Comparing the Use of Measured and Smoothed Data in Forecasting Visual Field Tests Using Deep Learning

Abstract

Objective

To evaluate the impact of training and testing deep learning (DL) models for visual field (VF) forecasting using input-target pairs in which the target is either the measured VF test result, or its smoothed counterpart constructed via linear regression.

Design

A retrospective data analysis study evaluating DL models for VF forecasting under multiple training and testing configurations.

Subjects and Controls

A total of 1400 subjects (healthy and glaucoma patients) with 19 437 reliable Humphrey VF (24-2 Swedish Interactive Threshold Algorithm) tests collected from longitudinal cohorts at the University of Pittsburgh and New York University.

Methods

Three DL-based pointwise VF forecasting methods were trained and tested under 4 different configurations formed by using measured and smoothed VF targets. Smoothed targets were constructed by applying linear regression over triplets of consecutive VF tests. Models were assessed using fivefold cross-validation and mean absolute error (MAE) as the training and testing metric.

Main Outcome Measures

Mean absolute error of forecasted VF test results under various training and testing configurations.

Results

Models trained and tested on smoothed VF targets consistently achieved lower MAEs compared to those trained and tested on measured VF targets. The performance improvements were most prominent in the 0.5- to 1.5-year forecast range. Furthermore, models trained with smoothed VF targets showed comparable performance when evaluated against measured VF targets.

Conclusions

Using smoothed VF targets for training improves forecasting accuracy by guiding DL models to learn long-term trends in the data rather than forcing them to model noise and short-term variabilities, which are prevalent in VF test data. This approach aligns with clinical goals of assessing meaningful functional changes over time and suggested to be considered in future DL-based VF modeling efforts.

Financial Disclosure(s)

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Glaucoma is a leading cause of vision impairment, which often remains undiagnosed and untreated in marginalized populations, with rising prevalence expected over the next decades.¹ While there is no single cure for glaucoma, proactive care is necessary for symptom management, personalized treatment, and slowing further damage and progression.²

Visual field (VF) testing using standard automated perimetry is a well-established method for longitudinal assessment of peripheral vision in glaucoma. Although VF testing is a widely accepted clinical method, it is: (1) prone to high test–retest variability; (2) subjective and need patient cooperation; and (3) time-consuming and tedious.3, 4, 5 Therefore, a variety of data processing methods have been developed over the years to standardize interpretation, facilitate timely detection, monitor progression, and support clinical decision making.^3,6, 7, 8, 9, 10, 11 Examples of common methods include VF progression analyses,^6,11 phenotype extraction for disease characterization,7, 8, 9 and structure–function mapping.¹⁰ These methods were mainly based on classical statistics and machine learning techniques, which have limited modeling capacity, rely heavily on manual feature engineering, and often require numerous prior observations to make predictions.¹²

Given the clinical importance of VF testing and the inherent limitations of both the test itself and traditional data processing approaches,3, 4, 5 researchers have increasingly adopted deep learning (DL) methods in recent years to address these challenges. Some notable DL applications for VF test data include, but are not limited to, VF test estimation,13, 14, 15, 16, 17 structure–function mapping,^18,19 VF test forecasting,20, 21, 22 VF progression detection either from VF data23, 24, 25 or structural data,²⁶ and clustering of VF loss patterns.²⁷

Regardless of the specific task or method, many of the mentioned DL studies involving VF data have utilized “measured” VF test data (i.e., raw threshold sensitivity or total deviation values) as the target outputs for model training and evaluation. However, due to the high test–retest variability inherent in VF testing,^4,5 clinicians are more interested in capturing long-term trends rather than modeling individual fluctuations. At the same time, the performance of DL models is highly dependent on the quality and consistency of the data used during training and evaluation. In clinical practice, clinicians often rely on temporal modeling approaches such as linear regression,⁶ which essentially provide a “smoothed” representation of VF test data by reducing variance and filtering out noise. Therefore, this study investigates how VF data should be utilized in DL applications. Specifically, whether to use the measured VF test results or their smoothed representations during training and evaluation. We examine the impact of this choice on the performance of pointwise VF forecasting methods,20, 21, 22 a task in which encouraging models to learn long-term trends is crucial due to the need for forecasting the future.

