**Purpose.**:
To detect localized glaucomatous structural changes usingproper 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.)

^{ 1 }Current techniques for detecting localized glaucomatous changes using confocal scanning laser ophthalmoscopy require a minimum of one,

^{ 2 }and up to three additional follow-up exams

^{ 3,4 }for specific detection of change in a follow-up. Optical diagnostic imaging of the retina and optic disk in clinics is among the top three fastest growing Medicare claims (code 92135) in the United States, increasing from 0.2 million claims in 2000 to 6.3 million claims in 2008 (personal communication, July 2010, William L. Rich III, MD, FACS, Medical Director for Health Policy, American Association of Ophthalmology). The number of these claims and associated costs are expected to increase further as the new generation of spectral domain optical coherence tomography is adopted increasingly in clinics. Therefore, it is essential to reduce testing required for accurate detection of glaucomatous change over time to improve detection of glaucomatous progression, shorten clinical trials for new glaucoma therapies, and reduce the burden on United States healthcare costs.

^{ 5,6 }In the previous work, glaucomatous changes were estimated using global summary parameters of change within the optic disk. These parameters provided high diagnostic accuracy (area under receiver operating curve) in experimental glaucoma in monkey eyes

^{ 6 }and in a clinical study population.

^{ 5 }Moreover, in contrast to current change detection techniques, which require one to three additional follow-ups to confirm change, POD requires no repeat testing to provide a similar diagnostic accuracy. In our study, we extend the POD framework to generate retinal change significance maps of confocal scanning laser ophthalmoscopy topographic series that identify specific retinal locations with significant changes from baseline, with corrections for multiple comparisons. Furthermore, we compare the diagnostic accuracies of POD, which requires no confirmatory follow-up exams, to that of topographic change analysis (TCA), which requires up to 3 additional confirmatory follow-up exams to detect progression.

^{ 4 }

*α*= 5% does not guarantee that the probability of incorrectly inferring glaucomatous changes in a follow-up using the joint statistical inference is at most 5%. Therefore, it is essential to account for the multiplicity of simultaneous tests while analyzing retinal image sequences (

*cf*. alternate views about multiple testing

^{ 7 –9 }).

^{ 10–12 }In a parametric framework, rejection regions (

*α*cutoff) for hypotheses in a family are derived using their marginal

*P*values.

^{ 12–14 }MCPs in non-parametric framework have more flexibility, and can characterize joint distribution of test statistics in a family while deriving rejection regions (e.g., joint distribution of spatial statistics that can account for spatial correlation among pixels in optical images).

^{ 15,16 }Utility of

*P*values in the non-parametric framework is a special case of normalizing test statistics before deriving rejection regions. The statistical image mapping (SIM) method developed for detecting glaucomatous changes uses a non-parametric MCP.

^{ 17 }The neuroimaging literature is rich with theoretical foundations, and examples of parametric and non-parametric MCPs.

^{ 18–22 }

^{ 14 }In single-step procedures, a common rejection region is estimated and applied for all tests in the family (e.g., Bonferroni correction). In sequentially rejective MCPs, individual tests in a family are evaluated sequentially, and their respective rejection regions (

*α*cutoffs) are adjusted at every step depending on the number of tests remaining to be evaluated at that step. Because rejection regions are adjusted sequentially, step-wise MCPs generally may have more power to detect changes than single-step MCPs.

^{ 12 }2) a generalized family-wise error rate control by Lehmann and Romano (a single-step MCP),

^{ 23 }and 3) a false discovery rate control method by Benjamini and Hochberg (a step-up MCP).

^{ 24 }We also derived criteria of glaucomatous progression for the POD framework and compared its diagnostic accuracy to Heidelberg Retina Tomograph (HRT; Heidelberg Engineering, GmbH, Heidelberg, Germany) TCA using liberal, moderate, and conservative criteria of progression proposed recently by Chauhan et al.

^{ 4 }

^{ 25 }; SAP visual field exams with <15% false-positives, <33% false-negatives, and <33% fixation losses, and no observable testing artifacts as determined by the UCSD Visual Field Assessment Center (VisFACT) were considered to be reliable. Stereo-photographs of fair to excellent quality by trained graders were considered to be of acceptable quality.

