Simultaneous Estimation and Variable Selection for Interval-Censored Data With Broken Adaptive Ridge Regression

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

“…Note that in the proposed variable selection procedure, we used Bernstein polynomials in the sieve approach and it is apparent that a similar method can be developed if one instead employs other smooth functions such as some spline functions. As mentioned above, Zhao et al 13 considered the same problem discussed here but only for the standard Cox model with linear covariate effects and the situation of p < n . In particular, their optimization algorithm cannot be used for or generalized to high‐dimensional covariate situation.…”

“…Variable selection has been discussed under many contexts and especially, a large literature has been established for the analysis of failure time data 1‐7 . However, most of the existing methods for failure time data only apply to right‐censored data, and as discussed by many authors, in practice, it is quite common that one may face interval‐censored data, a more general type of failure time data that included right‐censored data as a special case 8‐13 . By interval‐censored data, we usually mean that the failure time of interest is observed only to belong to an interval and among others, one field that commonly generates such data is medical follow‐up studies or clinical trials.…”

“…Among them, Scolas et al 19 and Wu and Cook 10 gave two parametric procedures and in particular, the latter assumed that the underlying unknown hazard function is a piecewise constant function. More recently, Zhao et al 13 proposed a broken adaptive ridge (BAR) regression approach 20 and established the asymptotic properties of the proposed method. Note that all three methods above apply only to the low‐dimensional ( n > p ) situation and only considered linear covariate effects.…”

A surrogateℓ0sparse Cox's regression with applications to sparse high‐dimensional massive sample size time‐to‐event data

“…On the other hand, it is also known to have some pitfalls such as instability and being unscalable to even moderate dimensional covariates. The broken adaptive ridge (BAR) estimator, defined as the limit of an iteratively reweighted ℓ 2 ‐penalization algorithm, was introduced to approximate the ℓ 0 ‐penalization problem and has been recently shown to possess some desirable selection, estimation, and clustering properties under the linear model and several other model settings . It is also computationally scalable to high‐dimensional covariates and stable for variable selection as discussed later in Remark of Section 2.…”

“…The broken adaptive ridge (BAR) estimator, defined as the limit of an iteratively reweighted 2 -penalization algorithm, was introduced to approximate the 0 -penalization problem and has been recently shown to possess some desirable selection, estimation, and clustering properties under the linear model and several other model settings. 10,[20][21][22] It is also computationally scalable to high-dimensional covariates and stable for variable selection as discussed later in Remark 2 of Section 2. However, the BAR method has yet to be rigorously studied for the Cox model.…”