Psychophysical Validation of a Novel Active Learning Approach for Measuring the Visual Acuity Behavioral Function

Using Hierarchical Bayesian Modeling to Enhance Statistical Inference on Contrast Sensitivity

Purpose

The purpose of this study is to introduce a nonparametric hierarchical Bayesian model (HBM) that enables advanced statistical inference on contrast sensitivity (CS) both at individual spatial frequencies (SFs) and across multiple SFs in clinical trials, where CS measurements are crucial for assessing safety and efficacy.

Methods

The HBM computes the joint posterior distribution of CS at six Food and Drug Administration-designated SFs across the population, individual, and test levels. It incorporates covariances at both population and individual levels to capture the relationship between CSs across SFs. A Bayesian inference procedure (BIP) is also used to estimate the posterior distribution of CS at each SF independently. Both methods are applied to a quantitative CSF (qCSF) dataset of 112 subjects and compared in terms of precision, test-retest reliability of CS estimates, sensitivity, accuracy, and statistical power in detecting CS changes.

Results

The HBM reveals correlations between CSs in pairs of SFs and provides significantly more precise estimates and higher test-retest reliability compared to the BIP. Additionally, it improves the average sensitivity and accuracy in detecting CS changes for individual subjects, as well as statistical power for detecting group-level CS changes at individual and combinations of multiple SFs between luminance conditions.

Conclusions

The HBM establishes a comprehensive framework to enhance sensitivity, accuracy, and statistical power for detecting CS changes in hierarchical experimental designs.

Translational Relevance

The HBM presents a valuable tool for advancing CS assessments in the clinic and clinical trials, potentially improving the evaluation of treatment efficacy and patient outcomes.

Quantifying the Functional Relationship Between Visual Acuity and Contrast Sensitivity Function

Purpose

Studies have reported that individuals with certain ocular disorders may have significant decreases in contrast sensitivity function (CSF) despite having normal or near normal visual acuity (VA). This study seeks to elucidate this phenomenon by investigating the relationship between VA and CSF.

Methods

We analyzed data from 14 eyes tested with Electronic Early Treatment Diabetic Retinopathy and quantitative CSF under four Bangerter foil conditions (n = 56). From the CSF data, we estimated peak gain, peak frequency, and contrast sensitivity acuity (CSA). We explored the correlations between VA and various CSF parameters and evaluated five predictive models of VA using CSA alone and in combination with additional CSF parameters through ridge regression.

Results

We found that similar VA scores can correspond with markedly different CSFs and observed significant correlations among all CSF parameters and between VA and each CSF parameter (all P < 0.001). The most effective predictive model, incorporating CSA and peak gain, explained 90.97% of the variance with a root mean squared error of 0.0676 logMAR, which is comparable with the average standard deviation of the VA scores (0.0627 logMAR) and accounted for 38.6% of the residual variance not explained by the CSA-alone model.

Conclusions

This study offers the first empirical inference of the quantitative relationship between VA and CSF, suggesting that various CSF parameter combinations can yield identical VA. This might help to explain why some clinical populations with normal or near-normal VA exhibit significant CSF deficits and calls for further research in different clinical settings.

Visual Function and Driving Performance Under Different Lighting Conditions in Older Drivers: Preliminary Results From an Observational Study

BACKGROUND

Age-related vision changes significantly contribute to fatal crashes at night among older drivers. However, the effects of lighting conditions on age-related vision changes and associated driving performance remain unclear.

OBJECTIVE

This pilot study examined the associations between visual function and driving performance assessed by a high-fidelity driving simulator among drivers 60 and older across 3 lighting conditions: daytime (photopic), nighttime (mesopic), and nighttime with glare.

METHODS

Active drivers aged 60 years or older participated in visual function assessments and simulated driving on a high-fidelity driving simulator. Visual acuity (VA), contrast sensitivity function (CSF), and visual field map (VFM) were measured using quantitative VA, quantitative CSF, and quantitative VFM procedures under photopic and mesopic conditions. VA and CSF were also obtained in the presence of glare in the mesopic condition. Two summary metrics, the area under the log CSF (AULCSF) and volume under the surface of VFM (VUSVFM), quantified CSF and VFM. Driving performance measures (average speed, SD of speed [SDspeed], SD of lane position (SDLP), and reaction time) were assessed under daytime, nighttime, and nighttime with glare conditions. Pearson correlations determined the associations between visual function and driving performance across the 3 lighting conditions.