**Table 1.**

**Table 1.**

Non-progressors | Progressors | ||

No. of eyes (No. of subjects) | 210 (148) | 36 (33) | |

Age (yrs.) | Mean (95% CI) | 61.4 (59.5, 63.4) | 64.7 (61.6, 67.7) |

Median (range) | 64.5 (18.1, 85.5) | 65.0 (48.3, 83.3) | |

No. HRT exams | Median (range) | 4 (4 to 8) | 5 (4 to 8) |

HRT follow-up yrs. | Median (range) | 3.6 (1.7 to 7.4) | 4.1 (2.4, 7.0) |

SAP mean deviation at baseline | Mean (95% CI) | −1.72 (−2.16, −1.28) | −3.65 (−5.45, −1.84) |

Median (range) | −0.95 (−30.13, 2.20) | −2.15 (−21.74, 1.72) | |

SAP PSD at baseline | Mean (95% CI) | 2.47 (2.18, 2.76) | 4.19 (2.87, 5.51) |

Median (range) | 1.73 (0.85, 13.32) | 2.30 (0.99, 13.18) | |

% abnormal disk from photo evaluation at baseline | 45.2% (95 of 210 eyes) | 77.1% (27 of 35 eyes)* | |

% abnormal visual field at baseline | 32.9% (69 of 210 eyes) | 52.8% (19 of 36 eyes) | |

% of both abnormal disk from photo evaluation and abnormal visual field at baseline | 19.5% (41 of 210 eyes) | 42.9% (15 of 35 eyes)* |

^{ 5,6 }and in the Appendix.

^{ 5,6 }Algorithmic details of building a baseline subspace, estimating baseline subspace representations, and new procedural improvements are described in the Appendix.

*P*value for the null hypothesis

_{0}: no mean retinal height change from baseline to follow-up) was estimated using a three-factor mixed-effects ANOVA as in HRT TCA

^{ 26 }: where

*h*represents retinal height at time

_{tℓi}*t*= 1,2; location within the superpixel ℓ = 1, … ,16, and scan

*i*= 1,2,3;

*T*is the time factor;

*L*is the location factor, and

*I*(

*T*) is the scan or image factor nested within

*T*; ε

*is the model error assumed to be independent, and distributed normally with a mean 0 and variance in TCA,*

_{tℓi}*P*values were estimated using the Satterthwaite's approximate F-test (Kutner et al., p. 1068

^{ 27 }) accounting for all variability related to time factor

*T*(i.e., $ \u2211 \u2113 = 1 16 S S T at \u2113 = S S T + S S T L $; Keppel and Wickens, p. 253

^{ 28 }). It should be noted that the three-factor mixed-effects ANOVA model was applied separately to each superpixel in each of the baseline-follow-up exam pair for each study eye.

*P*value is less than or equal to

*P*cutoff. The

*P*cutoff was estimated using a variety of type I error control procedures that are described below. Red superpixels correspond to glaucomatous changes or noise and green superpixels correspond to treatment (improvement) or noise.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

*P*value after controlling for family-wise type I error using the 3 MCPs listed below.

*P*values of all tests.

*p*} be the set of marginal

_{1}...p_{N}*P*values of all tests in the family, where

*N*is the number of superpixels within the disk. Let

*α*be the family-wise level of significance (0.05 for Bonferroni Correction and Benjamini-Hochberg Procedure; 0.01 for Lehmann-Romano Procedure).

_{FW}*P*values of locations with an increase in mean retinal height from baseline were set to 1. For green superpixels,

*P*values of locations with a decrease in mean retinal height from baseline were set to 1.

^{ 12,14 }such that when there are no changes, the probability

*P (*at least one type I error)

*≤ α*.

_{FW}*P*value cutoff of

*α*/

_{FW}*N*to all tests to determine their significance.

*k*-FWER procedure controls the generalized family-wise error rate or the probability of making at least

*k*false-positive errors,

^{ 23 }such that when there are no changes,

*P*(at least

*k*type I error)

*≤ α*.

_{FW}*k-*FWER procedure increases the common rejection region from

*α*/

_{FW}*N*to

*k*×

*α*/

_{FW}*N*. Because there may be a few locations with true but non-glaucomatous changes in retinal measurements (e.g., due to illumination changes or eye movements), controlling for one or more false-positive errors (as in Bonferroni correction) is unnecessarily stringent. Therefore, the

*k*-FWER procedure allows up to

*k*false-positive errors (a few errors should not change the validity of the overall family-wise hypothesis), and also minimizes type II error (or maximizes detection of changes) while controlling type I error.

