Principled sure independence screening for Cox models with ultra-high-dimensional covariates

Research output: Contribution to journalArticlepeer-review

Abstract

It is rather challenging for current variable selectors to handle situations where the number of covariates under consideration is ultra-high. Consider a motivating clinical trial of the drug bortezomib for the treatment of multiple myeloma, where overall survival and expression levels of 44760 probesets were measured for each of 80 patients with the goal of identifying genes that predict survival after treatment. This dataset defies analysis even with regularized regression. Some remedies have been proposed for the linear model and for generalized linear models, but there are few solutions in the survival setting and, to our knowledge, no theoretical support. Furthermore, existing strategies often involve tuning parameters that are difficult to interpret. In this paper, we propose and theoretically justify a principled method for reducing dimensionality in the analysis of censored data by selecting only the important covariates. Our procedure involves a tuning parameter that has a simple interpretation as the desired false positive rate of this selection. We present simulation results and apply the proposed procedure to analyze the aforementioned myeloma study.

Original languageEnglish (US)
Pages (from-to)397-411
Number of pages15
JournalJournal of Multivariate Analysis
Volume105
Issue number1
DOIs
StatePublished - Feb 2012
Externally publishedYes

Keywords

  • Cox model
  • Multiple myeloma
  • Sure independence screening
  • Ultra-high-dimensional covariates
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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