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

TL;DR

This study addresses dynamic, individual-level risk prediction using rich longitudinal biomarker histories and overcomes limitations of joint/landmark models in high-dimensional settings. It develops a four-step framework that (i) models marker histories with generalized mixed models, (ii) derives trajectory summaries, (iii) applies multiple survival prediction methods (Cox, Penalized-Cox, sPLS-DR, RSF) to high-dimensional summaries, and (iv) combines predictions via a Super Learner. In simulations, penalized-Cox performs best for simple linear relationships, while Random Survival Forests excel with nonlinear associations; both often outperform traditional Cox models. The framework is demonstrated in two real-world contexts: death prediction in primary biliary cholangitis and age-specific all-cause mortality in the elderly, showing improved predictive performance when leveraging the full longitudinal history. Overall, the method provides a scalable, flexible approach to dynamic prediction that can incorporate diverse marker types, handle measurement error, and extend to competing risks, with an R implementation available to practitioners.

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.

Figures (6)

• Figure 1: Illustration of individual dynamic prediction of an event computed using history of multiple repeated markers (here 6). The individual probability of event is computed from a landmark time to a horizon time by using the information on the markers trajectories collected up to the landmark time.
• Figure 2: Multi-layer cross-validation framework: (A) Overall cross-validation to assess the predictive performances on independent samples, (B) Intermediate-layer cross-validation for the superlearner only performed on the learning sample to determine the weights. A final internal cross-validation (or Bootstrap for RSF) is done to tune each method.
• Figure 3: Simulation results over 250 replicates when considering 18 summaries associated to the event either assuming a linear form (figure A) or non-linear form (figure B). Methods are assessed using Mean Square Error of Prediction (MSEP), Brier Score (BS) and Area Under the ROC Curve (AUC). $(*)$ symbol indicates the presence of MSEP values above 0.2, but not displayed.
• Figure 4: Assessment (figure A) and weights in superlearner (figure B) of 3-years death survival probability in primary biliary cholangitis patients using information collected up to 4 years over 50 replicates. Methods are assessed using Brier Score (BS) and Area Under the ROC Curve (AUC).
• Figure 5: Assessment of 3-year survival probability in primary biliary cholangitis patients using baseline information on the 11 biomarkers and 3 covariates (figure A), baseline information and repeated measures collected up to 4 years of either serum bilirubin (figure B), albumin (figure C) or presence of platelets (figure D). The 10-fold cross-validation was replicated 50 times. The figure displays the difference (in percentage) of Brier Score (BS) and Area Under the ROC Curve (AUC) compared to the method using all the information with positive values for BS and negative values for AUC indicating a lower predictive accuracy.