovascular diseases who experience disease-related short-term events, such as hospitalizations, often exhibit diverse long-term survival outcomes compared to others. In this study, we aim to improve the prediction of long-term survival probability by incorporating two short-term events using a flexible varying coefficient landmark model. Our objective is to predict the long-term survival among patients who survived up to a pre-specified landmark time since the initial admission. Inverse probability weighting estimation equations are formed based on the information of the short-term outcomes before the landmark time. The kernel smoothing method with the use of cross-validation for bandwidth selection is employed to estimate the time-varying coefficients. The predictive performance of the proposed model is evaluated and compared using predictive measures: area under the receiver operating characteristic curve and Brier score. Simulation studies confirm that parameters under the landmark models can be estimated accurately and the predictive performance of the proposed method consistently outperforms existing methods that either do not incorporate or only partially incorporate information from two short-term events. We demonstrate the practical application of our model using a community-based cohort from the Atherosclerosis Risk in Communities (ARIC) study.