RESULTS

Of the 20 drivers included, the average age was 70.3 years; 55% were male. Poor photopic VA was significantly correlated with greater SDspeed (r=0.26; P<.001) and greater SDLP (r=0.31; P<.001). Poor photopic AULCSF was correlated with greater SDLP (r=-0.22; P=.01). Poor mesopic VUSFVM was significantly correlated with slower average speed (r=-0.24; P=.007), larger SDspeed (r=-0.19; P=.04), greater SDLP (r=-0.22; P=.007), and longer reaction times (r=-0.22; P=.04) while driving at night. For functional vision in the mesopic condition with glare, poor VA was significantly correlated with longer reaction times (r=0.21; P=.046) while driving at night with glare; poor AULCSF was significantly correlated with slower speed (r=-0.32; P<.001), greater SDLP (r=-0.26; P=.001) and longer reaction times (r=-0.2; P=.04) while driving at night with glare. No other significant correlations were observed between visual function and driving performance under the same lighting conditions.

CONCLUSIONS

Visual functions differentially affect driving performance in different lighting conditions among older drivers, with more substantial impacts on driving during nighttime, especially in glare. Additional research with larger sample sizes is needed to confirm these results.

Quantification of expected information gain in visual acuity and contrast sensitivity tests

We make use of expected information gain to quantify the amount of knowledge obtained from measurements in a population. In the first application, we compared the expected information gain in the Snellen, ETDRS, and qVA visual acuity (VA) tests, as well as in the Pelli-Robson, CSV-1000, and qCSF contrast sensitivity (CS) tests. For the VA tests, ETDRS generated more expected information gain than Snellen. Additionally, the qVA test with 15 rows (or 45 optotypes) generated more expected information gain than ETDRS, whether scored with VA threshold alone or with both VA threshold and VA range. Regarding the CS tests, CSV-1000 generated more expected information gain than Pelli-Robson, and the qCSF test with 25 trials generated more expected information gain than CSV-1000, whether scored with AULCSF or with CSF at six spatial frequencies. The active learning-based qVA and qCSF tests have the potential to generate more expected information gain than traditional paper chart tests. Although we have specifically applied it to compare VA and CS tests, expected information gain is a general concept that can be used to compare measurements in any domain.

Quantification of Expected Information Gain in Visual Acuity and Contrast Sensitivity Tests

We introduce expected information gain to quantify measurements and apply it to compare visual acuity (VA) and contrast sensitivity (CS) tests. We simulated observers with parameters covered by the visual acuity and contrast sensitivity tests and observers based on distributions of normal observers tested in three luminance and four Bangerter foil conditions. We first generated the probability distributions of test scores for each individual in each population in the Snellen, ETDRS and qVA visual acuity tests and the Pelli-Robson, CSV-1000 and qCSF contrast sensitivity tests and constructed the probability distributions of all possible test scores of the entire population. We then computed expected information gain by subtracting expected residual entropy from the total entropy of the population. For acuity tests, ETDRS generated more expected information gain than Snellen; scored with VA threshold only or with both VA threshold and VA range, qVA with 15 rows (or 45 optotypes) generated more expected information gain than ETDRS. For contrast sensitivity tests, CSV-1000 generated more expected information gain than Pelli-Robson; scored with AULCSF or with CS at six spatial frequencies, qCSF with 25 trials generated more expected information gain than CSV-1000. The active learning based qVA and qCSF tests can generate more expected information than the traditional paper chart tests. Although we only applied it to compare visual acuity and contrast sensitivity tests, information gain is a general concept that can be used to compare measurements and data analytics in any domain.

Collective endpoint of visual acuity and contrast sensitivity function from hierarchical Bayesian joint modeling

Clinical trials typically analyze multiple endpoints for signals of efficacy. To improve signal detection for treatment effects using the high-dimensional data collected in trials, we developed a hierarchical Bayesian joint model (HBJM) to compute a five-dimensional collective endpoint (CE5D) of contrast sensitivity function (CSF) and visual acuity (VA). The HBJM analyzes row-by-row CSF and VA data across multiple conditions, and describes visual functions across a hierarchy of population, individuals, and tests. It generates joint posterior distributions of CE5D that combines CSF (peak gain, peak frequency, and bandwidth) and VA (threshold and range) parameters. The HBJM was applied to an existing dataset of 14 eyes, each tested with the quantitative VA and quantitative CSF procedures in four Bangerter foil conditions. The HBJM recovered strong correlations among CE5D components at all levels. With 15 qVA and 25 qCSF rows, it reduced the variance of the estimated components by 72% on average. Combining signals from VA and CSF and reducing noises, CE5D exhibited significantly higher sensitivity and accuracy in discriminating performance differences between foil conditions at both the group and test levels than the original tests. The HBJM extracts valuable information about covariance of CSF and VA parameters, improves precision of the estimated parameters, and increases the statistical power in detecting vision changes. By combining signals and reducing noise from multiple tests for detecting vision changes, the HBJM framework exhibits potential to increase statistical power for combining multi-modality data in ophthalmic trials.

