Aniseikonia Tests: The Role of Viewing Mode, Response Bias, and Size-Color Illusions

Measuring aniseikonia tolerance range for stereoacuity - a tool for the refractive surgeon

Objective

No method exists to measure aniseikonia tolerance in stereoacuity. The brain can compensate for 2%–3% aniseikonia (i.e. 2–3 dioptres of anisometropia) without impairing stereoacuity; however, a substantial proportion of anisometropic patients experience problems caused by disruptions of sensory fusion due to surgically induced aniseikonia. We hypothesized that individual differences in tolerance to aniseikonia exist and sought to develop a method to measure aniseikonia tolerance.

Methods

A total of 21 eye‐healthy phakic individuals older than 50 years of age and 11 patients awaiting clear lens extraction were included. Patients were tested with best corrected near and distance visual acuity, cover/uncover test, eye dominance test, stereoacuity threshold (TNO test), slit lamp examination and ocular coherence tomography. The stereoacuity threshold was determined with aniseikonia induced by different size lenses ranging from 1% to 9% magnification of both eyes in increments of 1%. The aniseikonia tolerance range (ATR) was defined as the percentage aniseikonia in which the stereoacuity threshold was maintained.

Results

We examined 32 patients with a median age of 65 (95% CI: 62–66 years), CDVA better than 6/7.5 (0.1 logMAR), and median near visual acuity better than 6/6 (0.0 logMAR). The median stereoacuity threshold was 60 arcsec (maximum 30, minimum 120). We observed large inter‐individual differences in ATR: 6/31 (19%) participants had an ATR of ≤1%, 1/31 (3%) had an ATR of 1‐5%, 7/31 (22%) had an ATR of 5‐10%, and 17/31 (54%) had an ATR of >10%.

Conclusion

We present a reliable method for measuring the amount of aniseikonia that a person can tolerate without impairing stereopsis. We report large inter‐individual differences in tolerance of aniseikonia.

Order effects in two-alternative forced-choice tasks invalidate adaptive threshold estimates

Adaptive psychophysical methods are widely used for the quick estimation of percentage points (thresholds) on psychometric functions for two-alternative forced-choice (2AFC) tasks. The use of adaptive methods is supported by numerous simulation studies documenting their performance, which have shown that thresholds can be reasonably estimated with them when their founding assumptions hold. One of these assumptions is that the psychometric function is invariant, but empirical evidence is mounting that human performance in 2AFC tasks needs to be described by two different psychometric functions, one that holds when the test stimulus is presented first in the 2AFC trial and a different one that holds when the test is presented second. The same holds when presentations are instead simultaneous at two spatial locations rather than sequential. We re-evaluated the performance of adaptive methods in the presence of these order effects via simulation studies and an empirical study with human observers. The simulation study showed that thresholds are severely overestimated by adaptive methods in these conditions, and the empirical study corroborated these findings. These results question the validity of threshold estimates obtained with adaptive methods that incorrectly assume the psychometric function to be invariant with presentation order. Alternative ways in which thresholds can be accurately estimated in the presence of order effects are discussed.

Clinical Aniseikonia in Anisometropia and Amblyopia

Purpose:

Clinically, aniseikonia (a perceived difference in shape and image size between the eyes) is often neglected in anisometropic amblyopia due to assumed measurement difficulties. Therefore, we currently lack evidence on whether correction of aniseikonia is beneficial. This study aimed to determine whether subjective aniseikonia is measurable in anisometropia with or without amblyopia.

Methods:

Participants (15–52 years) with Anisometropic Amblyopia (n = 7), Anisometropia without amblyopia (n = 6) and Isometropic Controls (n = 6) were recruited. Subjective aniseikonia was measured using three clinical techniques: Robertson Technique (RT) (penlight and Maddox rod), Aniseikonia Inspector Version 3 (AI3), and the New Aniseikonia Test booklet (NAT), and a psychophysical adaptive method, the Contrast-balanced Aniseikonia Test (CAT), where dichoptic contrast adjustments compensate for any suppression.

Results:

Eighteen participants completed all tests, one Anisometropic Amblyopia participant could only complete the CAT and NAT due to fusion loss. The Anisometropic Amblyopia group exhibited the most aniseikonia (range –1.50–+10.50%) followed by Anisometropic Controls (range –3.30–+4.50%) and Isometropic Controls (range –1.50–+3.28%). There was a significant trend of more subjective aniseikonia with increasing amounts of anisometropia across all four tests (AI3 r = 0.630, p = 0.005; NAT r = 0.542, p = 0.017; RT r = 0.499, p = 0.035; CAT r = 0.440, p = 0.059. Bland Altman analysis demonstrated clinically significant levels of variability between the tests.

Conclusions:

Subjective aniseikonia can be reliably measured in patients with anisometropia and suppression. Subjective aniseikonia measurement is recommended as four of the most commonly used clinical tests did not support the 1% per dioptre rule of thumb.

