**Purpose.**:
We evaluated Progression of Patterns (POP) for its ability to identify progression of glaucomatous visual field (VF) defects.

**Methods.**:
POP uses variational Bayesian independent component mixture model (VIM), a machine learning classifier (MLC) developed previously. VIM separated Swedish Interactive Thresholding Algorithm (SITA) VFs from a set of 2,085 normal and glaucomatous eyes into nine axes (VF patterns): seven glaucomatous. Stable glaucoma was simulated in a second set of 55 patient eyes with five VFs each, collected within four weeks. A third set of 628 eyes with 4,186 VFs (mean ± SD of 6.7 ± 1.7 VFs over 4.0 ± 1.4 years) was tested for progression. Tested eyes were placed into suspect and glaucoma categories at baseline, based on VFs and disk stereoscopic photographs; a subset of eyes had stereophotographic evidence of progressive glaucomatous optic neuropathy (PGON). Each sequence of fields was projected along seven VIM glaucoma axes. Linear regression (LR) slopes generated from projections onto each axis yielded a degree of confidence (DOC) that there was progression. At 95% specificity, progression cutoffs were established for POP, visual field index (VFI), and mean deviation (MD). Guided progression analysis (GPA) was also compared.

**Results.**:
POP identified a statistically similar number of eyes (*P* > 0.05) as progressing compared with VFI, MD, and GPA in suspects (3.8%, 2.7%, 5.6%, and 2.9%, respectively), and more eyes than GPA (*P* = 0.01) in glaucoma (16.0%, 15.3%, 12.0%, and 7.3%, respectively), and more eyes than GPA (*P* = 0.05) in PGON eyes (26.3%, 23.7%, 27.6%, and 14.5%, respectively).

**Conclusions.**:
POP, with its display of DOC of progression and its identification of progressing VF defect pattern, adds to the information available to the clinician for detecting VF progression.

^{ 1,2 }The time course of glaucomatous deterioration is generally years. The goal of management is to detect the disease in the early stage and to intervene to prevent progression at any stage. To manage glaucoma successfully, a glaucoma specialist needs to know whether an eye with glaucomatous damage is stable or progressively deteriorating and, if so, the rate of that deterioration.

^{ 3–7 }This variability is noise that can mask a weak signal of progression in serial VF tests.

^{ 8 }mean deviation (MD), or guided progression analysis (GPA), are statistical methods that use linear classification methods to represent the rate and magnitude of change or use analysis of variance to identify change outside the limits of short term variability.

^{ 8,9 }These statistical methods distinguish between two classes of eyes, stable glaucoma and progressing glaucoma.

^{ 10,11 }The premise we are testing is that this rigorous mathematical method will detect more eyes with progression of glaucomatous VF patterns over time than current rules derived primarily from clinical experience.

^{ 12–14 }

^{ 15 }

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

*y*value of the regressed line represents the overall offset of the severity value from the cluster mean at a particular time, and the slope represents the estimated rate of change of severity over time along the axis (VIM-defined VF pattern). We use the difference between the

*mx*values on the regressed line at the initial and last visits,

*mΔx*, as a surrogate for the slope of the regressed line (see Appendix).

^{th}percentile. Since POP sought only deterioration of VFs, POP used a single-tail CI in the direction of deterioration.

**Table 1.**

**Table 1.**

C2-A1 | C2-A2 | C3-A1 | C3-A2 | C3-A3 | C3-A4 | C3-A5 | VFI | MD |

0.821 | 0.852 | 0.825 | 0.810 | 0. 935 | 0.822 | 0.855 | 0.501 | 0.500 |

*t*-distribution of the rate of change around the estimated mean slope produced by regression accounted for the variability of the field in an individual eye. The percentage of area under the

*t*-distribution curve of slopes for a test eye sequence that was outside of the limit of stability was the estimated DOC that the glaucomatous VF defect was deteriorating (Fig. 3). Any percentage could have been used to make the binary decision whether the glaucoma was progressing or not; for comparison purposes, progression was defined as the presence of a proportion of the

*t*-distribution equal to or greater than the cutoff located outside the CL for stability.

^{ 9 }regardless of specificity in the stable group.

