Functional ensemble survival tree: Dynamic prediction of Alzheimer’s disease progression accommodating multiple time‐varying covariates

With the exponential growth in data collection, multiple time-varying 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.