Variable selection for high‐dimensional partly linear additive Cox model with application to Alzheimer's disease

Abstract

Variable selection has been discussed under many contexts and especially, a large literature has been established for the analysis of right‐censored failure time data. In this article, we discuss an interval‐censored failure time situation where there exist two sets of covariates with one being low‐dimensional and having possible nonlinear effects and the other being high‐dimensional. For the problem, we present a penalized estimation procedure for simultaneous variable selection and estimation, and in the method, Bernstein polynomials are used to approximate the involved nonlinear functions. Furthermore, for implementation, a coordinate‐wise optimization algorithm, which can accommodate most commonly used penalty functions, is developed. A numerical study is performed for the evaluation of the proposed approach and suggests that it works well in practical situations. Finally the method is applied to an Alzheimer's disease study that motivated this investigation.

Variable Selection for Interval‐censored Failure Time Data

“…In addition to the references mentioned earlier, other references discussing the same or similar type of the algorithm given earlier include Wu et al . (2020) and Zhao et al . (2020b), who provided some justifications both numerically and theoretically.…”

“…First, we will consider the situation where for subject i , in addition to the covariate , there exists another q ‐dimensional vector of covariates that may have non‐linear effects and are preferred to be included in the model, . One example of such situations is that may denote some treatment indicators and baseline covariates and thus should be included in the model always, while represents high‐dimensional genetic predictors (Wu et al ., 2020). Then we will discuss the situation where instead of model (1), the failure times of interest T i s follow the linear transformation model described in the succeeding text.…”

“…A more specific example of interval‐censored failure time data is given by Alzheimer's Disease Neuroimaging Initiative (ADNI), a longitudinal follow‐up study that started in 2004 and was designed to develop clinical, imaging, genetic and biochemical biomarkers for the early detection and tracking of the Alzheimer's disease (AD) (Li et al ., 2017; Wu et al ., 2020; Li et al ., 2020a). In the study, the participants were recruited across North America and followed and reassessed periodically to track the pathology of the disease as it progresses.…”

Bayesian Knockoff Generators for Robust Inference Under Complex Data Structure

“…Candidate features include 11 baseline neuropsychological assessment indices; MRI volumetric data of ventricles, hippocampus, whole brain, entorhinal, fusiform gyrus, middle temporal gyrus, and intracerebral volume at the first visit; and single nucleotide polymorphisms (SNPs) that may have effects on the risk of developing AD. To reduce the number of SNPs, we follow the practice of Wu et al (2020), who applied sure independent screening (Fan et al, 2010) and retained the top 500 SNPs. Here, baseline neuropsychological assessment indices and MRI volumetric data are continuous covariates, whereas for each SNP, homozygous without Thymine (coded 0), heterozygous or homozygous with Thymine (coded 1 and 2 separated) naturally form a categorical covariate with three categories.…”

“…Our method identified 3 SNPs, rs1386236, rs1475950 and rs2428754 to be important predictors as well. Among them, rs1475950 and rs2428754 were also found to be important by Wu et al (2020). SNP rs1386236 is part of the gene LUZP2, which controls the produce of leucine zipper protein 2.…”