Functional Ensemble Survival Tree: Dynamic Prediction of Alzheimer’s Disease Progression Accommodating Multiple Time-Varying Covariates

Abstract

With the exponential growth in data collection, multiple timevarying biomarkers are commonly encountered in clinical studies, along with rich set of baseline covariates. This paper is motivated by addressing a critical issue in the field of Alzheimer's disease (AD) in which we aim to predict the time for AD conversion in people with mild cognitive impairment to inform prevention and early treatment decisions. Conventional joint models of biomarker trajectory with time-to-event data rely heavily on model assumptions and may not be applicable when the number of covariates is large. This thus motivated us to consider a functional ensemble survival tree framework to characterize the joint effects of both functional and baseline covariates in predicting disease progression. The proposed framework incorporates multivariate functional principal component analysis to characterize the changing patterns of multiple time-varying neurocognitive biomarker trajectories and then nest these features within an ensemble survival tree in predicting the progression of AD. We provide a fast implementation of the algorithm that accommodates personalized dynamic prediction that can be updated as new observations are gathered to reflect the patient's latest prognosis. The algorithm is empirically shown to perform well in simulation studies and is illustrated through the analysis of data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We provide implementation of our proposed method in R package funest.

Prediction models of colorectal cancer prognosis incorporating perioperative longitudinal serum tumor markers: a retrospective longitudinal cohort study

“…In consideration of the correlation between the FPC scores of CEA, CA19-9, and CA125, multivariate principal components analysis (MFPCA) [ 24 , 25 ] was applied to characterize the changing patterns of the multivariate longitudinal processes. MFPCA indirectly modeled the correlations among the three tumor markers via the correlations among their FPC scores.…”

Random survival forests for dynamic predictions of a time-to-event outcome using a longitudinal biomarker

“…We extend this in the heart valve data application where we explore the use of a model for the longitudinal marker to impute the marker value, as in [ 46 ]. However, alternative specifications can be considered using other summary measures such as the marker slope, or using a function of multiple time-varying covariates to grow trees [ 24 , 25 ]. The ability of RSFs to deal with correlation among its predictors allows for us to include and evaluate multiple marker specifications when building the predictive model.…”

“…A new definition of the receiver operating characteristic curve has also been developed for evaluating the performance of RSF [ 23 ]. Approaches to handle multiple longitudinal covariates have been proposed that reduce the dimensionality of the covariates and subsequently apply RSF to dynamically predict the event [ 24 , 25 ]. In our proposal, RSFs fit at each landmark time can incorporate updated longitudinal information in survival prediction while requiring no assumptions about the relationship between the longitudinal trajectory and the survival process.…”

Dynamic prediction with time‐dependent marker in survival analysis using supervised functional principal component analysis

“…Chen and Lei, 6 Lin et al, 7 and Nie and Cao 8 proposed to estimate FPCs which are only nonzero in a small interval in order to enhance the interpretability of FPCs. Other studies involving FPCA jointly with survival data can be found in Yan et al, 9 Wang et al, 10 and Jiang et al, 11 for example. However, FPCA does not consider the relationship between the functional predictor and the response variable.…”