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R. A. Bilonick, G. Wollstein, H. Ishikawa, L. Kagemann, M. L. Gabriele, K. A. Townsend, J. S. Schuman; Using a Latent Variable Model to Characterize Bias and Imprecision of Optic Nerve Head Measurements. Invest. Ophthalmol. Vis. Sci. 2007;48(13):5482.
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© ARVO (1962-2015); The Authors (2016-present)
To quantify the relative bias and imprecision of three devices used to measure the optic nerve head by employing latent variable modeling (LVM).
The linear measurement error model for measurement xij is: xij = αi + ßi µj + εij where intercept αi and slope ßi characterize the relative bias for device i with the product of the ß's equals one, εij is the random error which is Normally distributed with mean zero and standard deviation σi, and µj is the true value for subject j. The variance of the µ's is σ2. Each of 85 subjects was measured for cup area by each of three devices: Heidelberg Retinal Tomograph (HRT, Heidelberg Engineering, Heidelberg, Germany), RTVue (high speed ultra high resolution optical coherence tomograph; Optivue, Fremont, CA) and Stratus Optical Coherence Tomograph (Stratus OCT, Carl Zeiss Meditec, Inc., Dublin, CA). A latent variable model related the unobserved m to the measured x according to the above equation. Maximum likelihood estimates of the parameters were computed using the open source structural equation program Mx.
Parameter estimates and 95% confidence intervals for cup area are shown in the table and indicate that Stratus OCT almost certainly had a higher imprecision than both HRT and RTVue and the slopes for RTVue and Stratus OCT were higher than for HRT.The resulting calibration equations are:RTVue = -0.064 + .42 HRTHRT = 0.045 + 0.704 RTVueStratus = 0.8 + .249 HRTHRT = -0.095 + 0.8 StratusStratus = 0.75 + 0.88 RTVueRTVue = -0.99 + 0.37 Stratus
The bias and imprecision were well-characterized by LVM as indicated by the narrow confidence intervals. LVM should be used instead of naive regression which distorts the bias. Bland-Altman plots of the paired differences as a function of the paired averages assume equal imprecision and thus would be misleading for this data.
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