Partially functional linear additive model for censored data with heavy-tailed distributions

In functional data analysis (FDA), the functional linear regression model (FLRM) is a popular method to describe the relationship between a scalar response and a functional predictor. The conventional approach for estimating FLRM relies on the normality assumption of the error terms. However, such analyzes may not yield robust inference when the linearity and normality assumptions are violated. In this paper, we develop a partially functional linear additive regression model for handling right- or left-censored data, where the error term follows scale mixtures of normal distributions. We use the B-spline method to approximate the additive nonparametric functions and the functional principal component analysis to estimate the slope function of the functional predictor. A Bayesian approach coupled with an efficient Markov chain Monte Carlo (MCMC) algorithm is developed to conduct statistical inference. The performance of the proposed method is evaluated through simulation studies and applied to a laryngeal squamous cell carcinoma study.