Anisometropic Amblyopia: Interocular Contrast and Viewing Luminance Effects on Aniseikonia

Purpose

To demonstrate an aniseikonia test for anisometropic amblyopia (ATAA) that uses variable viewing luminance at different interocular contrast levels.

Methods

The test consists of a direct size comparison task based on a computer. The subject is asked to adjust the size of a dichoptically dissociated paired square target. One square was always presented at 100% contrast to the amblyopic eye/nondominant eye, whereas its counterpart was presented to the fellow eye at six contrast levels. Measurements were performed at two luminance backgrounds: (1) a white square on a black background (WoB) and (2) a black square on a white background (BoW). To test the feasibility of this approach, 16 patients with anisometropic amblyopia and 23 normal controls were recruited.

Results

The Aniseikonia Index (AI) calculated from the ATAA increased when the difference in the interocular contrast increased in both the patients with anisometropic amblyopia and controls under BoW and WoB conditions. The mean AI differed dramatically between the BoW and WoB conditions in patients with amblyopia but not in normal subjects.

Conclusions

Our model predicted interocular differences in contrast to the measurement of aniseikonia. Execution of the AI in individuals with amblyopia should consider that their responses to different luminance viewing conditions could be asymmetric.

Translational Relevance

The ATAA has the potential to optimize optical correction for the management of aniseikonia in individuals with anisometropic amblyopia.

The Do's and Don'ts of Psychophysical Methods for Interpretability of Psychometric Functions and Their Descriptors

Many areas of research require measuring psychometric functions or their descriptors (thresholds, slopes, etc.). Data for this purpose are collected with psychophysical methods of various types and justification for the interpretation of results arises from a model of performance grounded in signal detection theory. Decades of research have shown that psychophysical data display features that are incompatible with such framework, questioning the validity of interpretations obtained under it and revealing that psychophysical performance is more complex than this framework entertains. This paper describes the assumptions and formulation of the conventional framework for the two major classes of psychophysical methods (single- and dual-presentation methods) and presents various lines of empirical evidence that the framework is inconsistent with. An alternative framework is then described and shown to account for all the characteristics that the conventional framework regards as anomalies. This alternative process model explicitly separates the sensory, decisional, and response components of performance and represents them via parameters whose estimation characterizes the corresponding processes. Retrospective and prospective evidence of the validity of the alternative framework is also presented. A formal analysis also reveals that some psychophysical methods and response formats are unsuitable for separation of the three components of observed performance. Recommendations are thus given regarding practices that should be avoided and those that should be followed to ensure interpretability of the psychometric function, or descriptors (detection threshold, difference limen, point of subjective equality, etc.) obtained with shortcut methods that do not require estimation of psychometric functions.

Evaluation of aniseikonia with an auto-stereoscopic smartphone

BACKGROUND

An auto-stereoscopic smartphone can produce 3D images without the need for the viewer to wear glasses. The purpose of this study was to evaluate whether this technology could be utilized to measure aniseikonia.

METHODS

A 2K auto-stereoscopic smartphone was used to imitate the Awaya new aniseikonia test. In test 1, four pairs of lenses combined with a trial frame were used to create 4 different magnification rates in 10 subjects. In test 2, 40 subjects whose anisometropia was higher than 2.00D were recruited.

RESULTS

No significant difference between the results of the Awaya new aniseikonia test and auto-stereoscopic smartphone test (Wilcoxon signed-rank test: test 1, P=0.85; test 2, P=0.53). Bland-Altman plots showed that the difference between the two tests was ≤1% in both tests 1 and 2.

CONCLUSIONS

An auto-stereoscopic smartphone can be an effective tool for evaluating aniseikonia.

Nonparametric tests for equality of psychometric functions

Many empirical studies measure psychometric functions (curves describing how observers' performance varies with stimulus magnitude) because these functions capture the effects of experimental conditions. To assess these effects, parametric curves are often fitted to the data and comparisons are carried out by testing for equality of mean parameter estimates across conditions. This approach is parametric and, thus, vulnerable to violations of the implied assumptions. Furthermore, testing for equality of means of parameters may be misleading: Psychometric functions may vary meaningfully across conditions on an observer-by-observer basis with no effect on the mean values of the estimated parameters. Alternative approaches to assess equality of psychometric functions per se are thus needed. This paper compares three nonparametric tests that are applicable in all situations of interest: The existing generalized Mantel-Haenszel test, a generalization of the Berry-Mielke test that was developed here, and a split variant of the generalized Mantel-Haenszel test also developed here. Their statistical properties (accuracy and power) are studied via simulation and the results show that all tests are indistinguishable as to accuracy but they differ non-uniformly as to power. Empirical use of the tests is illustrated via analyses of published data sets and practical recommendations are given. The computer code in MATLAB and R to conduct these tests is available as Electronic Supplemental Material.