*k-*FWER control, we allowed at most 5% of tests within the disk as false-positives (

*k*= 5% of

*N*). A common

*P*value cutoff was estimated as

*k*×

*α*/

_{FW}*N*(a common rejection region) and applied to all tests.

^{ 14,24 }

- The
*P*values of all tests within the optic disk {*p*_{1}…*p*} are arranged in increasing order as_{N}*pˆ*_{1}≤*pˆ*_{2}≤ … ≤*pˆ*, where_{N}*pˆ*_{i}is the ordered*P*value of testDisplay Formula - Each test in disk
Display Formula was evaluated one at a time in the decreasing order of their significance (i.e., from*pˆ*to_{N}*pˆ*_{1}). The*P*value cutoff for the*i*th hypothesis was estimated using Sime's inequality as $ i N \xd7 \alpha F W $

*i*th test and all subsequent tests from

*i*th test that meets this terminal condition.

^{ 29 }

*K*-FWER procedure controlled the probability that there were at most

*k*false-positive errors, with

*k*as 5% of number of superpixels in disk. Therefore, glaucomatous change in a study eye was defined as one or more follow-ups (without any confirmation requirement) with retinal height decrease from baseline ≥0 μm and OPR >5%.

*k-*FWER using various minimum retinal height reduction criteria of ≥20, ≥50, ≥75, and ≥100 μm in conjunction with the type I error criterion of OPR >5%.

*P*< 5%) decrease in retinal height from baseline were tagged as red superpixels, and red superpixels with fewer than four red superpixels as neighbors were discarded.

^{ 4 }were evaluated:

- Liberal criteria
*:*One or more follow-ups with a largest cluster of red superpixels in disk ≥0.5% of disk area with retinal height decrease ≥20 μm from baseline. - Moderate criteria
*:*One or more follow-ups with a largest cluster of red superpixels in disk ≥1% of disk area with retinal height decrease ≥50 μm from baseline. - Conservative criteria
*:*One or more follow-ups with a largest cluster of red superpixels in disk ≥2% of disk area with retinal height decrease ≥100 μm from baseline.

*k*-FWER and FDR procedures provided a sensitivity of 78%, specificity of 86% in longitudinal normals, and a specificity of 43% in non-progressing eyes.

**Table 2.**

**Table 2.**

Method | Type I Error Controlled | Type I Error Control Approach | Progression Criteria | Diagnostic Accuracy (Reduction in Retinal Height from Baseline ≥0 μm) | ||

Progressors: Sensitivity, N = 36 Eyes (95% CI) | Longitudinal Normals: Specificity, N = 21 Eyes (95% CI) | Non-progressors: Specificity, N = 210 Eyes (95% CI) | ||||

POD with Bonferroni Correction | FWER | Bonferroni Correction: FWER ≤5% | At least 1 follow-up with OPR >0% | 100% (99–100%) | 0% (0–0%) | 0% (0–2%) |

POD with k-FWER control | k-FWER | Lehmann & Romano 2005: k-FWER ≤1% | At least 1 follow-up with OPR >5% | 78% (63–93%) | 86% (68–100%) | 43% (36–50%) |

POD with FDR control | FDR | Benjamini & Hochberg 1995: FDR ≤5% | At least 1 follow-up with OPR >5% | 78% (63–93%) | 86% (68–100%) | 43% (36–50%) |

*k*-FWER and FDR procedures, unweighted accuracy was estimated as an average of their respective sensitivities and specificities. For progressing eyes versus longitudinal normals, unweighted accuracies were 50% for Bonferroni correction, and 82% for

*k*-FWER and FDR procedures. For progressing versus non-progressing eyes, unweighted accuracies were 50% for Bonferroni correction, and 60.5% for

*k*-FWER and FDR procedures.

*k*-FWER control in conjunction with a minimum retinal height change criterion (MRHC) of ≥50 μm resulted in a favorable balance of sensitivity and specificity (Table 3). In contrast to the criterion of MRHC ≥ 0 μm, MRHC ≥50 μm resulted in a slightly lower sensitivity (50 vs. 0 μm: 61% vs. 78%), and better specificity in normals (95% vs. 85%) and in non-progressing eyes (60% vs. 43%). Increasing MRHC to 100 μm reduced sensitivity to 33% with no change in specificity in normals (95%), and further improved specificity in non-progressing eyes (79%).

