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.

Hierarchical Bayesian modeling of contrast sensitivity functions in a within-subject design.

Recent development of the quick contrast sensitivity function (qCSF) method has made it possible to obtain accurate, precise, and efficient contrast sensitivity function (CSF) assessment. To improve statistical inference on CSF changes in a within-subject design, we developed a hierarchical Bayesian model (HBM) to compute the joint distribution of CSF parameters and hyperparameters at test, subject, and population levels, utilizing information within- and between-subjects and experimental conditions. We evaluated the performance of the HBM relative to a non-hierarchical Bayesian inference procedure (BIP) on an existing CSF dataset of 112 subjects obtained with the qCSF method in three luminance conditions (Hou, Lesmes, Kim, Gu, Pitt, Myung, & Lu, 2016). We found that the average d's of the area under log CSF (AULCSF) and CSF parameters between pairs of luminance conditions at the test-level from the HBM were 33.5% and 103.3% greater than those from the BIP analysis of AULCSF. The increased d' resulted in greater statistical differences between experimental conditions across subjects. In addition, simulations showed that the HBM generated accurate and precise CSF parameter estimates. These results have strong implications for the application of HBM in clinical trials and patient care.

New Technologies for Outcome Measures in Glaucoma: Review by the European Vision Institute Special Interest Focus Group.

Glaucoma is the leading cause of irreversible blindness worldwide, with an increasing prevalence. The complexity of the disease has been a major challenge in moving the field forward with regard to both pathophysiological insight and treatment. In this context, discussing possible outcome measures in glaucoma trials is of utmost importance and clinical relevance. A recent meeting of the European Vision Institute (EVI) special interest focus group was held on "New Technologies for Outcome Measures in Retina and Glaucoma," addressing both functional and structural outcomes, as well as translational hot topics in glaucoma and retina research. In conjunction with the published literature, this review summarizes the meeting focusing on glaucoma.

A novel Bayesian adaptive method for mapping the visual field.

Measuring visual functions such as light and contrast sensitivity, visual acuity, reading speed, and crowding across retinal locations provides visual-field maps (VFMs) that are extremely valuable for detecting and managing eye diseases. Although mapping light sensitivity is a standard glaucoma test, the measurement is often noisy (Keltner et al., 2000). Mapping other visual functions is even more challenging. To improve the precision of light-sensitivity mapping and enable other VFM assessments, we developed a novel hybrid Bayesian adaptive testing framework, the qVFM method. The method combines a global module for preliminary assessment of the VFM's shape and a local module for assessing individual visual-field locations. This study validates the qVFM method in measuring light sensitivity across the visual field. In both simulation and psychophysics studies, we sampled 100 visual-field locations (60° × 60°) and compared the performance of qVFM with the qYN procedure (Lesmes et al., 2015) that measured light sensitivity at each location independently. In the simulations, a simulated observer was tested monocularly for 1,000 runs with 1,200 trials/run, to compare the accuracy and precision of the two methods. In the experiments, data were collected from 12 eyes (six left, six right) of six human subjects. Subjects were cued to report the presence or absence of a target stimulus, with the luminance and location of the target adaptively selected in each trial. Both simulations and a psychological experiment showed that the qVFM method can provide accurate, precise, and efficient mapping of light sensitivity. This method can be extended to map other visual functions, with potential clinical signals for monitoring vision loss, evaluating therapeutic interventions, and developing effective rehabilitation for low vision.

Assessing reading performance in the periphery with a Bayesian adaptive approach: The qReading method.

