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The estimation of branching curves in the presence of subject‐specific random effects
Author(s) -
Elmi Angelo,
Ratcliffe Sarah J.,
Guo Wensheng
Publication year - 2014
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6289
Subject(s) - smoothing spline , smoothing , random effects model , spline (mechanical) , mathematics , branching (polymer chemistry) , nonlinear system , point process , econometrics , curve fitting , b spline , computer science , statistics , mathematical analysis , physics , medicine , meta analysis , materials science , quantum mechanics , composite material , bilinear interpolation , thermodynamics , spline interpolation
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.