Health Research and Policy

Abstract

DATE: May 2, 2013
TIME: 1:15 - 3:00 pm
LOCATION: Medical School Office Building, Rm x303
TITLE: Longitudinal Functional Regression Models with Structured Penalties
SPEAKER: Jaroslaw Harezlak, Assistant Professor
Indiana University Fairbanks Schools of Public Health and School of Medicine, Indianapolis, IN

Collection of functional data has vastly grown in the past decade, including functional data collected longitudinally. For example, in the HIV Neuroimaging Consortium (HIVNC) study, metabolite spectra were obtained using magnetic resonance spectroscopy (MRS) from multiple brain regions at a number of study time points. Analysis of such data usually follows a two-step procedure: (1) metabolite concentration extraction and (2) association study of extracted features and outcome of interest.

Our approach does not rely on this frequently unreliable feature extraction. Instead, it incorporates prior scientific knowledge to estimate regression function associating the whole functional profile with the outcome without explicitly extracting the feature characteristics. Specifically, we propose a method for functional linear model estimation using partially empirical eigenvectors for regression (PEER) in the longitudinal data setting. Our method allows the regression function to vary across both time and space. We derive the estimator's statistical properties and discuss their connections to the generalized singular value decomposition (GSVD). The results of the simulation studies and an application to the analysis of HIV patients' neurocognitive impairment as a function of the metabolite profiles are presented.

Joint work with Madan G. Kundu and Timothy W. Randolph.

Suggested readings:
Randolph, T.W., Harezlak, J., Feng, Z. (2012), Structured penalties for functional linear models—partially empirical eigenvectors for regression, Electronic Journal of Statistics; : 6:323–353. http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ejs/1331216629.

Kundu, M.G., Harezlak, J., Randolph, T.W. (2012) Longitudinal Functional Models with Structured Penalties,
http://arxiv.org/pdf/1211.4763.pdf.

Harezlak J, Buchthal S, Taylor M, Schifitto G, Zhong J, Daar E, Alger J, Singer E, Campbell T, Yiannoutsos C, Cohen R, Navia B; the HIV Neuroimaging Consortium. (2011), Persistence of HIV-associated cognitive impairment, inflammation, and neuronal injury in era of highly active antiretroviral treatment. AIDS; 25(5):625–33.
(in pdf).

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