Methods

Dataset

We started with a longitudinal data set consisting of 19 642 VF tests from 1762 individuals, including both glaucoma patients and healthy controls, collected at the University of Pittsburgh and New York University. All procedures adhered to the tenets of the Declaration of Helsinki and were approved by the Institutional Review Boards of the University of Pittsburgh and New York University. The study was conducted in compliance with the Health Insurance Portability and Accountability Act. Written informed consent was obtained from all participants at the time of data collection, and the current analysis was performed retrospectively. Eligible patients had a best-corrected visual acuity of 20/60 or better and a refractive error between –6.0 and +3.0 diopters. Individuals were excluded if they had a history of intraocular surgeries or any ocular conditions other than glaucoma that could affect OCT scanning or retinal layer thickness measurements.

Each subject underwent a series of Humphrey VF assessments using the 24-2 Swedish Interactive Threshold Algorithm (SITA 24-2; Zeiss). Examinations were spaced ≥3 months apart, with a mean interval of 342 days between visits (range: 90-2400 days). We removed VF tests that exhibited fixation losses above 33% or false-positive/false-negative error rates greater than 15%. Also, we removed patients with <3 VF tests, as building smoothed VF targets requires ≥3 VFs. The final data set consisted of 15 262 high quality VF tests from 1400 participants. On average, subjects were 63.2 ± 12.7 years old at baseline, with 6.26 ± 3.42 VF visits per subject. The mean deviation (MD) across the data set averaged –5.5 ± 7.4 dB. A detailed summary of demographic characteristics, disease severity categories, progression rates, and visit statistics is provided in Table 1.

Table 1.

Demographic Table

Characteristics	Value
Number of VF tests	15 262
Number of subjects	1400
Gender
Female	738 (number of subjects)
Male	662
Eye laterality
Right	1159 (number of eyes)
Left	1156
Disease severity
Healthy (MD ≥ –2 dB)	1038 (number of eyes)
Mild (–6 dB ≤ MD < –2 dB)	588
Moderate (–12 dB ≤ MD < –6 dB)	375
Severe (MD < –12 dB)	314
Mean MD slope (dB/yr) ± SD:	–0.21 ± 0.98
Average number of visits per subject	6.26 ± 3.42
Average interval between visits	342 days (range: 90–-2400 days)
Minimum number of days between visits	90 days
Average age on first visit	63.2 ± 12.7 years

MD = mean deviation; SD = standard deviation; VF = visual field.

Study Design

Pointwise VF forecasting is the problem of predicting an entire VF test result (all sensitivity thresholds or total deviations) at a future time point, based on a given series of past VF tests. Using DL models, this problem is typically addressed by training the model on input-target pairs of data samples, where the model takes as input one or more prior VF tests with their corresponding time displacement(s) and predicts the target VF test at a specified future time. Time displacements can be defined relative to the latest VF test (baseline) in the input by assigning negative values to the earlier tests, zero to the baseline, and positive value to the future VF test.^20,22,28 When only a single prior VF test is used as input, only the future time displacement is included.²¹

Inspired by clinicians’ emphasis on identifying long-term trends, we first applied a simple smoothing procedure to construct a smoothed representation of the measured VF data and then defined multiple training and testing configurations to assess the impact of using smoothed versus measured VF data as targets. The target smoothing procedure is illustrated in Figure 1 and Figure 2. In Figure 1, all VF tests at a specific test location from a patient with 8 visits are plotted as a function of time. For each series of 3 consecutive VF tests, we fit a linear regression using the measured test values and used the predicted value at the third time point as the “smoothed VF target.” For patients with more than 3 tests, each series of 3 consecutive tests is processed similarly to construct the corresponding smoothed VF target. This approach reduces the variance in the target data and produces VF targets that are more aligned with preceding tests.

