Logistic Regression With Brownian-Like Predictors

• 成果类型: Article
• 署名作者: Lindquist, Martin A.; McKeague, Ian W.
• 署名单位: Columbia University; Columbia University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08496
• 发表日期: 2009
• 页码: 1575-1585
• 关键词: Change-point; estimators; maximum; disease; models; signal

摘要

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 tinder 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.