Dynamic Survival Prediction by Landmarking Using Parametric Proportional Hazards Models

Landmarking is a dynamic prediction technique used for analysing time-to-event data with time-dependent covariates. The landmark approach enables us to update the survival probability and the hazard rate of patients, as new covariate information becomes available during the follow-up. These dynamic updations can be made by fitting survival models for individuals who are still at risk at each landmark time point. In this study, we propose parametric proportional hazards (PPH) models to exploit the relation between lifetime and time-dependent covariates, which updates the survival probability and the hazard rate using landmarking approach. We use the Weibull and Gompertz PPH models for dynamic survival prediction. Inference procedures are carried out using maximum likelihood estimation method. We conduct Monte Carlo simulation studies to validate the finite sample behavior of the proposed dynamic prediction model. The practical utility of the procedures is illustrated by applying them to a real dataset on primary biliary cirrhosis disease.