Individual dynamic prediction of clinical endpoint from large dimensional longitudinal biomarker history: a landmark approach

Abstract

The individual data collected throughout patient follow-up constitute crucial information for assessing the risk of a clinical event, and eventually for adapting a therapeutic strategy. Joint models and landmark models have been proposed to compute individual dynamic predictions from repeated measures to one or two markers. However, they hardly extend to the case where the complete patient history includes much more repeated markers possibly. Our objective was thus to propose a solution for the dynamic prediction of a health event that may exploit repeated measures of a possibly large number of markers. We combined a landmark approach extended to endogenous markers history with machine learning methods adapted to survival data. Each marker trajectory is modeled using the information collected up to landmark time, and summary variables that best capture the individual trajectories are derived. These summaries and additional covariates are then included in different prediction methods. To handle a possibly large dimensional history, we rely on machine learning methods adapted to survival data, namely regularized regressions and random survival forests, to predict the event from the landmark time, and we show how they can be combined into a superlearner. Then, the performances are evaluated by cross-validation using estimators of Brier Score and the area under the Receiver Operating Characteristic curve adapted to censored data. We demonstrate in a simulation study the benefits of machine learning survival methods over standard survival models, especially in the case of numerous and/or nonlinear relationships between the predictors and the event. We then applied the methodology in two prediction contexts: a clinical context with the prediction of death for patients with primary biliary cholangitis, and a public health context with the prediction of death in the general elderly population at different ages. Our methodology, implemented in R, enables the prediction of an event using the entire longitudinal patient history, even when the number of repeated markers is large. Although introduced with mixed models for the repeated markers and methods for a single right censored time-to-event, our method can be used with any other appropriate modeling technique for the markers and can be easily extended to competing risks setting.