**Table 2.**

**Table 2.**

Age, y | MD, dB | PSD, dB | |||

Dataset | Source | n | Mean ± SD | Mean ± SD | Mean ± SD |

2 (Stable) | Stable eyes | 55 | 70.3 ± 10.0 | −8.7 ± 6.6 | 7.4 ± 4.21 |

3 (Test) | Total test eyes | 628 | 60.0 ± 12.2 | −1.8 ± 2.9 | 2.7 ± 2.6 |

UCSD | 343 | 62.0 ± 12.5 | −1.9 ± 2.6 | 2.5 ± 2.3 | |

NYEE | 126 | 57.4 ± 11.0 | −2.6 ± 3.5 | 3.4 ± 3.4 | |

UAB | 159 | 57.7 ± 11.5 | −1.0 ± 2.8 | 2.6 ± 2.4 |

**Table 3.**

**Table 3.**

Suspects* | Glaucoma:† VF + GON | Total | PGON‡ | ||

n | 478 | 150 | 628 | 76 | |

Mean ± SD | |||||

Characteristics at baseline | Age | 59.1 ± 12.0 | 62.9 ± 12.2 | 65.4 ± 9.91 | |

MD [dB] | −0.89 ± 1.86 | −4.74 ± 3.73 | −2.70 ± 3.22 | ||

PSD [dB] | 1.88 ± 1.14 | 5.42 ± 3.79 | 3.78 ± 3.39 | ||

Number of Eyes (Percent of n) Rate of Decline in VIM Units | |||||

Progression detected | POP | 18 (3.8%), r = −2.01 | 24 (16.0%), r = −2.93 | 42 | 20 (26.3%), r = −2.93 |

VFI | 13 (2.7%), r = −1.43 | 23 (15.3%), r = −1.60 | 36 | 18 (23.7%), r = −1.65 | |

MD | 27 (5.6%), r = −1.72 | 18 (12.0%), r = −1.84 | 45 | 21 (27.6%), r = −1.89 | |

GPA | 14 (2.9%) | 11 (7.3%) | 25 | 11 (14.5%) |

*P*= 0.05) for all eyes tested.

**Figure 4.**

**Figure 4.**

*P*= 0.01) and GPA (

*P*= 0.03). No other comparisons were significantly different (all

*P*≥ 0.10). In the glaucoma group, LR of both POP and VFI identified significantly more eyes as progressed than GPA (

*P*= 0.01 and

*P*= 0.02, respectively); no other comparisons were significantly different (all

*P*≥ 0.06). Finally, in the PGON group, LR of both POP and MD identified significantly more eyes as progressed than GPA (

*P*= 0.05 and

*P*= 0.02, respectively; no other comparisons were significantly different; all

*P*≥ 0.17).

^{ 3–7 }Although increased VF variability masks progression, the widespread use of this test necessitates the development of effective methods that extract progression information from VFs. Unlike currently accepted techniques for detecting progression, POP seeks to optimize the change information in the VF and to account for test variability by focusing on the axis with the best SNR.

^{ 16 }Several studies have suggested less than ideal agreement between functional- and structural-based change detection.

^{ 17–19 }This difference suggests that combining both field and structural tests to detect progression might find more progressing eyes. Additionally, statistically accounting for seven chances to detect progression in POP may have led to an overly conservative detection method. For example, assigning a cutoff proportion based on 95% specificity for each axis in POP classifies progression in many more eyes than VFI or MD, but the overall specificity of POP is reduced because there are seven chances to find progression in POP compared with one in VFI or MD.

^{ 20 }The lesser performance of GPA could be an example of these limitations. A good pattern recognition approach can learn from data how to approach the ideal separation of the classes given the available features, and it can do so without human input and, thus, without the risk of human bias. The indication that POP was as good a detector of progression validates a rigorous mathematical approach to separating progressing from stable eyes, giving POP the potential to be a useful tool for interpreting VF change.

^{ 10,11 }VIM classifies multi-dimensional data into mutually exclusive clusters and, within each cluster, simultaneously uses ICA to extract the local features to create and align its own set of statistically independent axes. Hence, VIM separates the original distribution of data into clusters and axes that have their own distinct patterns. Our application of VIM represents SITA VF data as axes (VF defect patterns; Fig. 1 in main text) within clusters of normal and glaucomatous fields; yielding two axes for the normal fields and seven axes for seven distinct glaucomatous VFs.

**Figure A1.**

**Figure A1.**

**Figure A2.**

**Figure A2.**

**Figure A3.**

**Figure A3.**

*m*and

*b*respectively, are obtained from where

*y*is the field severity (in VU) on axis

_{tae}*a*for the field obtained at the time of visit

*t*projected onto axis

*a*for sample

*e*;

*x*is the time at visit

_{te}*t*for sample

*e*;

*m̂*is the estimated slope (of severity change) of the regression line for sample

_{te}*e*on axis

*a*;

*b̂*

_{ae}is the estimated field severity at baseline (

*x*

_{1e }= 0) for sample

*e*on axis

*a*; and

*ϵ̂*is the estimated offset from the regression line to

_{tae}*y*for visit

_{tae}*t*. The offsets are errors that are minimized as a result of LR.

*m̂*for stable data (Fig. A1).

*R̂*is used as a surrogate for the expected mean of the slope of the regression line and fluctuation range for the rate of change or slope

*m*of a stable eye. The response range is better than max range, (

*y*–

_{max}*y*) or the difference between the first and last visits (

_{min}*y*

_{5}−

*y*

_{1}) in that the regression is a smoothing operation that is less dominated by outliers.