**Table 3.**

**Table 3.**

MRHC Criterion | Diagnostic Accuracy | ||

Progressors: Sensitivity, N = 36 Eyes (95% CI) | Longitudinal Normals: Specificity, N = 21 Eyes (95% CI) | Non-progressors: Specificity, N = 210 Eyes (95% CI) | |

MRHC ≥0 μm | 78% (63–93%) | 86% (68–100%) | 43% (36–50%) |

MRHC ≥20 μm | 67% (50–83%) | 86% (68–100%) | 51% (44–58%) |

MRHC ≥50 μm | 61% (44–78%) | 95% (84–100%) | 60% (54–67%) |

MRHC ≥75 μm | 44% (27–62%) | 95% (84–100%) | 70% (64–77%) |

MRHC ≥100 μm | 33% (17–50%) | 95% (84–100%) | 79% (73–85%) |

*k*-FWER control of the example normal and progressing eyes using various MRHC cutoffs. It can be noted that the

*k*-FWER procedure detected glaucomatous changes in the second follow-up (February 2005 with OPR >5% in Fig. 2 versus Fig. 3, except when using the MRHC ≥100 μm criterion).

**Figure 3.**

**Figure 3.**

^{ 4 }the liberal criterion provided high sensitivity, and the conservative criterion provided high specificity for TCA. Specificity in our normal eyes was relatively lower using the liberal criterion (current study versus Chauhan et al.

^{ 4 }62% vs. 81%), and higher using moderate (100% vs. 94%) and conservative criteria (100% vs. 97%). Sensitivity was relatively lower using the liberal (86% vs. 94%), moderate (53% vs. 77%), and conservative criteria (17% vs. 35%). Figures 4 and 3, respectively, show HRT TCA change significance maps of the example normal and progressing eyes.

**Table 4.**

**Table 4.**

TCA Criterion (Chauhan et al. ^{4}) | Diagnostic Accuracy | ||

Progressors: Sensitivity, N = 36 Eyes (95% CI) | Longitudinal Normals: Specificity, N = 21 Eyes (95% CI) | Non-progressors: Specificity, N = 210 Eyes (95% CI) | |

Liberal criterion | 86% (73–99%) | 62% (39–85%) | 21% (16–27%) |

Moderate criterion | 53% (35–70%) | 100% (98–100%) | 70% (64–77%) |

Conservative criterion | 17% (3–30%) | 100% (98–100%) | 94% (91–98%) |

**Figure 4.**

**Figure 4.**

*α*, POD further improves the confidence of changes detected in other retinal locations.

_{FW}^{ 4 }because some of the study eyes had only up to 3 follow-ups. The small differences in TCA diagnostic sensitivity (95% confidence intervals [CI] overlap) that we observed in our study versus that of Chauhan et al.

^{ 4 }may be due partly to the inclusion of the 3 of 3 confirmation strategy, and may be due to possible differences in magnitude of progression, disease severity, and other characteristics between the study populations.

**Figure 5.**

**Figure 5.**

^{ 6 }For example, image alignment errors in locations with steep edges, such as in neuroretinal rim and regions with blood vessels, may be detected as significant changes (because of increased longitudinal error variability in such locations due to time-location interaction effects in ANOVA).

*IOVS*2006;47:ARVO E-Abstract 4349), and further investigated by Bowd et al.

^{ 3 }and Chauhan et al.

^{ 4 }appear to be a useful anatomical criterion of glaucomatous change (based on shallow versus deep changes) in addition to statistical criteria based on measurement errors. In the POD framework, a minimum required height change (MRHC) of 50 μm along with type I error control significantly improved the diagnostic specificity of the POD

*k*-FWER procedure in the non-progressing eyes (by 17%) from 43% (95% CI 36–50%) at MRHC ≥0 μm to 60% (54–67%) at MRHC ≥50 μm. This statistically significant increase of specificity (non-overlapping 95% CIs) with MRHC criterion indicates the possibility that some of the non-progressing eyes had shallow glaucomatous changes during our study period, and may show progression detectable by stereophotographs and visual fields outside the duration of this study. This is a subject of a future study when sufficient follow-up becomes available. The best MRHC criterion for the POD framework appears to be from 0 to 50 μm depending on the desired specificity in the non-progressing eyes (specificity in normals is high in this range).

