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Sparse estimation of Cox proportional hazards models via approximated information criteria.

ABSTRACT: We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the ?0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterization step so that it reduces to one unconstrained nonconvex yet smooth programming problem, which can be solved efficiently as in computing the maximum partial likelihood estimator (MPLE). Furthermore, the reparameterization tactic yields an additional advantage in terms of circumventing postselection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration.

SUBMITTER: Su X

PROVIDER: S-EPMC4982849 | biostudies-literature | 2016 Sep

REPOSITORIES: biostudies-literature

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Sparse estimation of Cox proportional hazards models via approximated information criteria.

Su Xiaogang X Wijayasinghe Chalani S CS Fan Juanjuan J Zhang Ying Y

Biometrics 20160212 3

We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the ℓ0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a ...[more]

PMID: 26873398

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Project description:BackgroundThe successful identification of breast cancer (BRCA) prognostic biomarkers is essential for the strategic interference of BRCA patients. Recently, various methods have been proposed for exploring a small prognostic gene set that can distinguish the high-risk group from the low-risk group.MethodsRegularized Cox proportional hazards (RCPH) models were proposed to discover prognostic biomarkers of BRCA from gene expression data. Firstly, the maximum connected network with 1142 genes by mapping 956 differentially expressed genes (DEGs) and 677 previously BRCA-related genes into the gene regulatory network (GRN) was constructed. Then, the 72 union genes of the four feature gene sets identified by Lasso-RCPH, Enet-RCPH, [Formula: see text]-RCPH and SCAD-RCPH models were recognized as the robust prognostic biomarkers. These biomarkers were validated by literature checks, BRCA-specific GRN and functional enrichment analysis. Finally, an index of prognostic risk score (PRS) for BRCA was established based on univariate and multivariate Cox regression analysis. Survival analysis was performed to investigate the PRS on 1080 BRCA patients from the internal validation. Particularly, the nomogram was constructed to express the relationship between PRS and other clinical information on the discovery dataset. The PRS was also verified on 1848 BRCA patients of ten external validation datasets or collected cohorts.ResultsThe nomogram highlighted that the importance of PRS in guiding significance for the prognosis of BRCA patients. In addition, the PRS of 301 normal samples and 306 tumor samples from five independent datasets showed that it is significantly higher in tumors than in normal tissues ([Formula: see text]). The protein expression profiles of the three genes, i.e., ADRB1, SAV1 and TSPAN14, involved in the PRS model demonstrated that the latter two genes are more strongly stained in tumor specimens. More importantly, external validation illustrated that the high-risk group has worse survival than the low-risk group ([Formula: see text]) in both internal and external validations.ConclusionsThe proposed pipelines of detecting and validating prognostic biomarker genes for BRCA are effective and efficient. Moreover, the proposed PRS is very promising as an important indicator for judging the prognosis of BRCA patients.

Dataset Information

Sparse estimation of Cox proportional hazards models via approximated information criteria.

Publications

Sparse estimation of Cox proportional hazards models via approximated information criteria.

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