Historical Functional Cox Regression, with an Application to Prediction of Multiple Sclerosis Lesions

• Activity Number: 485
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Philip Reiss* and Elizabeth M. Sweeney and Jonathan Gellar
• Companies: New York University and Johns Hopkins Bloomberg School of Public Health and Mathematica Policy Research
• Keywords: biomarker ; Cox proportional hazards model ; historical functional regression ; longitudinal data ; magnetic resonance imaging ; multiple sclerosis

Abstract

Historical functional regression was originally developed as a form of function-on-function linear regression: the responses and predictors are defined on a common time domain and the response can be explained by values of the predictor only up to the present time, leading to a bivariate coefficient function supported on a triangular region. Recently, coefficient functions of this type have formed the basis of a novel historical functional Cox model for time-to-event data. The historical Cox model relates the log hazard to not only the present values but also earlier values of a time-varying biomarker. We demonstrate how, by means of this approach, one or more time series of magnetic resonance imaging sequences can serve as predictors of lesion incidence in multiple sclerosis. This application entails sharing information among separate historical models for a set of brain regions, and sheds light on the time lag between early warning signals and clinical manifestation.