Fast Estimation of Regression Parameters in a Broken Stick Model for Longitudinal Data

• Activity Number: 82
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Ritabrata Das* and Moulinath Banerjee and Bin Nan
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: change-point ; broken-stick ; menopause ; hormone profile ; women health

Abstract

Estimation of change-point(s) in the broken-stick model has significant applications in modeling important biological phenomena. A computationally economical likelihood-based approach for estimating change-point(s) efficiently in both cross-sectional and longitudinal settings is presented. This method, based on local smoothing in a shrinking neighborhood of each change-point, is shown via simulations to be computationally more viable than existing methods that rely on search procedures, with dramatic gains in the multiple change-point case. The proposed estimates are shown to have square-root n-consistency and asymptotic normality -- in particular, they are asymptotically efficient in the cross-sectional setting -- allowing us to provide meaningful statistical inference. As our primary and motivating application, the Michigan Bone Health and Metabolism Study cohort data is analyzed to describe patterns of change in log-estradiol levels, before and after the final menstrual period, for which a two change-point broken-stick model appears to be a good fit.