Figure 1.

Example of constructing smoothed VF targets for a single VF test location. This patient underwent 8 VF tests. The horizontal axis represents the number of days since the first visit, while the vertical axis shows the measured sensitivity threshold (TH) values for test location 31 (TH31). Blue circles () indicate the measured threshold values across visits. In each series of 3 consecutive tests, the third test serves as the target in a supervised learning configuration. To construct the smooth targets, a linear regression is fit to each series of 3 measured values (blue circles), and the resulting smoothed VF target is shown as a red diamond (). The fitted lines are shown in green, with dots indicating the projections of the measured values onto their respective regression lines. In general, the smoothed VF tests exhibit lower variance compared to their corresponding actual values. VF = visual field.

Figure 2.

Schematic illustration of a series of 3 consecutive measured VF tests and the smoothed version of the third (right most) test. Each test location in the smoothed VF test was computed as described in Figure 1, by projecting the third test’s value onto the linear regression line fitted to the 3 measured VF tests for that specific location. For supervised learning, either the actual third VF test or its smoothed counterpart can be used as the training target. VF = visual field.

The entire smoothed VF test (smoothed target) is formed by combining the smoothed VF target values across all test locations. Figure 2 schematically illustrates an example series of 3 consecutive measured VF tests and their corresponding smoothed VF test. In a supervised learning configuration, which requires input-target pairs, the third measured VF test (c) or its smoothed version (d) can be used as the target, with the first 2 tests (a and b) serving as the input.

Using input-target pairs formed from either measured or smoothed VF targets, we evaluated the following 4 training/testing configurations for DL-based pointwise VF forecasting:

• 1.Measured VF targets for both training and testing.
• 2.Measured VF targets for training; smoothed VF targets for testing
• 3.Smoothed VF targets for both training and testing.
• 4.Smoothed VF targets for training; measured VF targets for testing.

Note that smoothed data were never used as input in any configuration, since models must operate on measured VF tests in clinical forecasting scenarios. However, smoothed VF targets can be used to guide models toward predictions that are more consistent with prior test measurements, as these targets already captured temporal dependencies across tests. Configuration 1 represents the standard approach, using measured VF targets for both training and testing. Configuration 3 uses smoothed VF targets throughout, while configurations 2 and 4 examine the effects of mismatched targets between training and testing to assess model generalizability and sensitivity to target definition.

To study each configuration, we trained and tested 3 DL-based pointwise VF forecasting methods: (1) recurrent neural network (RNN),²⁰ (2) CascadeNet-5,²¹ a convolutional neural network, and (3) Hybrid-VF-Net,²² which combines an RNN with a convolutional neural network equipped with depthwise transformers.²⁹ CascadeNet-5 uses a single prior VF test and a future time displacement as input, while the RNN and Hybrid-VF-Net models use 2 prior VF tests along with their corresponding time displacements. In addition to these learning-based methods, we included an identity (no-change) model as a simple baseline comparator. The identity model predicts no change from the baseline VF, defined as the most recent available VF test, and reflects the common clinical assumption of stability in slowly progressing, treated patients.

To perform these comparisons, the data were properly reshaped and normalized, and mean absolute error (MAE) was used as the evaluation metric during both training and testing. All methods were reimplemented and carefully tuned to ensure fair and optimal performance. Further details can be found in our previous study.²² We partitioned the data set for fivefold cross-validation without patient overlap. In each fold, approximately 20% of the data were used for testing, while the remaining data were split into 65% for training and 15% for validation.