*x*, is set to be equally spaced between 0 and 1 (0.00, 0.25, 0.50, 0.75, and 1.00 for visits 1, 2, 3, 4, and 5, respectively), for five data points for permutation

_{taep}*P*, and the field severity,

*y*, is the permuted axis projection. For example,

_{taep}*y*can be ordered by (

_{tae}*y*

_{1ae },

*y*

_{2ae },

*y*

_{3ae },

*y*

_{4ae },

*y*

_{5ae }), (

*y*

_{3ae },

*y*

_{2ae },

*y*

_{1ae },

*y*

_{5ae },

*y*

_{4ae }), and so on according to the permutation order.

^{th}percentile (Fig. 3 in the main text). Since the 95% cutoff for stability represents 95% true negative rate, it also represents 95% specificity.

*t*-distribution PDF of the response range (representing the slope) is generated from the LR. The approximated distribution (Fig. 3) is wider when the serial data points are more scattered (larger

*ε*s), and narrower when the data are more closely aligned to the estimated mean regression line (smaller

*ε*s). The distribution surrounded by 95% CLs of the response range is called a 95% prediction interval (triangle, Fig. 3), which is used to display the variability of the slope for an individual test eye in Figure 3. The proportion of this generated PDF outside of the stability cutoff represents the certainty level of progression (pink part of triangle in Fig. 3).

*m̂*is the estimated slope of the current sequence of axis projections; μ

_{ae}_{m},

*S*is the estimated mean and standard error of slope

_{m}*m*; and

_{ae}*T = x*−

_{last}*x*is the time difference of the first and the last measurements in a particular sequence. In PDF, we have the overall PDF of stable eyes empirically derived from stable data and the individual PDF estimated for each test eye modeled as a

_{first}*t*–distribution. The steps are:

- Determine stable PDF: acceptable rate of change in severity for 95% of stable eyes built from the empirical distribution of rates of change in 6600 permutations in the stable group.
- Account for test eye PDF: generate a
*t*-distribution of regression slope built from a given eye's variability (in 5 to 20 visits), modeled by Student's*t*-distribution - Compute the POP score and DOC using stable and test eye PDFs: where
*DOCa,CL@95%*is the DOC using 95% CL for axis*a*for stable eyes;*Ra,CL@95%*is the designated CL of response range from stable data for axis*a*;*F*_{ t,v=n−2}is the cumulative*t*-distribution function; and*ν*is degrees of freedom, which is*n*− 2 for the*t*-distribution in LR. - Progression determination: test eye is designated progressed if, on any axis,
*DOCa,CL@95%*(*eye*) greater than*DOC*. The proportion of the PDF of the test eye that is outside the 95% CL for stable eyes must be equal to or greater than the cutoff in the DOC (Table 1 in main text) for the particular axis (Figs. 3, A3)._{a,cutoff}

^{ 8 }and MD score

^{(12)}Please see the Methods section of the main text for details about VFI and MD. For each VF test, POP generated the severity value on each of the seven POP axes, while MD scoring and VFI calculation generated a single global severity. Since POP could look for progression on seven axes compared with one measure for VFI and MD, POP would have more opportunity to find progressing eyes than MD and VFI. Setting each of the seven axes at 95% specificity lowered the overall specificity for POP, which increased the number of eyes classified as progressing.

*t*-distribution that had to be outside the 95% CI for each axis (Table 1 in main text) was derived from the teaching set of stable data to identify 95% of the test set of stable data as stable (95% specificity) for VFI, MD, and the overall POP score. Whereas the

*t*-distribution cutoffs for VFI and MD were 0.50, the cutoffs for the POP axes range from 0.81 to 0.935.

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**M.H. Goldbaum**, None;

**I. Lee**, None;

**G. Jang**, None;

**M. Balasubramanian**, None;

**P.A. Sample**, Alcon (F), Carl Zeiss Meditec (F);

**R.N. Weinreb**, Pfizer (F, R), Carl Zeiss Meditec (F, C, R), Alcon (C, R), Allergan (C, R);

**J.M. Liebmann**, Alcon (F, C), Carl Zeiss Meditec (F), Allergan (C), Pfizer (C);

**C.A. Girkin**, Alcon (F, C), Allergan (C), Pfizer (C), Carl Zeiss Meditec (R);

**D.R. Anderson**, None;

**L.M. Zangwill**, Carl Zeiss Meditec (F);

**M.-J. Fredette**, None;

**T.-P. Jung**, None;

**F.A. Medeiros**, Alcon (F, C, R), Allergan (F, C), Pfizer (F, C), Carl Zeiss Meditec (R);

**C. Bowd**, Allergan (F), Pfizer (F), Alcon (R)