Domain-Interaction Functional Regression Models for Functions with Varying Domains

• Activity Number: 368
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jonathan Gellar*+ and Elizabeth Colantuoni and Dale Needham and Ciprian M. Crainiceanu
• Companies: Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health and Johns Hopkins School of Medicine and The Johns Hopkins University
• Keywords: Functional Data Analysis ; Functional Regression ; Longitudinal Covariates ; Longitudinal Data Analysis ; Nonparametric statistics

Abstract

We study the relationship between a functional predictor and a scalar response, when the functional predictor falls on a different domain for each subject. Such data is commonly encountered when the functional covariate is measured over time, and each subject is followed for a different length of time. Traditional approaches to this problem consist of collapsing a subject's entire function to a single summary statistic, which is inefficient as it throws away much of the data. We introduce a new class of regression models, which we call Domain-Interaction Functional Regression models, which are flexible enough to account for a functional predictor of varying length. We use this framework to contract a model that relates in-hospital mortality to Sequential Organ Failure Assessment (SOFA) score, measured as a function over time in among patients in the intensive care unit (ICU). Our models out-perform existing methodology and offer new insights into the relationship between organ failure and mortality in the ICU.