Results

Errors across Training and Testing Configurations

Table 2 presents the experimental results of the pointwise VF forecasting methods across the training and testing configurations defined in the previous section. Configuration 1, which shows training and testing with measured VF targets, resulted in the highest errors across all compared methods, whereas using smoothed VF targets in configurations 2 and 3 led to lower errors. Across nearly all configurations, Hybrid-VF-Net generally outperformed other methods, showing a performance advantage. Notably, its performance in configuration 1 is comparable to that of RNN and CascadeNet-5 in configuration 3. The last column (configuration 4) shows that when the compared methods are trained on smoothed VF targets but evaluated against measured VF targets, their performance is on par with those trained directly on measured VF targets (configuration 1).

Table 2.

Mean Absolute Error (MAE) Results (in Decibels) of Pointwise Visual Field (VF) Forecasting Methods under Four TRN and TST Configurations

Method Name	Different Train and Test Configurations
		(1)	(2)	(3)	(4)
	TRN	Measured IN	Measured IN	Measured IN	Measured IN
		Measured TG	Measured TG	Smoothed TG	Smoothed TG
	TST	Measured IN	Measured IN	Measured IN	Measured IN
		Measured TG	Smoothed TG	Smoothed TG	Measured TG
Identity		2.65	2.07	2.07	2.65
RNN		2.50	2.22	2.16	2.49
CascadeNet-5		2.42	2.02	1.93	2.45
Hybrid-VF-Net		2.13	1.97	1.73	2.20

IN = input; RNN = recurrent neural network; TG = target; TRN = training; TST = testing.

Each configuration specifies whether measured or smoothed VF data were used as targets (TG) during training and/or testing, while measured VF data were always used as inputs (IN) in all configurations. Corresponding statistical comparisons between methods are summarized in Table 3.

Although linear regression was not included in Table 2 because the primary experimental design focuses on short-sequence forecasting using 1 or 2 prior VF tests, we evaluated a pointwise linear regression model on the subset of eyes with ≥3 prior VF tests under configuration 1 (measured VF targets). The linear regression model achieved an MAE of 3.71 dB, which was inferior to both the identity baseline (2.65 dB) and all DL models.

To further quantify the differences observed in Table 2, we performed a comprehensive statistical comparison across forecasting methods and training/testing configurations. The results of these analyses are summarized in Table 3. For each configuration, pairwise comparisons were conducted on a per-fold basis (fivefold cross-validation) using the paired Wilcoxon signed-rank test. This analysis assessed (1) whether each method differed significantly from the identity baseline and (2) whether Hybrid-VF-Net differed significantly from CascadeNet-5, which was consistently the second-best method.

Table 3.

Summary of Statistical Comparisons Corresponding to the Training and Testing Configurations Reported in Table 2

Different Train and Test Configurations	Were All Other Methods Different than Identity?	Were Hybrid-VF-Net and CascadeNet-5 Statistically Different?
(1)	✔ P values < 0.005 in all folds	✔ P values < 0.05 in 4/5 folds
(2)	✘	✔ P values < 0.05 in all folds
(3)	✔ All methods except RNN P values < 0.005 in all folds	✘ P values < 0.05 in 1/5 folds
(4)	✔ P values < 0.005 in all folds	✔ P values < 0.05 in 4/5 folds

RNN = recurrent neural network.

For each configuration, pairwise comparisons were performed per fold (fivefold cross-validation) using the paired Wilcoxon signed-rank test. The first column summarizes statistical differences from identity, and the second summarizes statistical differences between Hybrid-VF-Net and CascadeNet-5. Checkmarks (✔) and crosses (✘) summarize the outcomes, with accompanying text indicating the significance threshold and the number of folds showing statistical significance.

Generally, all methods could show statistically significant improvements over the identity baseline, except in configuration 2, where there were no consistent statistical differences. Corresponding MAEs in Table 2 showed modest differences. In configuration 3, RNN was not significantly different than identity. Also, the difference between CascadeNet-5 and Hybrid-VF-Net was not significant. Configurations (2) and (3) show the use of smoothed VF targets reduced model separability, due to the reduced variance of targets. Overall, the other statistical test results support the numerical trends observed in Table 2 and demonstrate that both the choice of training/testing targets and the forecasting architecture significantly influence VF forecasting accuracy.