Quantifying Uncertainty of the Estimated Visual Acuity Behavioral Function With Hierarchical Bayesian Modeling

Purpose

The goal of this study is to develop a hierarchical Bayesian model (HBM) to better quantify uncertainty in visual acuity (VA) tests by incorporating the relationship between VA threshold and range across multiple individuals and tests.

Methods

The three-level HBM consisted of multiple two-dimensional Gaussian distributions of hyperparameters and parameters of the VA behavioral function (VABF) at the population, individual, and test levels. The model was applied to a dataset of quantitative VA (qVA) assessments of 14 eyes in 4 Bangerter foil conditions. We quantified uncertainties of the estimated VABF parameters (VA threshold and range) from the HBM and compared them with those from the qVA.

Results

The HBM recovered covariances between VABF parameters and provided better fits to the data than the qVA. It reduced the uncertainty of their estimates by 4.2% to 45.8%. The reduction of uncertainty, on average, resulted in 3 fewer rows needed to reach a 95% accuracy in detecting a 0.15 logMAR change of VA threshold or both parameters than the qVA.

Conclusions

The HBM utilized knowledge across individuals and tests in a single model and provided better quantification of the uncertainty of the estimated VABF, especially when the number of tested rows was relatively small.

Translational Relevance

The HBM can increase the accuracy in detecting VA changes. Further research is necessary to evaluate its potential in clinical populations.

Do Impairments in Visual Functions Affect Skiing Performance?

Nordic and alpine skiing-related visual tasks such as identifying hill contours, slope characteristics, and snow conditions increase demands on contrast processing and other visual functions. Prospective observational studies were conducted to assess the relationships between skiing performance and a broad range of visual functions in nordic and alpine skiers with vision impairments. The study hypothesized that contrast sensitivity (CS), visual acuity (VA), and visual field (VF) would be predictive of skiing performance. Binocular static VA, CS, light sensitivity, glare sensitivity, glare recovery, dynamic VA, translational and radial motion perception, and VF were assessed in elite Para nordic (n = 26) and Para alpine (n = 15) skiers. Skiing performance was assessed based on skiers’ raw race times. Performance on the visual function tests was compared with skiing performances using Kendall’s correlations (with and without Bonferroni–Holm corrections) and linear multivariable regressions (p < 0.05 considered significant). None of the vision variables were significantly correlated with performance in Para nordic or Para alpine skiing after Bonferroni–Holm corrections were applied. Before applying the corrections, VF extent (ρ = -0.37, p = 0.011), and static VA (ρ = 0.26, p = 0.066) demonstrated the strongest correlations with Para nordic skiing performance; in Para alpine skiing, static VA and CS demonstrated the strongest correlations with downhill (static VA: ρ = 0.54, p = 0.046, CS: ρ = -0.50, p = 0.06), super G (static VA: ρ = 0.50, p = 0.007, CS: ρ = -0.51, p = 0.017), and giant slalom (static VA: ρ = 0.57, p = 0.01, CS: ρ = -0.46, p = 0.017) performance. Dynamic VA and VF were significantly associated with downhill (ρ = 0.593, p = 0.04) and slalom (ρ = -0.49, p = 0.013) performances, respectively. Static VA was a significant predictor of giant slalom [(F(3,11) = 24.71, p < 0.001), and R of 0.87], super G [(F(3,9) = 17.34, p = 0.002), and R of 0.85], and slalom [(F(3,11) = 11.8, p = 0.002), and R of 0.80] performance, but CS and VF were not. Interestingly, static VA and CS were highly correlated in both Para nordic (ρ = -0.60, p < 0.001) and Para alpine (ρ = -0.80, p < 0.001) skiers. Of the vision variables, only static VA and VF were associated with skiing performance and should be included as the in Para nordic and Para alpine classifications. The strong correlations between static VA and CS in these skiers with vision impairment may have masked relationships between CS and skiing performance.