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Richard Bilonick, Bo Wang, Zach Nadler, Gadi Wollstein, Hiroshi Ishikawa, Yun Ling, Larry Kagemann, Joel Schuman; Using a Structural Equation Measurement Model (SEMM) for Nested Data to Describe Agreement among Lamina Cribrosa Pore Segmentation Methods. Invest. Ophthalmol. Vis. Sci. 2013;54(15):3515.
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© ARVO (1962-2015); The Authors (2016-present)
Lamina cribrosa (LC) consists of pores and beams. OCT images of LC consist of 1000's of pixels. Segmentation assigns each pixel either pore (1) or beam (0). We compared a computer algorithm (A) and manual by 2 experts, B and Z.
6 pixels were sampled from each image from 1 eye of each of 29 healthy and glaucoma subjects. Pixels (1-6) were on a grid with each cell being 100 × 100 pixels wide (see Figure). SEMM allowed for correlation among the nested pixels based on the distance between the pixels - see the path diagram for the case of 4 pixels (1-4). The unknown propensity μ for a pixel to be a pore was represented by a latent variable (LV), Normally distributed with mean 0 and standard deviation 1 [N(0,1)]. Each measurement (X) was either 0 or 1. These X's are assumed to come from a continuous LV (χ) that is N(0,1). Each method has a threshold c such that if χ≦c then X=0, else 1. Because binary Xs provide less information than continuous, grey scale level (GSL, 0-255) was included as an indicator for μ. The darker the GSL, the greater μ. ρ1, ρ2, ρ3 (for methods A, B, and Z) and ρ4 (for GSL) can be interpreted as the correlation between the indicator and μ. The 15 pairwise correlations among the 6 μ can be represented by just 4 correlations (P1, P2, P3 and P4) that correspond to the four distances reducing the number of parameters. The expected covariance matrix is ΛS-1Λ'+R where for only 4 pixels, the Λ and S matrices are shown in the figure and R is a matrix with residual variances on the diagonal. Parameters were estimated by maximum likelihood using the OpenMx R package.
The outcomes (see Table) showed that A found 30 pores, B found 26, and Z found 24. Unlike SEMM, the table does not account for nested data. SEMM showed that A and B were most highly correlated with pore propensity (ρ1=ρ2=0.99) while Z's correlation was ρ3=0.96 and GSL was ρ4=0.76. A had the lowest threshold (0.96), B the next highest (1.05) and Z the highest (1.09), agreeing with the simple frequencies that Z is less likely to declare a pore. The Ps were near 0 for the grid spacing used.
All methods were highly correlated with pore propensity while GSL was substantially less correlated. The methods differ in the probability of transitioning from beam to pore. A similar model can be applied easily to any study of agreement based on nested data.
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