title: Cox Regression Models with Functional Covariates for Survival Data.
abstract: We extend the Cox proportional hazards model to cases when the exposure is a densely sampled functional process, measured at baseline. The fundamental idea is to combine penalized signal regression with methods developed for mixed effects proportional hazards models. The model is fit by maximizing the penalized partial likelihood, with smoothing parameters estimated by a likelihood-based criterion such as AIC or EPIC. The model may be extended to allow for multiple functional predictors, time varying coefficients, and missing or unequally-spaced data. Methods were inspired by and applied to a study of the association between time to death after hospital discharge and daily measures of disease severity collected in the intensive care unit, among survivors of acute respiratory distress syndrome.
authors.affiliation: Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA.
authors.forename: Jonathan E
authors.initials: JE
authors.lastname: Gellar
authors.affiliation: Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA.
authors.forename: Elizabeth
authors.initials: E
authors.lastname: Colantuoni
authors.affiliation: Pulmonary & Critical Care Medicine, and Physical Medicine & Rehabilitation, School of Medicine, Johns Hopkins University, Baltimore, MD, USA.
authors.forename: Dale M
authors.initials: DM
authors.lastname: Needham
authors.affiliation: Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA.
authors.forename: Ciprian M
authors.initials: CM
authors.lastname: Crainiceanu
keywords: Cox proportional hazards model; functional data analysis; intensive care unit; nonparametric statistics; survival analysis