The aim of this paper is to develop a weighted functional linear Cox regression model that accounts for the association between a failure time and a set of functional and scalar covariates. We formulate the weighted functional linear Cox regression by incorporating a comprehensive three-stage estimation procedure as a unified methodology. Specifically, the weighted functional linear Cox regression uses a functional principal component analysis to represent the functional covariates and a high-dimensional Cox regression model to capture the joint effects of both scalar and functional covariates on the failure time data. Then, we consider an uncensored probability for each subject by estimating the important parameter of a censoring distribution. Finally, we use such a weight to construct the pseudo-likelihood function and maximize it to acquire an estimator. We also show our estimation and testing procedures through simulations and an analysis of real data from the Alzheimer's Disease Neuroimaging Initiative.
Keywords: Censoring distribution; functional principal component; hazard function; pseudo-likelihood function; score test.