Localized glaucomatous change detection within the proper orthogonal decomposition framework

Abstract

Purpose: To detect localized glaucomatous structural changes using proper orthogonal decomposition (POD) framework with false-positive control that minimizes confirmatory follow-ups, and to compare the results to topographic change analysis (TCA).

Methods: We included 167 participants (246 eyes) with ≥4 Heidelberg Retina Tomograph (HRT)-II exams from the Diagnostic Innovations in Glaucoma Study; 36 eyes progressed by stereo-photographs or visual fields. All other patient eyes (n = 210) were non-progressing. Specificities were evaluated using 21 normal eyes. Significance of change at each HRT superpixel between each follow-up and its nearest baseline (obtained using POD) was estimated using mixed-effects ANOVA. Locations with significant reduction in retinal height (red pixels) were determined using Bonferroni, Lehmann-Romano k-family-wise error rate (k-FWER), and Benjamini-Hochberg false discovery rate (FDR) type I error control procedures. Observed positive rate (OPR) in each follow-up was calculated as a ratio of number of red pixels within disk to disk size. Progression by POD was defined as one or more follow-ups with OPR greater than the anticipated false-positive rate. TCA was evaluated using the recently proposed liberal, moderate, and conservative progression criteria.

Results: Sensitivity in progressors, specificity in normals, and specificity in non-progressors, respectively, were POD-Bonferroni = 100%, 0%, and 0%; POD k-FWER = 78%, 86%, and 43%; POD-FDR = 78%, 86%, and 43%; POD k-FWER with retinal height change ≥50 μm = 61%, 95%, and 60%; TCA-liberal = 86%, 62%, and 21%; TCA-moderate = 53%, 100%, and 70%; and TCA-conservative = 17%, 100%, and 84%.

Conclusions: With a stronger control of type I errors, k-FWER in POD framework minimized confirmatory follow-ups while providing diagnostic accuracy comparable to TCA. Thus, POD with k-FWER shows promise to reduce the number of confirmatory follow-ups required for clinical care and studies evaluating new glaucoma treatments. (ClinicalTrials.gov number, NCT00221897.).

Conflict of interest statement

Disclosure: M. Balasubramanian, None; D.J. Kriegman, None; C. Bowd, Pfizer (F); M. Holst, None; R.N. Weinreb, Carl Zeiss Meditec, Inc. (C), Heidelberg Engineering, GmbH (F), Optovue, Inc. (C), Topcon Medical Systems, Inc. (F, C), Nidek (F); P.A. Sample, Carl Zeiss Meditec, Inc. (F), Haag-Streit (F); L.M. Zangwill, Carl Zeiss Meditec, Inc. (F), Heidelberg Engineering, GmbH (F), Optovue Inc. (F), Topcon Medical Systems, Inc. (F)

Figures

Figure 1.

POD k-FWER change significance maps of the example normal eye. Change maps indicate locations with likely glaucomatous changes (red superpixels) and treatment effects or improvement (green superpixels). (d–g) Optic disk region cropped for clarity; change maps indicate that no significant changes were detected from baseline (without any confirmation requirement). (e–g) Application of the minimum retinal height change criterion resulted in a slight reduction in the OPR.

Figure 2.

POD k-FWER change significance maps of an example progressing eye. Change maps indicate locations with likely glaucomatous changes (red superpixels) and treatment effects or improvement (green superpixels). (d–g) Optic disk region is cropped for clarity. (d) The POD k-FWER detected significant glaucomatous changes (OPR >5%) in the second follow-up exam in February 2005. Application of the minimum retinal height change criterion of ≥20 μm (e), ≥50 μm (f), and ≥100 μm (g) resulted in a slight reduction in the observed positive rates. It can be noted that there was a slight reduction in OPR from 2006 to 2007, which is not reflected in the TCA maps (RC % area) due to the confirmation requirement in (Fig. 3b–e).

Figure 3.

TCA change significance maps of the example progressing eye as in the HRT TCA software (b), and using the liberal (c), moderate (d), and conservative (e) criteria of progression. The change maps (b–e; optic disk region cropped for clarity) indicate locations with likely glaucomatous changes (red superpixels) and treatment effects or improvement (green superpixels). (c–e) TCA detected significant glaucomatous changes (based on height change and red-cluster RC criteria) in the fourth follow-up exam in November 2006.

Figure 4.

TCA change significance maps of the example normal eye as in the HRT TCA software (b), and using the liberal (c), moderate (d), and conservative (e) criteria of progression. The change maps (b–e, optic disk region cropped for clarity) indicate retinal locations with likely glaucomatous changes (red superpixels) and treatment effects or improvement (green superpixels). (c–e) TCA detected no significant glaucomatous change (based on height change and red-cluster RC criteria) in the normal eye.

Figure 5.

POD change significance maps of the progressing eye (in Figs. 2 and 3) illustrating a hypothetical example of changing the baseline (a–c). After a change in baseline, the POD framework generates change significance maps from the next follow-up onwards. The POD framework also can use all available exams until the new baseline to improve specificity. By using both exams from 2001 and 2002 as baseline, the POD framework results in a decrease in the positive rate (c), indicating that some of the changes observed when using the 2002 exam only as baseline (b) could be explained by the inter-exam variability between 2001 and 2002.

Figure A1.

Baseline subspace representation of each follow-up scan (topography) of the example normal eye (Fig. 1) and the example progressing eye (Fig. 2). Baseline subspace representations are topographic projections (with a quadratic equality constraint) of each follow-up scan on to the baseline subspace of the eye. Single topographies are represented as points in a 3-D space using their respective subspace coefficients (α1,α2,α3) with indices 0, 1, 2, and so forth. Index 0 represents the location of an observed single topography at baseline, and indices 1 and above represent the location of baseline subspace representations. Baseline topographies nearest to their respective follow-up are clustered more closely to the observed baseline topographies for the example normal eye in (a) in contrast to the example progressing eye in (b).