Reading is a crucial visual activity and a fundamental skill in daily life. Rapid Serial Visual Presentation (RSVP) is a text-presentation paradigm that has been extensively used in the laboratory to study basic characteristics of reading performance. However, measuring reading function (reading speed vs. print size) is time-consuming for RSVP reading using conventional testing procedures. In this study, we develop a novel method, qReading, utilizing the Bayesian adaptive testing framework to measure reading function in the periphery. We perform both a psychophysical experiment and computer simulations to validate the qReading method. In the experiment, words are presented using an RSVP paradigm at 10° in the lower visual field. The reading function obtained from the qReading method with 50 trials exhibits good agreement (i.e., high accuracy) with the reading function obtained from a conventional method (method of constant stimuli [MCS]) with 186 trials (mean root mean square error: 0.12 log10 units). Simulations further confirm that the qReading method provides an unbiased measure. The qReading procedure also demonstrates excellent precision (half width of 68.2% credible interval: 0.02 log10 units with 50 trials) compared to the MCS method (0.03 log10 units with 186 trials). This investigation establishes that the qReading method can adequately measure the reading function in the normal periphery with high accuracy, precision, and efficiency, and is a potentially valuable tool for both research and clinical assessments.

Bayesian adaptive assessment of the reading function for vision: The qReading method.

Reading is a fundamental skill that can be significantly affected by visual disabilities. Reading performance, which typically is measured as reading speed with a reading chart, is a key endpoint for quantifying normal or abnormal vision. Despite its importance for clinical vision, existing reading tests for vision are time consuming and difficult to administer. Here, we propose a Bayesian adaptive method, the qReading method, for automated assessment of the reading speed versus print size function. We implemented the qReading method with a word/nonword lexical decision task and validated the method with computer simulations and a psychophysical experiment. Computer simulations showed that both the interrun standard deviation and intrarun half width of the 68.2% credible interval of the estimated reading speeds from the qReading method were less than 0.1 log10 units after 150 trials, with a bias of 0.05 log10 units. In the psychophysical experiment, reading functions measured by the qReading and Psi methods (Kontsevich & Tyler, 1999) in a word/nonword lexical decision task were compared. The estimated reading functions obtained with the qReading and Psi methods were highly correlated (r = 0.966 ± 0.004, p < 0.01). The precision of the qReading method with 225 trials was comparable to that of the Psi method with 450 trials. We conclude that the qReading method can precisely and accurately assess the reading function in much reduced time, with great promise in both basic research and clinical applications.

Development of pattern vision following early and extended blindness.

Visual plasticity peaks during early critical periods of normal visual development. Studies in animals and humans provide converging evidence that gains in visual function are minimal and deficits are most severe when visual deprivation persists beyond the critical period. Here we demonstrate visual development in a unique sample of patients who experienced extended early-onset blindness (beginning before 1 y of age and lasting 8-17 y) before removal of bilateral cataracts. These patients show surprising improvements in contrast sensitivity, an assay of basic spatial vision. We find that contrast sensitivity development is independent of the age of sight onset and that individual rates of improvement can exceed those exhibited by normally developing infants. These results reveal that the visual system can retain considerable plasticity, even after early blindness that extends beyond critical periods.

Sensory adaptation as optimal resource allocation.

Visual adaptation is expected to improve visual performance in the new environment. This expectation has been contradicted by evidence that adaptation sometimes decreases sensitivity for the adapting stimuli, and sometimes it changes sensitivity for stimuli very different from the adapting ones. We hypothesize that this pattern of results can be explained by a process that optimizes sensitivity for many stimuli, rather than changing sensitivity only for those stimuli whose statistics have changed. To test this hypothesis, we measured visual sensitivity across a broad range of spatiotemporal modulations of luminance, while varying the distribution of stimulus speeds. The manipulation of stimulus statistics caused a large-scale reorganization of visual sensitivity, forming the orderly pattern of sensitivity gains and losses. This pattern is predicted by a theory of distribution of receptive field characteristics in the visual system.

qPR: An adaptive partial-report procedure based on Bayesian inference.

Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6-8 cue delays or 600-800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function.

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

Evaluating the performance of the quick CSF method in detecting contrast sensitivity function changes.

