Abstract

Collecting longitudinal health information has become more and more common thanks to the advancement of technologies to measure biometrical outcomes and to store and process data. These technological advancements have led to an increasing availability of repeated measurement data that can be used to monitor a subject’s health status and disease progression, making it possible to update predictions of the probability to experience an adverse event each time a new measurement is taken. However, until recently there was a lack of statistical methods that could handle many longitudinal covariates as predictors of survival.

Over the last 5 years, the increasing availability of repeated measurements in biomedical studies has fostered the development of several new statistical methods [1-6] for the dynamic prediction of survival outcomes in settings where a large, potentially high-dimensional number of longitudinal covariates is available. These methods differ in both how they model the trajectories of the longitudinal covariates (multivariate functional PCA or mixed-effects models), and how they specify the relationship between the longitudinal covariates and the survival outcome of interest (Cox model or random survival forests). Because these methods are still quite new, little is known about their applicability, limitations and performance when applied to real-world data.

In this talk I will review these methodological developments, and discuss how their different modelling choices can have an impact on the possibility to accommodate unbalanced study designs and on computing time. Furthermore, I will present the results of a systematic comparison [7] of the predictive performance of these methods based on several real-world datasets that differ in terms of survival outcome, sample size, number of longitudinal covariates, and length of the follow-up. I will conclude with an overview of the advantages and limitations of each method, discussing possible avenues for future methodological developments.

References:
1. Li, K., & Luo, S. (2019). Dynamic prediction of Alzheimer’s disease progression using features of multiple longitudinal outcomes and time‐to‐event data. Statistics in Medicine, 38(24), 4804–4818.
2. Signorelli, M., Spitali, P., Szigyarto, C. A., The MARK‐MD Consortium, & Tsonaka, R. (2021). Penalized regression calibration: A method for the prediction of survival outcomes using complex longitudinal and high‐dimensional data. Statistics in Medicine, 40(27), 6178–6196.
3. Signorelli, M. (2024). pencal: An R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. To appear in: The R Journal. Preprint: arXiv:2309.15600.
4. Lin, J., Li, K., & Luo, S. (2021). Functional survival forests for multivariate longitudinal outcomes: Dynamic prediction of Alzheimer’s disease progression. Statistical Methods in Medical Research, 30(1), 99–111.
5. Devaux, A., Proust-Lima, C., & Genuer, R. (2023). Random Forests for time-fixed and time-dependent predictors: The DynForest R package. Preprint: arXiv:2302.02670.
6. Gomon, D., Putter, H., Fiocco, M., & Signorelli, M. (2024). Dynamic prediction of survival using multivariate functional principal component analysis: A strict landmarking approach. Statistical Methods in Medical Research, 33 (2), 256-272.
7. Signorelli, M., & Retif, S. (2024). An empirical appraisal of methods for the dynamic prediction of survival with numerous longitudinal predictors. Preprint: arXiv:2403.14336.