Parameter Estimation in Multivariate Single Index Model

• Activity Number: 431
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Jingwei Wu* and Hanxiang Peng and Wanzhu Tu
• Companies: Indiana University School of Medicine and Indiana University Purdue University Indianapolis and Indiana University School of Medicine
• Keywords: multivariate outcomes ; single index model ; p-spline ; mixed effect model ; asymptotics ; consistency

Abstract

Index measures are commonly used in medical research and clinical practice, primarily for quantification of health risks in individual subjects or patients. Construction of medical indices has largely been based on heuristic arguments, although the acceptance of these indices usually requires objective validation, preferably against multiple outcomes. In this presentation, we propose an analytical framework for index development in the context of multiple clinical outcomes. Methodologically, the proposed model represents a multivariate extension to the traditional single-index model. We use penalized cubic spline to construct the index components, and splines are estimated directly by penalizing nonlinear least squares and can be implemented using existing software. We show the existence, root-n consistency, and asymptotic normality of all parameter estimators under suitable regularity conditions. This development provides a theoretical foundation for large sample inferences concerning parameters of interest. Finite sample performance of such proposed method is evaluated in a simulation study.