LIMBARE: An Advanced Linear Mixed-Effects Breakpoint Analysis With Robust Estimation Method With Applications to Longitudinal Ophthalmic Studies

Tingfang Lee, Joel S. Schuman, Maria de los Angeles Ramos Cadena, Yan Zhang, Gadi Wollstein, Jiyuan Hu

Research output: Contribution to journalArticlepeer-review


Purpose: Broken stick analysis is a widely used approach for detecting unknown breakpoints where the association between measurements is nonlinear. We propose LIMBARE, an advanced linear mixed-effects breakpoint analysis with robust estimation, especially designed for longitudinal ophthalmic studies. LIMBARE accommodates repeated measurements from both eyes and over time, and it effectively addresses the presence of outliers. Methods: The model setup of LIMBARE and the computing algorithm for point and confidence interval estimates of the breakpoint were introduced. The performance of LIMBARE and other competing methods was assessed via comprehensive simulation studies and application to a longitudinal ophthalmic study with 216 eyes (145 subjects) followed for an average of 3.7 ± 1.3 years to examine the longitudinal association between structural and functional measurements. Results: In simulation studies, LIMBARE showed the smallest bias and mean squared error for estimating the breakpoint, with an empirical coverage probability of corre-sponding confidence interval estimates closest to the nominal level for scenarios with and without outlier data points. In the application to the longitudinal ophthalmic study, LIMBARE detected two breakpoints between visual field mean deviation (MD) and retinal nerve fiber layer thickness and one breakpoint between MD and cup-to-disc ratio, whereas the cross-sectional analysis approach detected only one and none, respectively. Conclusions: LIMBARE enhances breakpoint estimation accuracy in longitudinal ophthalmic studies, and the cross-sectional analysis approach is not recommended for future studies. Translational Relevance: Our proposed method and companion R package provide a valuable computational tool for advancing longitudinal ophthalmology research and exploring the association relationships among ophthalmic variables.

Original languageEnglish (US)
Article number19
JournalTranslational Vision Science and Technology
Issue number1
StatePublished - Jan 2024


  • breakpoint analysis
  • robust breakpoint detection
  • structural–functional association

ASJC Scopus subject areas

  • Ophthalmology
  • Biomedical Engineering


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