Statistical Modelling 15 (3) (2015), 256–278
Cox regression models with functional covariates for survival data
Jonathan E. Gellar
Department of Biostatistics,
Bloomberg School of Public Health,
Johns Hopkins University,
Baltimore, MD, USA
e-mail: jgellar1@jhu.edu
Elizabeth Colantuoni
Department of Biostatistics,
Bloomberg School of Public Health,
Johns Hopkins University,
Baltimore, MD, USA
Dale M. Needham
Pulmonary & Critical Care Medicine,
and Physical Medicine & Rehabilitation,
School of Medicine,
Johns Hopkins University,
Baltimore, MD, USA
Ciprian M. Crainiceanu
Department of Biostatistics,
Bloomberg School of Public Health,
Johns Hopkins University,
Baltimore, MD, USA
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.
Keywords:
functional data analysis; Survival analysis; Cox proportional hazards model; nonparametric statistics; intensive care unit.
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