Psychophysical Tests Do Not Identify Ocular Dominance Consistently

Classical sighting or sensory tests are used in clinical practice to identify the dominant eye. Several psychophysical tests were recently proposed to quantify the magnitude of dominance but whether their results agree was never investigated. We addressed this question for the two most common psychophysical tests: The perceived-phase test, which measures the cyclopean appearance of dichoptically presented sinusoids of different phase, and the coherence-threshold test, which measures interocular differences in motion perception when signal and noise stimuli are presented dichoptically. We also checked for agreement with three classical tests (Worth 4-dot, Randot suppression, and Bagolini lenses). Psychophysical tests were administered in their conventional form and also using more dependable psychophysical methods. The results showed weak correlations between psychophysical measures of strength of dominance with inconsistent identification of the dominant eye across tests: Agreement on left-eye dominance, right-eye dominance, or nondominance by both tests occurred only for 11 of 40 observers (27.5%); the remaining 29 observers were classified differently by each test, including 14 cases (35%) of opposite classification (left-eye dominance by one test and right-eye dominance by the other). Classical tests also yielded conflicting results that did not agree well with classification based on psychophysical tests. The results are discussed in the context of determination of ocular dominance for clinical decisions.

Aniseikonia and anisometropia: implications for suppression and amblyopia

Aniseikonia is a difference in the perceived size or shape of images between eyes, and can arise from a variety of physiological, neurological, retinal, and optical causes. Aniseikonia is associated with anisometropia, as both anisometropia itself and the optical correction for anisometropia can cause aniseikonia. Image size differences above one to three per cent can be clinically symptomatic. Common symptoms include asthenopia, headache and diplopia in vertical gaze. Size differences of three and more impair binocular visual functions such as binocular summation and stereopsis. Above five per cent of aniseikonia, binocular inhibition or suppression tend to occur to prevent diplopia and confusion. Aniseikonia can be measured using a range of techniques and can be corrected or reduced by prescribing contact lenses or specially designed spectacle lenses. Subjective testing of aniseikonia is the only way to accurately measure the overall perceived amount of aniseikonia. However, currently it is not routinely assessed in most clinical settings. At least two-thirds of patients with amblyopia have anisometropia, thus we may expect aniseikonia to be common in patients with anisometropic amblyopia. However, aniseikonia may not be experienced by the patient under normal binocular viewing conditions if the image from the amblyopic eye is of poor quality or is too strongly suppressed for image size differences to be recognised. This lack of binocular simultaneous perception in amblyopia may also prevent the measurement of aniseikonia, as most common techniques require direct comparisons of images seen by each eye. Current guidelines for the treatment of amblyopia advocate full correction of anisometropia to equalise image clarity, but do not address aniseikonia. Significant image size differences between eyes may lead to suppression and abnormal binocular adaptations. It is possible that correcting anisometropia and aniseikonia simultaneously, particularly at the initial diagnosis of anisometropia, would reduce the need to develop suppression and improve treatment outcomes for anisometropic amblyopia.

Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects exist or whether they are empirically meaningful. Hence, raising conclusions from the outcomes of statistical analyses is subject to limitations. NHST has been criticized for its misuse and the misconstruction of its outcomes, also stressing its inability to meet expectations that it was never designed to fulfil. Ironically, alternatives to NHST are identical in these respects, something that has been overlooked in their presentation. Three of those alternatives are discussed here (estimation via confidence intervals and effect sizes, quantification of evidence via Bayes factors, and mere reporting of descriptive statistics). None of them offers a solution to the problems that NHST is purported to have, all of them are susceptible to misuse and misinterpretation, and some bring around their own problems (e.g., Bayes factors have a one-to-one correspondence with p values, but they are entirely deprived of an inferential framework). Those alternatives also fail to cover a broad area of inference not involving distributional parameters, where NHST procedures remain the only (and suitable) option. Like knives or axes, NHST is not inherently evil; only misuse and misinterpretation of its outcomes needs to be eradicated.

The Indecision Model of Psychophysical Performance in Dual-Presentation Tasks: Parameter Estimation and Comparative Analysis of Response Formats

Psychophysical data from dual-presentation tasks are often collected with the two-alternative forced-choice (2AFC) response format, asking observers to guess when uncertain. For an analytical description of performance, psychometric functions are then fitted to data aggregated across the two orders/positions in which stimuli were presented. Yet, order effects make aggregated data uninterpretable, and the bias with which observers guess when uncertain precludes separating sensory from decisional components of performance. A ternary response format in which observers are also allowed to report indecision should fix these problems, but a comparative analysis with the 2AFC format has never been conducted. In addition, fitting ternary data separated by presentation order poses serious challenges. To address these issues, we extended the indecision model of psychophysical performance to accommodate the ternary, 2AFC, and same-different response formats in detection and discrimination tasks. Relevant issues for parameter estimation are also discussed along with simulation results that document the superiority of the ternary format. These advantages are demonstrated by fitting the indecision model to published detection and discrimination data collected with the ternary, 2AFC, or same-different formats, which had been analyzed differently in the sources. These examples also show that 2AFC data are unsuitable for testing certain types of hypotheses. matlab and R routines written for our purposes are available as Supplementary Material, which should help spread the use of the ternary format for dependable collection and interpretation of psychophysical data.