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Building generalized linear models with ultrahigh dimensional features: A sequentially conditional approach.

Authors
  • Zheng, Qi1
  • Hong, Hyokyoung G2
  • Li, Yi3
  • 1 Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, Kentucky.
  • 2 Department of Statistics and Probability, Michigan State University, East Lansing, Michigan.
  • 3 Department of Biostatistics, University of Michigan, Ann Arbor, Michigan.
Type
Published Article
Journal
Biometrics
Publisher
Wiley (Blackwell Publishing)
Publication Date
Mar 01, 2020
Volume
76
Issue
1
Pages
47–60
Identifiers
DOI: 10.1111/biom.13122
PMID: 31350909
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

Conditional screening approaches have emerged as a powerful alternative to the commonly used marginal screening, as they can identify marginally weak but conditionally important variables. However, most existing conditional screening methods need to fix the initial conditioning set, which may determine the ultimately selected variables. If the conditioning set is not properly chosen, the methods may produce false negatives and positives. Moreover, screening approaches typically need to involve tuning parameters and extra modeling steps in order to reach a final model. We propose a sequential conditioning approach by dynamically updating the conditioning set with an iterative selection process. We provide its theoretical properties under the framework of generalized linear models. Powered by an extended Bayesian information criterion as the stopping rule, the method will lead to a final model without the need to choose tuning parameters or threshold parameters. The practical utility of the proposed method is examined via extensive simulations and analysis of a real clinical study on predicting multiple myeloma patients' response to treatment based on their genomic profiles. © 2019 The International Biometric Society.

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