Latent Growth Curve Model for Calibration between Measurements Obtained by Multiple Devices

Abstract

 

Purpose

 

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.

 

Methods

 

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 χ_j =I + S t_j +ξ_j, where χ_j stands for the true thickness at j^th time point, I stands for the latent intercept and S for the latent slope, t_j for the time point, ξ_j for the error term. Observed device 1 and device 2 measurements are modeled as linear functions of the unknown true thicknesses ( χ ): D_i =α_i + β_i χ_j +ε_ij, where D_i stands for the value measured by device i, α_i stands for intercept and β_i for slope, ε_ij 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.

 

Results

 

Estimates of the relevant functions of the model parameters are shown in Table 1. For macular measurements, the average growth curve is χ_j = 246.91 - 0.037 t_j, the calibration curve is D₃ =88.67+0.58 D₂; For RNFL, the average growth curve is χ_j =101.69-0.0013 t_j, the calibration curve is D₃=10.31+0.744 D₂. The trends and calibration curves fit the data well.

 

Conclusions

 

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.

 

 

Keywords: 459 clinical (human) or epidemiologic studies: biostatistics/epidemiology methodology