*k*-FWER error rate minimizes false-negatives (type II error) in addition to controlling false-positives. In our study, we evaluated a single-step

*k*-FWER control procedure. A step-down control of

*k*-FWER also has been proposed to minimize further false-negatives while controlling false-positives (Lehmann-Romano,

^{ 23 }p. 1139). Lehmann-Romano also proposed controlling a false discovery proportion (FDP) error rate, that is a ratio of number of false-positives to total number of positives (Lehmann and Romano,

^{ 23 }p. 1146). In contrast to the Benjamini-Hochberg FDR control, FDP control provides a strict upper bound for false-positives and shows promise for applications in glaucoma.

*α*/

_{FW}*N*becomes so low and results in stringent statistical discoveries. Similarly, in single-step

*k*-FWER and step-up FDR procedures, it can be shown that when the number of true negatives

*h*is low, the actual level of significance applied is bounded by

_{0}*h*/N ×

_{0}*α*which is far less than the desired level

_{FW,}*α*, thus leading to more conservative discoveries (see proof of Theorem 2.1.i in Lehmann-Romano 2005

^{23}). In our study,

*P*value cutoffs based on Bonferroni correction were not overly conservative (refer to sensitivity of Bonferroni correction in Table 2). Because the probability of making at least one false-positive (FWER) was controlled, we defined glaucomatous progression by Bonferroni correction when more than one retinal location within disk changed over time, which resulted in poor specificity (i.e., was anti-conservative). For example, at a family-wise level of significance

*α*of 0.05, the Bonferroni cutoff for an eye with

_{FW}*N*= 1000 superpixels within the optic disk region is 0.00005. Although the Bonferroni cutoff is extremely small, it is very likely that at least one superpixel has a

*P*value less than 0.00005 (e.g.,

*P*value = 0). Therefore, the criterion of glaucomatous progression derived using Bonferroni correction, based on the fact that it controls the probability of making at least one type I error, provided poor specificities.

*k*-FWER and Benjamini-Hochberg FDR procedures provided a higher overall accuracy (unweighted accuracy = 82%) than Bonferroni correction (50%) for progressing eyes versus longitudinal normal eyes. In contrast to FDR, the

*k*-FWER procedure provides a strict upper bound for the anticipated false-positive rate after type I error control to detect glaucomatous progression. Therefore, the

*k*-FWER procedure has a theoretical advantage over the FDR procedure in the context of deriving a criterion of glaucomatous progression.

**Figure A1.**

**Figure A1.**

*P*values of individual tests of significance in a parametric framework that are simple to implement using existing statistical software.

^{ 15,30–32 }In general, type I error control in a non-parametric framework requires more computing power than its parametric counterpart.

*α*to

_{FW}*α*, where

_{FW}/M*M*is the number of follow-up exams. The task of optic nerve head image sequence analysis involves detecting retinal locations with significant decrease in retinal height (glaucomatous changes or noise effect) and increase in retinal height (treatment effects or noise effects). Because this involves directional decisions, directional errors known as type III statistical error

^{ 14,15 }also are introduced. Controlling for longitudinal type I error and directional type III errors may improve the diagnostic accuracy.

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**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)

^{ 5,6 }Let

**T**= $ { T 1 b , \u2026 , T N b } $ be a set of

^{b}*N*single topographies (optic disk region cropped) of an eye at baseline. The POD baseline subspace of the eye is constructed as a linear subspace

*M*=

*L*(

*ϕ*

_{1, … ,}

*ϕ*). The basis vectors {

_{N}*ϕ*

_{1, … ,}

*ϕ*} are estimated from the baseline topographies

_{N}**T**using the method of snapshots,

^{b}^{ 34,35 }or the reduced singular value decomposition

^{ 36,37 }as we described previously.

^{ 6 }

*l*norm by orthogonal projection of follow-up topographies in the baseline subspace.

_{2}^{ 5,6 }In this current study, we estimated the nearest baseline topographies (or baseline subspace representations) for each follow-up exam by minimizing a normalized

*l*norm

_{2}^{ 38 }subject to regularization constraints (regularization details below). Use of a normalized

*l*norm (similar to normalized correlation) is expected to improve estimates of the nearest baseline topographies for a follow-up exam by accounting for illumination differences between baseline and follow-up.

