June 2022
Volume 63, Issue 7
Open Access
ARVO Annual Meeting Abstract  |   June 2022
The estimation of breakpoints in piecewise-linear association models for longitudinal studies
Author Affiliations & Notes
  • TingFang Lee
    Department of Ophthamology, NYU Langone Health, New York, New York, United States
    Division of Biostatistics, Department of Population Health, NYU Langone Health, New York, New York, United States
  • Jiyuan Hu
    Division of Biostatistics, Department of Population Health, NYU Langone Health, New York, New York, United States
  • María de los Angeles Ramos Cadena
    Department of Ophthamology, NYU Langone Health, New York, New York, United States
  • Joel S Schuman
    Department of Ophthamology, NYU Langone Health, New York, New York, United States
    Center for Neural Science, NYU College of Arts and Sciences, New York, United States
  • Gadi Wollstein
    Department of Ophthamology, NYU Langone Health, New York, New York, United States
    Center for Neural Science, NYU College of Arts and Sciences, New York, United States
  • Footnotes
    Commercial Relationships   TingFang Lee None; Jiyuan Hu None; María de los Angeles Ramos Cadena None; Joel Schuman Aerie Pharmaceuticals, Inc, Boehringer Ingelheim, Carl Zeiss Meditec, Ocular Therapeutix, Inc., Opticient, Perfuse, Inc., Regeneron, Inc, SLACK Incorporated, Code C (Consultant/Contractor), Aerie Pharmaceuticals, Inc., Ocular Therapeutix, Inc., Opticient,, Code O (Owner), Carl Zeiss Meditec, Massachusetts Eye and Ear Infirmary and Massachusetts Institute of Technology, New York University, Ocugenix, Tufts University, University of Pittsburgh, Code P (Patent), Carl Zeiss Meditec, Ocugenix, Code R (Recipient); Gadi Wollstein None
  • Footnotes
    Support  NIH R01-EY013178 , P30-EY013079 and unrestricted grant from Research to Prevent Blindness.
Investigative Ophthalmology & Visual Science June 2022, Vol.63, 2045 – A0486. doi:
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      TingFang Lee, Jiyuan Hu, María de los Angeles Ramos Cadena, Joel S Schuman, Gadi Wollstein; The estimation of breakpoints in piecewise-linear association models for longitudinal studies. Invest. Ophthalmol. Vis. Sci. 2022;63(7):2045 – A0486.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose : The commonly used approach in ophthalmology to determine the breakpoints in brokenstick analysis in either longitudinal or cross-sectional studies is by using the data as if it was acquired cross-sectionally which does not consider repeated measurements per eye. The purpose of this study is to introduce and evaluate alternative approaches of brokenstick analysis in longitudinal studies.

Methods : Four methods for estimating the breakpoints in longitudinal studies were evaluated: 1) segmented mixed model (SEG) using an iterative procedure, 2) backfitting algorithm of the mixed-effect segmented model (MLE), 3) robust backfitting that incorporates the least trimmed squares (LTS) to accommodate outliers, and 4) bootstrap method that uses segmented linear model by resampling longitudinal data cross-sectionally. These methods were compared with the conventional approach where cross-sectional analysis is used by aggregating repeated measurements. A simulation study was conducted to evaluate the performance of each method by comparing bias and mean square error (MSE) in which two breakpoints were simulated. We further apply these methods to a clinical longitudinal study with 216 eyes (145 subjects) of which 164 had open angle glaucoma, 45 glaucoma suspects, and 7 healthy eyes, followed for an average of 3.7±1.3 years, and evaluate the temporal association between visual field mean deviation (MD) and retinal nerve fiber layer (RNFL) thickness.

Results : The simulation study showed all methods performed well in prediction accuracy while the cross-sectional method fail to capture the breakpoints (Table). Among the 4 proposed methods, the average bias and MSE of SEG and MLE are smaller than LTS and bootstrap. In the clinical longitudinal study, the results from SEG indicated that 2 breakpoints at MD = -15.5 and -4.56 dB exist with a significant difference between the rate of change before and after each breakpoint (p<0.001) (Figure). Using the cross-sectional approach, a single breakpoint was detected at -6.67 dB.

Conclusions : SEG is recommended in studies with complex dependencies such as repeated measurements and correlations between two eyes because of the accuracy and computational stability. As illustrated, the cross-sectional approach in this setting is not recommended due to the marked differences in the analysis outcome noted in the simulation and clinical data.

This abstract was presented at the 2022 ARVO Annual Meeting, held in Denver, CO, May 1-4, 2022, and virtually.

 

 

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