Group selection in the Cox model with a diverging number of covariates

Huang, Jian; Liu, Li; Liu, Yanyan; Zhao, Xingqiu

doi:10.5705/ss.2013.061

Cited by 16 publications

(43 citation statements)

References 25 publications

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“…To choose a tuning parameter, we can use the generalized cross validation by following Huang et al 13 : truel˜k(bold-italicβtrue^)n{1−d^(λn)/n}2…”

Section: Model Selection With Adaptive Group Bridge Under Case-cohortmentioning

confidence: 99%

“…where d^(λn) is the number of non-zero coefficients given λ n . To estimate the covariance matrix of bold-italicβtrue^≠0, we can use a quadratic approximation as in Fan and Li 21 and Huang et al 13 It can be estimated as follows: {∇2l˜(bold-italicβtrue^)+Υ(bold-italicβtrue^,bold-italicθtrue^)}−1Covtrue^{∇l˜(bold-italicβtrue^)}{∇2l˜(bold-italicβtrue^)+Υ(bold-italicβtrue^,bold-italicθtrue^)}−1 where Υ(bold-italicβtrue^,bold-italicθtrue^)=diag{∑Ag∍mθ^m1−1/γ…”

Section: Model Selection With Adaptive Group Bridge Under Case-cohortmentioning

confidence: 99%

“…Huang et al. 13 studied the group bridge to select variables at bi-level, that is, at group and within-group levels. However, they showed the group variable selection consistency only, not the bi-level variable selection consistency.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bi-level variable selection for case-cohort studies with group variables

Kim

Ahn

2018

Stat Methods Med Res

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The case-cohort design is an economical approach to estimate the effect of risk factors on the survival outcome when collecting exposure information or covariates on all patients is expensive in a large cohort study. Variables often have group structure such as categorical variables and highly correlated continuous variables. The existing literature for case-cohort data is limited to identifying non-zero variables at individual level only. In this article, we propose a bi-level variable selection method to select non-zero group and within-group variables for case-cohort data when variables have group structure. The proposed method allows the number of variables to diverge as the sample size increases. The asymptotic properties of the estimator including bi-level variable selection consistency and the asymptotic normality are shown. We also conduct simulations to compare our proposed method with some existing method and apply them to the Busselton Health data.

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“…To choose a tuning parameter, we can use the generalized cross validation by following Huang et al 13 : truel˜k(bold-italicβtrue^)n{1−d^(λn)/n}2…”

Section: Model Selection With Adaptive Group Bridge Under Case-cohortmentioning

confidence: 99%

Section: Model Selection With Adaptive Group Bridge Under Case-cohortmentioning

confidence: 99%

See 1 more Smart Citation

Bi-level variable selection for case-cohort studies with group variables

Kim

Ahn

2018

Stat Methods Med Res

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“…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 .…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Zhu

et al. 2020

Statistics in Medicine

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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.

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“…The problem of analyzing time to event data arises in a number of applied fields, such as medicine, biology, public health, and epidemiology (Cockeran et al, 2019;Emura et al, 2012). Nowadays, high dimensional gene expression data are increasingly used for modeling various clinical outcomes to facilitate disease diagnosis, disease prognosis, and prediction of treatment outcome (Jian Huang et al, 2014). Regression modeling is a standard practice to study jointly the effects of multiple predictors on a response.…”

Section: Introductionmentioning

confidence: 99%

Gene selection in Cox regression model based on a new adaptive penalized method

Alskal

Algamal

2020

IJASP

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The common issues of high dimensional gene expression data for survival analysis are that many of genes may not be relevant to their diseases. Gene selection has been proved to be an effective way to improve the result of many methods. The Cox proportional hazards regression model is the most popular model in regression analysis for censored survival data. In this paper, an adaptive penalized Cox proportional hazards regression model is proposed, with the aim of identification relevant genes and provides high classification accuracy, by combining the Cox proportional hazards regression model with the weighted least absolute shrinkage and selection operator (LASSO) method. Experimental results show that the proposed method significantly outperforms two competitor methods in terms of the area under the curve and the number of the selected genes.

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Group selection in the Cox model with a diverging number of covariates

Cited by 16 publications

References 25 publications

Bi-level variable selection for case-cohort studies with group variables

Bi-level variable selection for case-cohort studies with group variables

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

Gene selection in Cox regression model based on a new adaptive penalized method

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