Variable selection for interval-censored and functional survival data

Abstract

Interval-censored data are a type of failure time data that is only known to belong to a time interval but cannot be observed precisely. Note that interval-censoring is often encountered in medical or health studies with periodic follow-ups nature and includes right- or left-censoring as a particular case. Moreover, the linear form of covariate effects in various survival models, such as the commonly used standard Cox model, may not always be a realistic assumption. To relax this, additive models, which assume nonlinear covariate effects, are useful alternatives to accommodate such nonlinearity. Recently, more and more attention has been drawn to the provision of variable selection for survival and functional data analysis when plenty of risk factors are available. But limited literature has investigated variable selection for the functional survival models with interval-censored data. In the dissertation, we shed light on variable selection for a series of additive survival models with high-dimensional interval-censored data via penalized estimation to address different statistical complexities. In Chapter 2, we will focus on high-dimensional variable selection for the nonparametric additive Cox model with interval-censored failure time data to identify important risk factors with potential nonlinear covariate effects. For the problem, we propose a penalized sieve maximum likelihood approach with the use of Bernstein polynomials approximation and group penalization. To implement the proposed method, an efficient group coordinate descent algorithm is developed and can be easily carried out for both low- and high-dimensional scenarios. Furthermore, a simulation study is performed to assess the performance of the presented approach and suggests that it works well in practice. The proposed method is applied to an Alzheimer's Disease Neuroimaging Initiative (ADNI) study to identify important and relevant genetic factors. In Chapter 3, we will extend the method given in Chapter 2 to a broad class of nonparametric additive transformation models. A two-step regularization estimation procedure that combines Bernstein polynomials expansions with a Poisson-based data augmentation penalized expectation-maximization (EM) algorithm is developed for implementation. The proposed method is assessed through an extensive simulation study, and the results suggest that it works well in various scenarios. Finally, we apply the presented method to the ADNI data described in Chapter 2 with demographic and clinical factors for illustration. In Chapter 4, we will perform the variable selection for a novel partially functional additive Cox model with both functional and scalar predictors under interval-censored failure time data and sparsely observed functional data. Specifically, we adopt Bernstein polynomials approximation to model the unspecified cumulative baseline hazard function and additive components and apply functional principal component analysis to extract functional features from trajectories of functional covariates. For implementation, a penalized sieve estimation approach with multiple group penalty functions is investigated, and a group coordinate descent algorithm is used. A simulation study is conducted to demonstrate the finite-sample performance of the proposed method. The method is applied to the ADNI study introduced in the previous two chapters for illustration.