_{2}^{ 38–40 }Regularization constraints were added to achieve intra-exam retinal height variance among baseline subspace representations of each follow-up exam similar to the intra-exam retinal height variability observed at the baseline of the eye.

*k*th single topography of a follow-up exam

*f*(optic disk region cropped and topographic measurements vectorized). Let

*k*th single follow-up topography $ T k f $; that is $ T\u02c6 k f $ is the baseline subspace representation of $ T k f $. The baseline subspace representation $ T\u02c6 k f $ is expressed as a linear combination of the basis vectors Φ as $ T\u02c6 k f = \Phi A $, where

*tr”*indicates a vector transpose operation. The subspace coefficients A of $ T\u02c6 k f $ are estimated by minimizing the normalized

*l*norm between $ T k f $ and $ T\u02c6 k f $as follows.

_{2}*c*and radius

*r*are estimated, respectively, as the centroid and the mean radius from the centroid of subspace coefficients of all single topographies at baseline

**T**. In case of HRT (i.e., 3 scans per exam), the hypercircle will be a sphere when one HRT exam is used at baseline; the hypercircle will be of dimension 6 when two HRT exams are used at baseline and so forth.

^{b}*f,*subspace coefficients of the first baseline scan $ T 1 b $ is used as the initial value for the iterative optimization function “fmincon”; to estimate $ T\u02c6 2 f $ of the second follow-up scan (2 of 3), subspace coefficients of the second baseline scan $ T 2 b $ is used as the initial value to “fmincon”; similarly, subspace coefficients of the third baseline scan (3 of 3) $ T 3 b $ is used as the initial value to “fmincon” to estimate the third baseline subspace representation $ T\u02c6 3 f $. For the example normal eye (Fig. 1) and progressing eye (Fig. 2), Figure A1 shows the locations of baseline subspace representations of each follow-up exam in their respective baseline subspaces.

*q*-value).

*q*.

- All follow-up scans are aligned with baseline scans of the eye using HRT software.
- In all baseline and follow-up single topographies, topographic measurements within the optic disk measurements are cropped for POD analysis and for inferring glaucomatous progression.
- A baseline subspace is constructed for each eye using single topographies at baseline.
- For each follow-up exam, a baseline subspace representation (i.e., topography “nearest” to a follow-up topography in the baseline subspace) is constructed by constrained projection of each follow-up topography onto the baseline subspace.
- In each scan, topographic measurements from neighboring 4 × 4 pixels are grouped into superpixels as in HRT TCA.
^{ 26 } - At each superpixel, a
*P*value representing the statistical significance of the observed change in mean retinal height from baseline is estimated using a three-factor mixed-effects ANOVA model as in HRT TCA.^{ 26 } - From the set of all
*P*values within optic disk in a follow-up exam, a*P*value cutoff that controls type I error at the desired false-positive rate*q*is estimated using Bonferroni correction, single-step Lehmann-Romano*k*-FWER and sequentially rejective Benjamini-Hochberg FDR type I error control procedures. Bonferroni correction and single-step Lehmann-Romano*k*-FWER provide a strict upper bound for anticipated false-positive rates (APR) after type I error control (i.e., APR = desired false-positive rate*q*). In contrast, Benjamini-Hochberg FDR procedure controls FDR at the desired level*q*only in the mean (or statistical expectation) sense. Due to lack of a strict upper bound for the level of FDR controlled, we chose the mean FDR controlled as the APR for the Benjamini-Hochberg FDR procedure (i.e., APR = desired false-positive rate*q*). - Retinal locations (superpixels) with significant decrease in mean retinal height between follow-up and the nearest baseline are identified as red superpixels and the locations with increase in mean retinal height are identified as green superpixels (Fig. 2). Significance of change is defined as locations with
*P*values ≤*P*value cutoff (*P*values estimated in Step 6;*P*value cutoff estimated in Step 7). - For each follow-up, an OPR is estimated as a ratio of number of red superpixels observed within the optic disk to total number of superpixels within the optic disk.
- Glaucomatous progression is defined as the presence of one or more follow-up exams with an OPR greater than the APR.