Analysis of VF Forecasting Horizon

As described in Methods, consecutive VF tests were extracted from the data set (Dataset) and used as input-target pairs for training and testing the compared VF forecasting methods. In Figure 3, yellow bars (right vertical axis) illustrate the distribution of VF data grouped by time displacements between the target and baseline VF tests. This distribution reveals that the majority of data fell into the 0.5-year and 1.5-year bins, indicating that in most cases, the models were asked to forecast VF outcomes 6 to 18 months ahead. In addition, the forecasting errors of the compared methods, measured in MAEs (left vertical axis), are overlaid on the distribution plot for configurations 1 and 3, corresponding to the exclusive use of measured and smoothed VF targets, respectively. This combined plot illustrates both the distribution of available data and the forecasting performance of each method as a function of time displacement.

Figure 3.

Line plots showing the forecasting errors (measured as MAE; left vertical axis) of the compared VF forecasting methods across different time displacement ranges. The errors are reported for both configuration 1 (solid lines) and configuration 3 (dashed lines). In addition, the distribution of VF test data grouped by time displacements is overlayed, with the right vertical axis indicating the percentage of total samples. MAE = mean absolute error; RNN = recurrent neural network; VF = visual field.

To further characterize sample-level forecasting uncertainty in prediction error, Figure 4 presents the forecasting errors previously shown in Figure 3 together with their corresponding 95% confidence intervals. In the first row, each method’s performance under configuration 1 (measured VF targets) is directly compared with its counterpart under configuration 3 (smoothed VF targets). Across all methods and most forecast horizons, training and testing with smoothed VF targets are associated not only with lower mean MAEs but also with consistently narrower confidence intervals, indicating both improved accuracy and reduced variability. This effect is most pronounced in the 0.5- to 1.5-year forecast range, which aligns with the higher data density observed in these time bins in Figure 3.

Figure 4.

Visual field forecasting performance with 95% confidence intervals across time horizons. The first row compares each VF forecasting method trained and tested only on measured VF targets (configuration 1) against the same method trained and tested only on smoothed VF targets (configuration 3). The second row compares VF forecasting performance across different methods using measured VF targets, while the third row presents the same intermethod comparison using smoothed VF targets only. MAE = mean absolute error; RNN = recurrent neural network; VF = visual field.

The second row compares forecasting performance across methods when measured VF targets are used (configuration 1). While Hybrid-VF-Net consistently achieves lower MAEs than the other methods, the confidence intervals show partial overlaps across methods, particularly at longer forecast horizons. This overlap reflects the increasing uncertainty associated with larger time displacements and highlights the challenges of long-term VF forecasting when using measured targets. The third row presents the corresponding intermethod comparison when smoothed VF targets are used (configuration 3). Under this configuration, confidence intervals are generally narrower across all methods and forecast horizons, and performance differences between methods are further compressed, reflecting the reduced variance of smoothed targets.

Effect of Severity of the Disease on VF Forecasting Performance

Disease severity influences the reliability of VF tests, and therefore, it can affect the performance of VF forecasting methods. Mean deviation summarizes the overall departure of a patient’s VF from age-matched normative data and is commonly used as a global indicator of disease severity, with more negative values corresponding to greater functional loss.

Figure 5 illustrates the effect of disease severity on VF forecasting performance by plotting MAE across bins of MD. Across all methods, forecasting error increased with worsening MD, reflecting the greater variability and reduced dynamic range associated with advanced disease. When models were trained and tested using smoothed VF targets (configuration 3), MAEs were consistently lower and confidence intervals narrower across nearly all MD bins compared to measured targets (configuration 1). This improvement was most pronounced in mild-to-moderate disease, where data density was highest, while errors increased more rapidly in severely damaged fields (MD < –20 dB), coinciding with sparse sample counts. Overall, these findings indicate that disease severity modulates VF forecasting performance, but that training and evaluating models with smoothed VF targets improves robustness across the full spectrum of disease severity.

