The estimation of branching curves in the presence of subject-specific random effects

• Published in: Statistics in medicine Vol. 33; no. 29; pp. 5166 - 5176
• Main Authors: Elmi, Angelo, Ratcliffe, Sarah J., Guo, Wensheng
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 20.12.2014; Wiley Subscription Services, Inc
• Subjects: Biometry - methods; branching curves; Childbirth & labor; Computer Simulation; curve registration; Data Interpretation, Statistical; Estimating techniques; Female; Hormones; Humans; Labor Stage, First - drug effects; Labor Stage, First - physiology; Longitudinal Studies; Medical statistics; mixed effects models; Models, Statistical; Oxytocics - administration & dosage; Oxytocics - pharmacology; Oxytocics - therapeutic use; Oxytocin - administration & dosage; Oxytocin - pharmacology; Oxytocin - therapeutic use; Pregnancy; Regression Analysis; Time Factors; Vaginal Birth after Cesarean - methods; Vaginal Birth after Cesarean - statistics & numerical data; Womens health; mixed effects models; curve registration; branching curves
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.6289

Branching curves are a technique for modeling curves that change trajectory at a change (branching) point. Currently, the estimation framework is limited to independent data, and smoothing splines are used for estimation. This article aims to extend the branching curve framework to the longitudinal data setting where the branching point varies by subject. If the branching point is modeled as a random effect, then the longitudinal branching curve framework is a semiparametric nonlinear mixed effects model. Given existing issues with using random effects within a smoothing spline, we express the model as a B‐spline based semiparametric nonlinear mixed effects model. Simple, clever smoothness constraints are enforced on the B‐splines at the change point. The method is applied to Women's Health data where we model the shape of the labor curve (cervical dilation measured longitudinally) before and after treatment with oxytocin (a labor stimulant). Copyright © 2014 John Wiley & Sons, Ltd.