The contrast sensitivity function (CSF) has shown promise as a functional vision endpoint for monitoring the changes in functional vision that accompany eye disease or its treatment. However, detecting CSF changes with precision and efficiency at both the individual and group levels is very challenging. By exploiting the Bayesian foundation of the quick CSF method (Lesmes, Lu, Baek, & Albright, 2010), we developed and evaluated metrics for detecting CSF changes at both the individual and group levels. A 10-letter identification task was used to assess the systematic changes in the CSF measured in three luminance conditions in 112 naïve normal observers. The data from the large sample allowed us to estimate the test-retest reliability of the quick CSF procedure and evaluate its performance in detecting CSF changes at both the individual and group levels. The test-retest reliability reached 0.974 with 50 trials. In 50 trials, the quick CSF method can detect a medium 0.30 log unit area under log CSF change with 94.0% accuracy at the individual observer level. At the group level, a power analysis based on the empirical distribution of CSF changes from the large sample showed that a very small area under log CSF change (0.025 log unit) could be detected by the quick CSF method with 112 observers and 50 trials. These results make it plausible to apply the method to monitor the progression of visual diseases or treatment effects on individual patients and greatly reduce the time, sample size, and costs in clinical trials at the group level.

Using 10AFC to further improve the efficiency of the quick CSF method.

The contrast sensitivity function (CSF) provides a fundamental characterization of spatial vision, important for basic and clinical applications, but its long testing times have prevented easy, widespread assessment. The original quick CSF method was developed using a two-alternative forced choice (2AFC) grating orientation identification task (Lesmes, Lu, Baek, & Albright, 2010), and obtained precise CSF assessments while reducing the testing burden to only 50 trials. In this study, we attempt to further improve the efficiency of the quick CSF method by exploiting the properties of psychometric functions in multiple-alternative forced choice (m-AFC) tasks. A simulation study evaluated the effect of the number of alternatives m on the efficiency of the sensitivity measurement by the quick CSF method, and a psychophysical study validated the quick CS method in a 10AFC task. We found that increasing the number of alternatives of the forced-choice task greatly improved the efficiency of CSF assessment in both simulation and psychophysical studies. The quick CSF method based on a 10-letter identification task can assess the CSF with an averaged standard deviation of 0.10 decimal log unit in less than 2 minutes.

Visual Function Measurements in Eyes With Diabetic Retinopathy: An Expert Opinion on Available Measures.

Clinical Relevance: Visual function impairment from diabetic retinopathy can have a considerable impact on patient's quality of life. Best-corrected visual acuity (BCVA) is most commonly used to assess visual function and guide clinical trials. However, BCVA is affected late in the disease process, is not affected in early disease, and does not capture some of the visual disturbances described by patients with diabetes. The goal of this report is to evaluate the relationship between diabetic retinal disease (DRD) and visual function parameters to determine which if any of them may be used in a future DRD staging system. Methods: The visual functions working group was 1 of 6 areas of DRD studied as part of the DRD staging system update, a project of the Mary Tyler Moore Vision Initiative. The working group identified 12 variables of possible interest, 7 of which were judged to have sufficient preliminary data to suggest an association with DR to warrant further review: microperimetry, static automated perimetry, electroretinogram (ERG) oscillatory potentials, flicker ERG, low luminance visual acuity (LLVA), contrast sensitivity (CS), and BCVA. The objective field analyzer (OFA) was added after subsequent in-person workshops. Results: Currently, the only visual function test available for immediate use is BCVA; the remaining tests are either promising (within 5 years) or have potential (>5 years) use. Besides BCVA, most visual function tests had a limited role in current clinical care; however, LLVA, CS, flicker ERG, and OFA demonstrated potential for screening and research purposes. Conclusions: Although current visual function tests are promising, future prospective studies involving patients with early and more advanced retinopathy are necessary to determine if these tests can be used clinically or as endpoints for clinical studies. Financial Disclosures: Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Visual Function Endpoints to Enable Dry AMD Clinical Trials.

The slow progression of non-exudative age-related macular degeneration (dry AMD) presents challenges for drug discovery. The standard endpoint used for ophthalmic clinical trials, best-corrected visual acuity, is insensitive to the early stages and slow progression of dry AMD. Effective drug discovery for dry AMD treatments will therefore require novel applications of more effective visual function endpoints. This review will present candidates for visual function endpoints for dry AMD clinical trials. The promising visual assessments include contrast sensitivity, reading speed, microperimetry, and dark adaptation. Their adoption as exploratory endpoints in future trials will be critical for determining their accuracy, precision, and applicability, and ultimately determine their value for drug discovery.

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.

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.