Figure 5.

Effect of disease severity on VF forecasting performance. Mean absolute error (MAE; left vertical axis) with 95% confidence intervals for the compared VF forecasting methods plotted across bins of MD, which serves as a surrogate for disease severity. Yellow bars represent the normalized distribution of samples within each MD bin (right vertical axis). The top-left panel shows performance when models are trained and tested using smoothed VF targets (configuration 3). The remaining panels compare each method’s performance under measured VF targets (configuration 1) versus smoothed VF targets (configuration 3) across MD bins. MAE = mean absolute error; MD = mean deviation; RNN = recurrent neural network; VF = visual field.

Effect of Test Reliability on VF Forecasting Performance

The reliability of VF tests plays a crucial role in determining the accuracy of VF forecasting. Visual field measurements are subject to patient-dependent factors such as fatigue, inattention, and learning effects, which are commonly quantified using reliability indices including false-positive rates, false-negative rates (FNRs), and fixation losses. Among these factors, FNR is reported to significantly affect VF assessment outcomes.³⁰

Figure 6 shows VF forecasting performance of the compared methods stratified by FNR bins. Across all methods and configurations, MAE increased monotonically with higher FNR, indicating degraded prediction accuracy as test reliability worsened. When models were trained and tested using smoothed VF targets (configuration 3), MAEs were consistently lower than those obtained with measured VF targets (configuration 1) across all FNR bins. The improvement associated with smoothing was evident even in the lowest FNR bin and became more pronounced at higher FNRs, where measured-target performance degraded more rapidly. Confidence intervals also tended to be narrower for smoothed targets, indicating reduced variability in forecasting error. The sample distribution was heavily skewed toward lower FNR bins, with fewer samples at higher FNRs, which coincided with increased uncertainty in the highest FNR bins.

Figure 6.

Mean absolute error (left vertical axis) with 95% confidence intervals for the compared VF forecasting methods stratified by false-negative rate as a commonly used VF test reliability index, grouped into bins. In top left panel, the yellow bars indicate the normalized distribution of samples within each reliability bin (right vertical axis). The other panels showing the results for models trained and tested using both configurations 1 and 3 (measured only and smoothed only). MAE = mean absolute error; VF = visual field.

Discussion

The results presented in Table 2 demonstrate a clear impact of target data choice on the accuracy of DL-based pointwise VF forecasting methods. Firstly, the high errors in configuration 1 suggest that relying solely on measured VF data for training and evaluation compromises accuracy by forcing models to learn noise and unnecessary short-term fluctuations. Notably, in configuration 2, where smoothed VF targets were used only for testing, the methods’ errors were reduced. This is particularly important given the clinical relevance of long-term trends in VF data. The results suggest that, even without training on smoothed data, the models inherently mitigate noise by capturing underlying patterns, resulting in improved performance when evaluated against smoothed VF targets.

The inferior performance of linear regression compared to the identity baseline further underscores the challenge of short-horizon forecasting using limited prior observations. When progression rates are small, slope estimation from only 3 VF tests may amplify measurement variability rather than capture true longitudinal change. Prior studies¹² have shown that a larger number of VF tests (e.g., ≥10) are often required to achieve regression-based forecasts with lower forecasting errors (approximately 2.5 dB). In contrast, DL models appear better able to balance stability and progression modeling under limited-input conditions by leveraging spatial and temporal patterns beyond simple slope estimation.

Nevertheless, using measured VF data as training targets (as in configurations 1 and 2) can hinder model performance by anchoring the learning process to noisy fluctuations rather than allowing the model to capture underlying trends. Therefore, in configuration 3, we used smoothed VF targets for both training and testing. As shown in Table 2, this setting resulted in the lowest errors, suggesting better capture of underlying patterns and stronger alignment with long-term trends. Training on targets that are already aligned with these trends helps guide the model more effectively and reduces the risk of overfitting to noise in the measured VF data.

