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Yun Ling, Richard Bilonick, Igor Bussel, Hiroshi Ishikawa, Gadi Wollstein, Larry Kagemann, Ian Sigal, Joel Schuman; Latent Growth Curve Model for Calibration between Measurements Obtained by Multiple Devices. Invest. Ophthalmol. Vis. Sci. 2013;54(15):3525.
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© ARVO (1962-2015); The Authors (2016-present)
Longitudinal macular and retinal nerve fiber layer (RNFL) measurements were obtained by two iterations of optical coherence tomography (OCT). Latent Growth Curve Models (LGCM) were used to calibrate the measurements obtained by the different devices to allow the computation of the trend of the measurements changing over time.
904 observations from 71 eyes (36 subjects) were available. Subjects were tested by two different iterations of OCT over the 10-year study. In this analysis, there were 23 macula measurement overlaps between generations, and 106 RNFL measurement overlaps. Visit times were irregularly spaced within and between subjects and some measurements were missing. The R statistical language and environment with OpenMx R package was used to fit the LGCMs. The LGCM models the true but unknown macular or RNFL values as a function of follow-up, that is χj =I + S tj +ξj, where χj stands for the true thickness at jth time point, I stands for the latent intercept and S for the latent slope, tj for the time point, ξj for the error term. Observed device 1 and device 2 measurements are modeled as linear functions of the unknown true thicknesses ( χ ): Di =αi + βi χj +εij, where Di stands for the value measured by device i, αi stands for intercept and βi for slope, εij for the error term. After fitting the calibration model, the RNFL measurements were “corrected” to allow the use of measurements from both iterations as a continuum, and a linear mixed effect model was fitted to get the individual slope for each eye.
Estimates of the relevant functions of the model parameters are shown in Table 1. For macular measurements, the average growth curve is χj = 246.91 - 0.037 tj, the calibration curve is D3 =88.67+0.58 D2; For RNFL, the average growth curve is χj =101.69-0.0013 tj, the calibration curve is D3=10.31+0.744 D2. The trends and calibration curves fit the data well.
SEM accounted for the correlations between eyes of each subject, correctly estimated growth curves measured by multiple devices by simultaneously calibrating measurements from different devices. Using SEMs made it possible to extend the length of subject profiles.
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