Longitudinally Measured Predictors: Approaches for Sufficient Dimension Reduction

• Activity Number: 111 - New Dimension Reduction and Statistical Learning Methods for Biomedical Data
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Efstathia Bura* and Liliana Forzani and Ruth Pfeiffer
• Companies: TU Wien and Universidad Nacional del Litoral and National Cancer Institute, NIH, HHS
• Keywords: biomarkers ; regression ; classification ; covariance structure

Abstract

We propose a method to combine several predictors (markers) that are measured repeatedly over time into a composite marker score without assuming a model and only requiring a mild condition on the predictor distribution. Assuming that the first and second moments of the predictors can be decomposed into a time and a marker component via a Kronecker product structure that accommodates the longitudinal nature of the predictors, we develop first-moment sufficient dimension reduction techniques to replace the original markers with linear transformations that contain sufficient information for the regression of the predictors on the outcome. These linear combinations can then be combined into a score that has better predictive performance than a score built under a general model that ignores the longitudinal structure of the data. Our methods can be applied to either continuous or categorical outcome measures. In simulations, we focus on binary outcomes and show that our method outperforms existing alternatives by using the AUC, the area under the receiver-operator characteristics (ROC) curve, as a summary measure of discriminatory ability.