In configurations 2 and 4, there is a mismatch between training and testing VF targets, allowing us to assess how models generalize across different target definitions. In configuration 2, models are trained on measured VF targets but evaluated against smoothed VF targets. As shown in Table 2, this configuration yields lower MAEs than configuration 1 across methods; however, Table 3 indicates that these numerical improvements do not consistently translate into statistically significant differences relative to the identity baseline. This behavior is expected, as evaluation against smoothed targets reduces target variance, thereby compressing performance differences across models and limiting the ability of hypothesis tests to detect small but meaningful improvements. Importantly, this result suggests that training on measured VF targets does not provide a clear advantage when performance is assessed against smoothed representations that emphasize longitudinal trends.

Configuration 4 represents the reverse mismatch, where models are trained on smoothed VF targets but evaluated against measured VF targets. Despite this mismatch, performance remains comparable to configuration 1, in which measured VF targets are used for both training and testing (Table 2), and statistically significant differences between methods are preserved (Table 3). Taken together with the superior performance observed in configuration 3, these findings indicate that training on smoothed VF targets improves model robustness and generalization without compromising accuracy on measured VF data. This behavior suggests that smoothing introduces a beneficial inductive bias during training, guiding models toward learning clinically relevant temporal trends while preventing overfitting to noise-driven fluctuations.

Statistical comparisons in Table 3 showed that smoothing VF targets meaningfully alters the learning behavior of the methods. Although training and testing with smoothed VF targets resulted in consistently lower MAEs (Table 2), the use of smoothed data reduced the statistical separability between strong VF forecasting methods. This effect is expected, as smoothing suppresses test–retest variability and compresses intermodel performance differences. Consequently, statistical tests became less sensitive to detecting small architectural advantages, particularly between Hybrid-VF-Net and CascadeNet-5. Importantly, this reduction in statistical power does not indicate inferior modeling performance; rather, it reflects that the compared methods are evaluated against targets that emphasize clinically meaningful long-term trends rather than their ability to learn noise-driven fluctuations. Therefore, smoothed VF targets may be more appropriate for assessing practical forecasting accuracy and clinical relevance.

From a clinical perspective, these findings support the use of smoothed VF targets during model development, particularly for applications focused on progression assessment and future risk estimation. Importantly, training on smoothed targets did not significantly degrade performance when evaluated on measured VF data (configuration 4), indicating that this strategy preserves practical applicability while improving robustness. Incorporating smoothed targets offers a principled way to align model optimization and evaluation with clinical interpretation, potentially leading to more reliable decision-support tools.

Figure 4 further clarifies the effect of target smoothing on both forecasting accuracy and uncertainty. In addition to lowering mean errors, smoothed VF targets consistently yield narrower confidence intervals across forecast horizons, indicating reduced variability in model predictions. It demonstrates that improvements associated with smoothed VF targets are not limited to average error reduction but also extend to increased robustness and consistency across time horizons.

The small performance difference between configurations 1 and 4 raises an important question: Why did training on smoothed VF targets lead to a small performance drop, particularly for Hybrid-VF-Net in configuration 4? To investigate this, we computed the difference between the average pointwise error matrices of the 2 configurations for this method (Fig 7). The largest discrepancies were found in peripheral locations, which are known to have higher test–retest variability. Therefore, the source of the slight performance drops in configuration 4 (with a mismatch) compared to configuration 1 originates from test locations with higher variability. Importantly, it implies that training on smoothed VF targets does not compromise accuracy on measured outcomes, while enabling improved performance when evaluated on smoothed VF targets (as in configuration 3). This observation further supports the use of smoothed VF targets in practical DL-based applications, especially for pointwise VF forecasting.

Figure 7.

Absolute difference between the pointwise error matrices of Hybrid-VF-Net under configurations 1 and 4.