Contrast Sensitivity Is Associated With Chorioretinal Thickness and Vascular Density of Eyes in Simple Early-Stage High Myopia.

Objective: To evaluate the contrast sensitivity function (CSF), chorioretinal thickness and vascular density as well as their relationships in subjects with simple early-stage high myopia. Methods: Eighty-one young subjects were enrolled in this study. They were categorized into the simple high myopia group (sHM, n = 51) and the low-moderate myopia group (control group, n = 30). Monocular CSF under best correction was measured with the qCSF method. Retinal superficial and deep vascular density, inner and outer retinal thickness and choroidal thickness were measured using optical coherence tomography angiography. Results: The area under log CSF (AULCSF) and cutoff spatial frequency (Cutoff SF) of the sHM group were significantly reduced compared to those of the control group (P = 0.003 and P < 0.001, respectively). The parafoveal and perifoveal retinal thickness, deep vascular density and choroidal thickness were also significantly reduced in the sHM group (all P < 0.05). Multiple regression analysis revealed that AULCSF was significantly correlated with retinal deep vascular density, outer retinal thickness in the parafoveal and perifoveal areas (all P < 0.05). Conclusion: Compared to low to moderate myopic eyes, patients with simple high myopia have thinner retinal and choroidal thickness, lower retinal vascular density, and reduced contrast sensitivity. Moreover, the CSF was correlated with the measures of chorioretinal structure and vasculature. The results suggest that the CSF is a sensitive functional endpoint in simple early-stage high myopia.

Evaluating the Performance of qVFM in Mapping the Visual Field of Simulated Observers With Eye Diseases.

PURPOSE: Recently, we developed a novel active learning framework, qVFM, to map visual functions in the visual field. The method has been implemented and validated in measuring light sensitivity and contrast sensitivity visual field maps (VFMs) of normal observers. In this study, we evaluated the performance of the qVFM method in mapping the light sensitivity VFM of simulated patients with peripheral scotoma, glaucoma, age-related macular degeneration (AMD), and cataract. METHODS: For each simulated patient, we sampled 100 locations (60 × 60 degrees) of the visual field and compared the performance of the qVFM method with a procedure that tests each location independently (the qYN method) in a cued Yes/No task. Two different switch modules, the distribution sampling method (DSM) and parameter delivering method (PDM), were implemented in the qVFM method. Simulated runs of 1,200 trials were used to compare the accuracy and precision of the qVFM-DSM, qVFM-PDM and qYN methods. RESULTS: The qVFM method with both switch modules can provide accurate, precise, and efficient assessments of the light sensitivity VFM for the simulated patients, with the qVFM-PDM method better at detecting VFM deficits in the simulated glaucoma. CONCLUSIONS: The qVFM method can be used to characterize residual vision of simulated ophthalmic patients. The study sets the stage for further investigation with real patients and potential translation of the method into clinical practice.

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.

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

Purpose: To evaluate the performance of the quantitative visual acuity (qVA) method in measuring the visual acuity (VA) behavioral function. Methods: We evaluated qVA performance in terms of the accuracy, precision, and efficiency of the estimated VA threshold and range in Monte Carlo simulations and a psychophysical experiment. We also compared the estimated VA threshold from the qVA method with that from the Electronic Early Treatment Diabetic Retinopathy Study (E-ETDRS) and Freiburg Visual Acuity Text (FrACT) methods. Four repeated measures with all three methods were conducted in four Bangerter foil conditions in 14 eyes. Results: In both simulations and psychophysical experiment, the qVA method quantified the full acuity behavioral function with two psychometric parameters (VA threshold and VA range) with virtually no bias and with high precision and efficiency. There was a significant correlation between qVA estimates of VA threshold and range in the psychophysical experiment. In addition, qVA threshold estimates were highly correlated with those from the E-ETDRS and FrACT methods. Conclusions: The qVA method can provide an accurate, precise, and efficient assessment of the full acuity behavioral function with both VA threshold and range. Translational Relevance: The qVA method can accurately, precisely, and efficiently assess the full VA behavioral function. Further research will evaluate the potential value of these rich measures for both clinical research and patient care.