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

Abstract

Background 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 patient history includes much more repeated markers. 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. Methods 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 the 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 adapted to survival data, namely regularized regressions and random survival forests, to predict the event from the landmark time. We also show how predictive tools can be combined into a superlearner. 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. Results 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 in primary biliary cholangitis, and a public health context with age-specific prediction of death in the general elderly population. Conclusions 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, the technique can be used with any other appropriate modeling technique for the markers and can be easily extended to competing risks setting.

On the importance of a clear definition of time horizon for time-to-event dynamic predictions: a systematic review and a concrete illustration in kidney transplantation

“…This systematic review con rmed the dominance of joint modeling for longitudinal and survival data (n = 42, 41%) and landmarking (n = 44, 43%) to develop dynamic predictions. To a lesser extent, we identi ed the emergence of machine learning approaches including deep learning (n = 14, 14%), with random survival forest [24][25][26] or neural networks [27,28] for instance. All articles referring to machine learning approaches were published after 2018.…”

Random survival forests with multivariate longitudinal endogenous covariates

“…Since these subsamples become more and more homogeneous regarding the event, the missing at random assumption of the mixed models becomes more and more valid. Compared with the other methodologies adapted to the large dimensional and longitudinal context, our methodology has the assets of (i) using all available information when landmark approaches 8,9 only include subjects still at risk at landmark time, resulting in a lack of efficiency 7 ; (ii) simultaneously analyzing the longitudinal and time-to-event processes when the other methods based on two-step RC 14,16,17 neglect the association leading to a potential bias in the prediction; (iii) allowing for complex and nonlinear association structures between the predictors and the event; (iv) allowing the analysis of potentially high-dimensional data (i.e. hundreds/thousands of predictors).…”

“…In the absence of an external sample (as in the application), the evaluation of the RSF performances can be incorporated into a K-fold cross-validation strategy: the random forest is built on K − 1 folds and dynamic predictions (considering data up to s only) are computed on the left-out fold. By replicating this on all the folds, estimated probabilities π⋆k (s, t − s) of event between s and t are finally obtained for the entire sample and the Brier Score can be computed according to equation (8). This strategy was adopted in the application and repeated 50 times to account for the 10-fold cross-validation variability.…”

“…5,7 The longitudinal information of intermittently measured and prone-to-error markers up to t can be included after a pre-processing step, by mixed models for instance. 1,3,8,9 In multivariate settings, the Cox model may be replaced by more advanced techniques coming from statistical learning and adapted to survival data 8,9 to account for the possibly large dimension of the predictors and their correlation. The landmark approach is relatively easy to implement and was shown to be robust to the misspecification of the marker trajectory or to the proportional assumption in the Cox model.…”

Dynamic Prediction of Mortality Using Longitudinally Measured Pediatric Sequential Organ Failure Assessment Scores: A Joint Modeling Approach*

“…Time-to-event data is modeled using a survival model where a function of the random effects part of the mixed effects model is used as a time-varying covariate in the survival model. The joint model is not the only approach that can be used for dynamic prediction; approaches such as landmarking and joint latent class models have been used in the literature (31)(32)(33)(34)(35)(36).…”