Broken Stick Model for Irregular Longitudinal Data

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Many longitudinal studies collect data that have irregular observation times, often
requiring the application of linear mixed models with time-varying outcomes. This paper
presents an alternative that splits the quantitative analysis into two steps. The first step
converts irregularly observed data into a set of repeated measures through the broken stick
model. The second step estimates the parameters of scientific interest from the repeated
measurements at the subject level. The broken stick model approximates each subject’s
trajectory by a series of connected straight lines. The breakpoints, specified by the user,
divide the time axis into consecutive intervals common to all subjects. Specification of
the model requires just three variables: time, measurement and subject. The model is
a special case of the linear mixed model, with time as a linear B-spline and subject as
the grouping factor. The main assumptions are: Subjects are exchangeable, trajectories
between consecutive breakpoints are straight, random effects follow a multivariate normal
distribution, and unobserved data are missing at random. The R package brokenstick
v2.5.0 offers tools to calculate, predict, impute and visualize broken stick estimates. The
package supports two optimization methods, including options to constrain the variancecovariance matrix of the random effects. We demonstrate six applications of the model:
Detection of critical periods, estimation of the time-to-time correlations, profile analysis,
curve interpolation, multiple imputation and personalized prediction of future outcomes
by curve matching.
Original languageEnglish
Pages (from-to)1-51
JournalJournal of Statistical Software
Volume106
Issue number7
DOIs
Publication statusPublished - 23 Mar 2023

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