Logistic regression with brownian-like predictors

Martin Lindquist, Ian W. Mckeague

Research output: Contribution to journalArticle

Abstract

This article introduces a new type of logistic regression model involving functional predictors of binary responses, and provides an extension of this approach to generalized linear models. The predictors are trajectories that have certain sample path properties in common with Brownian motion. Time points are treated as parameters of interest, and confidence intervals are developed under prospective and retrospective (case-control) sampling designs. In an application to functional magnetic resonance imaging data, signals from individual subjects are used to find the portion of the time course that is most predictive of the response. This allows the identification of sensitive time points specific to a brain region and associated with a certain task, which can be used to distinguish between responses. A second application concerns gene expression data in a case-control study involving breast cancer, where the aim is to identify genetic loci along a chromosome that best discriminate between cases and controls.

Original languageEnglish (US)
Pages (from-to)1575-1585
Number of pages11
JournalJournal of the American Statistical Association
Volume104
Issue number488
DOIs
Publication statusPublished - Dec 2009
Externally publishedYes

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Keywords

  • Brownian motion
  • Empirical process
  • Functional logistic regression
  • Functional magnetic resonance imaging
  • Gene expression
  • Lasso
  • M-estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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