Conditional Kaplan-Meier Estimator with Functional Covariates for Time-to-Event Data

Due to the wide availability of functional data from multiple disciplines, the studies of functional data analysis have become popular in the recent literature. However, the related development in censored survival data has been relatively sparse. In this work, we consider the problem of analyzing time-to-event data in the presence of functional predictors. We develop a conditional generalized Kaplan-Meier (KM) estimator that incorporates functional predictors using kernel weights and rigorously establishes its asymptotic properties. In addition, we propose to select the optimal bandwidth based on a time-dependent Brier score. We then carry out extensive numerical studies to examine the finite sample performance of the proposed functional KM estimator and bandwidth selector. We also illustrated the practical usage of our proposed method by using a data set from Alzheimer's Disease Neuroimaging Initiative data.