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 language | English (US) |
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Pages (from-to) | 1575-1585 |
Number of pages | 11 |
Journal | Journal of the American Statistical Association |
Volume | 104 |
Issue number | 488 |
DOIs | |
State | Published - Dec 2009 |
Externally published | Yes |
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