Efficient estimation of breakpoints in piecewise-linear mixed-effects models for longitudinal ophthalmic studies
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Link to bioRxiv paper: http://biorxiv.org/cgi/content/short/2023.01.27.525884v1?rss=1

Authors: Lee, T., Schuman, J., Ramos Cadena, M. d. l. A., Zhang, Y., Wollstein, G., Hu, J.

Abstract: Purpose: Broken stick analysis is a useful approach to detect the unknown breakpoints where association between measurements change. Currently, most longitudinal studies aggregate measurements obtained from all visits without considering the repeated measurements from a given eye so that segmented linear models can be applied to such "compressed" cross-sectional data. The purpose of this study is to introduce an advanced robust segmented mixed model (RSMM) which accommodates longitudinal measurements from both eyes, and is robust to outliers. Methods: The model setup and parameter estimation algorithm of RSMM was introduced. The performance of all competing methods were assessed via comprehensive simulation studies and application to a longitudinal ophthalmic study with 216 eyes (145 subjects) followed for 3.7{+/-}1.3 years to examine the longitudinal association between structural and functional measurements. Results: In the simulation studies, the breakpoint estimates of RSMM exhibit smallest bias and mean squared error (MSE), with empirical coverage probability closest to the nominal level for scenarios with and without outlier data points. In the application to the longitudinal ophthalmic study, results of RSMM indicated the existence of two breakpoints between visual field mean deviation (MD) and retinal nerve fiber layer thickness (RNFL) and one breakpoint between MD and cup to disc ratio (CDR) while the cross-sectional analysis approach only detected one and none, respectively. Conclusions: RSMM improves the estimation accuracy of breakpoints for longitudinal ophthalmic studies. The conventional cross-sectional analysis approach is not recommended for future studies.

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