Using a Latent Variable Model to Characterize Bias and Imprecision of Optic Nerve Head Measurements

Abstract

 

Purpose:

 

To quantify the relative bias and imprecision of three devices used to measure the optic nerve head by employing latent variable modeling (LVM).

 

Methods:

 

The linear measurement error model for measurement x_ij is: x_ij = α_i + ß_i µ_j + ε_ij where intercept α_i and slope ß_i characterize the relative bias for device i with the product of the ß's equals one, ε_ij is the random error which is Normally distributed with mean zero and standard deviation σ_i, and µ_j 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.

 

Results:

 

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  

 

Conclusions:

 

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.

 

Clinical Trial:

 

www.clinicaltrials.gov NTC00343746

 

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