The study was performed in accordance with the ethical principles specified in the Declaration of Helsinki, the Good Clinical Practice (GCP), and regulatory requirements. The study included 256 eyes from 256 patients with POAG at early, moderate, advanced stages. All patients were managed at the Burnazyan Federal Biophysical Center and Ophthalmological Center in Moscow between January 2019 and December 2023, with each eye observed for at least 36 months.

Inclusion criteria comprised a diagnosis of POAG at early, moderate, or advanced stages based on the presence of elevated intraocular pressure (IOP), neuroretinal rim thinning, and focal or diffuse RNFL defects with corresponding visual field changes [18]. All study participants additionally had a spherical equivalent between − 6.0 D and + 6.0 D, astigmatism ≤ 2.0 D, and an open anterior chamber angle ≥ 30° on gonioscopy.

Exclusion criteria encompassed any media opacities precluding reliable OCT or visual field testing (for example, dense cataract or corneal scar), as well as unreliable visual field examinations (defined by fixation losses > 20% or false positives/negatives > 15%), fewer than five reliable visual field tests, prior intraocular surgery (including cataract extraction, trabeculectomy, or laser trabeculoplasty), systemic disorders affecting ocular perfusion or neural function (such as diabetes mellitus, systemic autoimmune disease, Parkinson’s disease, Alzheimer’s disease, or dementia), and the use of systemic miotics or other medications known to alter pupil size.

Patients meeting the inclusion and exclusion criteria were stratified by disease stage. The first cohort comprised from patients with early-stage POAG, while the second cohort comprised eyes from patients with moderate and advanced stages of the disease. All patients underwent a standardized ophthalmic evaluation at each visit, including medical history review, visual acuity testing, autorefraction, slit-lamp biomicroscopy, ophthalmoscopy, gonioscopy, IOP measurement using the Ocular Response Analyzer (ORA; Reichert, USA), pachymetry (SP-100; Tomey, Germany), and standard automated perimetry with the SITA Standard 24 − 2 protocol (Humphrey Field Analyzer; Carl Zeiss Meditec, USA). Spectral-domain OCT and OCT angiography were performed using the RTVue XR Avanti device with AngioVue OCTA capability (Optovue, Inc., USA).

Glaucomatous optic neuropathy progression rates were determined from both perimetric and OCT data. Guided Progression Analysis (GPA) software on the Humphrey Field Analyzer II was used to assess visual field progression by trend analysis of the VFI and by event analysis. Progression was considered statistically significant when the slope of the 24 − 2 VFI trend had p < 0.05. Only reliably flagged test points were included in the calculation of mean progression rates. Standard automated perimetry was performed every 6 months. A study eye was classified as “progressing” when either the event analysis or the trend analysis indicated significant progression. To eliminate confounding by cataract, eyes with documented cataract progression - defined as a decrease of two or more lines of visual acuity on at least two visits due to lens opacity - were excluded from perimetric progression analysis.

Changes in RNFL and GCC thickness were analyzed using the built-in trend analysis software of the RTVue XR Avanti OCT (Optovue, Inc.). Three consecutive scans were acquired at each visit, and only scans with a signal strength index (SSI) > 45 were included. Structural progression was defined by a statistically significant negative slope (p < 0.05) of the regression line for RNFL or GCC thickness over time.

At the end of follow-up, each patient received an expert-graded progression category based on these criteria: (1) slow progression, defined by a rate of progression (ROP) in VFI of 0.5–1.0% per year and ROP in RNFL and GCC thickness of < 1 μm/year; (2) moderate progression, defined by ROP in VFI of 1.0–2.0% per year and ROP in RNFL and GCC of 1–2 μm/year; and (3) rapid progression, defined by ROP in VFI > 2.0% per year and ROP in RNFL and GCC > 2 μm/year [18, 19].

For building the prognostic model of glaucomatous optic neuropathy (GON) progression rate, we employed Ranked Partial Least Squares Discriminant Analysis (Ranked PLS-DA) - an innovative variation of PLS-DA that accounts for class ranking and implements soft discrimination in multiclass classification [20].

The application of Ranked PLS-DA is particularly relevant for the cases involving small patient cohorts, complex multicollinearity, and the need for model interpretability. This method has been demonstrated to possess several advantages over conventional approaches - it takes into account the predictor redundancy and correlation, while enabling correct selection of the most significant variables influencing disease outcomes. Ranked PLS-DA is especially effective when class hierarchy exists or smooth transitions occur between severity levels or progression rates, which is typical for ophthalmological applications.

The fundamental principle of Ranked PLS-DA is its ability to model ordinal relationships between classes while maintaining the flexibility of soft classification. Unlike traditional hard classification methods that unambiguously assign samples to the predefined categories, this approach recognizes that disease progression exists on a continuum, allowing for probabilistic assignments that better reflect clinical reality. This is particularly valuable in glaucoma research, where the boundaries between slow, moderate, and rapid rates of progression are indistinct.

The method develops a projection onto the latent space that maximize the separation between ordered classes while preserving the underlying data structure. This dual optimization ensures both high discriminatory power and biological relevance of the resulting model. The soft discrimination capability allows identification of borderline cases that may require enhanced monitoring or individualized treatment approaches.

Variable selection was performed using a novel wrapper method [21], based on the sequential removal of variables from the model. Variables were retained if their removal significantly decreased model performance, ensuring that only the most predictive parameters were included in the final model.

For model optimization and validation, an augmented test set was generated using Procrustes Cross-Validation (PCV) [22]. This method creates a validation set that can be utilized analogously to an independent test set, providing reliable performance assessment while allowing the use of limited clinical data. The PCV approach is particularly valuable in medical applications where large datasets are challenging to obtain, as it provides consistent validation metrics without requiring an additional cohort of patients.

Model performance was evaluated using multiple complementary metrics including sensitivity, specificity, total efficiency (TEFF), and area under the ROC curve (AUC) [23]. This comprehensive evaluation framework ensures robust assessment of the model’s predictive capabilities across different performance dimensions, providing clinicians with confidence in the model’s sustainability for real-world applications.