In Analysis of VF Forecasting Horizon, we evaluated VF forecasting methods at different future time points using the same data set under 2 settings: configuration 1 with measured VF targets and configuration 3 with smoothed VF targets. Figure 3 demonstrates that across all compared VF forecasting methods, configuration 3 (which uses smoothed VF targets) consistently leads to better outcomes compared to configuration 1 (which uses measured VF targets). This indicates that smoothed VF targets help models learn the underlying trends in the data more effectively. As expected, forecasting errors are lowest for the 1-year bin, which contain the majority of the samples. Beyond 1.5 years, MAEs exhibit a consistent upward trend with increasing time displacement, indicating the greater difficulty of long-term forecasting, likely driven by both data sparsity and the inherent challenge of predicting far into the future. The performance gains of configuration 3 over configuration 1 are most notable in the 0.5- to 1.5-year range, where data are more abundant and short-term to mid-term progression patterns are likely more stable. However, as time displacement increases, the performance gap between the 2 configurations narrows, suggesting that the benefits of smoothing diminish in long-term forecasting, likely due to greater uncertainty and fewer training examples with larger time displacements.

The stratified analyses by disease severity (Effect of Severity of the Disease on VF Forecasting Performance) further clarify how target smoothing influences VF forecasting behavior across different stages of glaucoma. As shown in Figure 5, forecasting errors increase with worsening MD, consistent with the known rise in test–retest variability and reduced functionality in advanced glaucoma. Importantly, smoothing VF targets improves forecasting accuracy across severity levels. The absolute difference in MAE between smoothed and measured targets appears larger in moderate to severe disease (MD < –6 dB), suggesting a potentially greater benefit in more advanced stages. However, this region contains fewer samples, resulting in wider confidence intervals and increased uncertainty in the estimates. In contrast, the improvements observed in mild to moderate glaucoma are supported by higher data density and narrower confidence intervals, indicating more consistent gains in this range.

Similarly, the analysis of test reliability (Fig 6) highlights the interaction between measurement noise and forecasting error. Visual field tests with poorer reliability indices were associated with higher forecasting errors across all methods. However, the consistent advantage observed when using smoothed VF targets indicates that smoothing acts as an implicit noise-regularization mechanism, improving model robustness to imperfect test conditions. Clinically, this is particularly relevant, as VF reliability often fluctuates over time and cannot be guaranteed in routine practice. Models trained with smoothed targets may therefore be better suited for deployment in clinical practice.

One of the key limitations of this study is that the smoothing procedure depends on the number of prior VF tests used for linear regression. This introduces a trade-off: using more prior tests may overlook short-term changes, while using fewer may result in increased variability. In this work, we limited the number of prior VF tests for smoothing to 3, as current DL-based VF forecasting methods are well-suited to handle 1 or 2 prior VF tests as input to forecast the future.²² This limitation also presents an opportunity: by varying the number of prior VF tests used in the smoothing procedure, one can generate targets that emphasize either short-term or long-term trends, enabling DL-based VF forecasting methods to be trained on progression patterns at different temporal scales.

Conclusion

In this study, we systematically evaluated the impact of target data definition on DL-based VF forecasting. Our results demonstrate that using smoothed VF targets, constructed via linear regression from consecutive VF tests, provides an intuitive and effective strategy to guide DL models toward learning long-term trends that align more closely with clinical priorities, by mitigating the influence of noise and reducing the need to model short-term fluctuations. This approach consistently improves forecasting accuracy, reduces variability, and enhances robustness across disease severities, forecasting horizons, and test reliability conditions. Importantly, training on smoothed VF targets does not compromise performance when models are evaluated against measured VF data. These findings suggest that incorporating smoothed VF targets during model development may improve the clinical utility of automated VF forecasting methods and can be considered in future DL applications for glaucoma monitoring and progression assessment.

Manuscript no. XOPS-D-25-00705.