Variable Selection for Partially Functional Additive Cox Model with Interval-censored Failure Time Data

Variable selection for failure time data plays an important role in many studies and has recently attracted a lot of attention. However, most of the existing methods focus on or apply only to linear covariate effects, limited models such as Cox model and/or right-censored data. In this chapter, we consider the problem under a novel partially functional additive Cox model with both functional and scalar predictors based on interval-censored failure time data. A penalized sieve variable selection and estimation approach with multiple group penalty functions is proposed. In the proposed method, we adopt Bernstein polynomial approximation to deal with unspecified cumulative baseline additive hazard functions, and the functional principal component analysis is utilized to extract functional features from trajectories of functional covariates. For the implementation of the approach, a group coordinate descent algorithm is developed. A simulation study is conducted to assess the finite sample performance of the proposed method, and the method is applied to an Alzheimer’s disease study with high-dimensional genetic and functional factors.