Haogang Zhu

Ophthalmic statistics note 5: diagnostic tests—sensitivity and specificity

This is the fifth statistics note produced by the Ophthalmic Statistics Group (OSG) which is designed to be a simple guide to ophthalmic researchers on a statistical issue with an applied ophthalmic example. The OSG is a collaborative group of statisticians who have come together with a desire to raise the statistical standards of ophthalmic researcher by increasing statistical awareness of common issues.

The influence of intersubject variability in ocular anatomical variables on the mapping of retinal locations to the retinal nerve fiber layer and optic nerve head.

PURPOSE To investigate the influence of intersubject variation in ocular parameters on the mapping of retinal locations to the retinal nerve fiber layer and optic nerve head. METHODS One hundred retinal nerve fiber layer (RNFL) bundle photographs from 100 subjects were optimized digitally and single RNFL bundles manually traced back to the ONH where their entry point was noted. A 24-2 visual field (VF) grid pattern was superimposed onto the photographs in order to relate VF test points to intersecting RNFL bundles and their entry angles into the ONH. Axial length, spherical equivalent, the position of the ONH in relation to the fovea, size, orientation, tilt, and shape of the ONH were assessed. Multilevel linear models were generated for predicting the entry angle of RNFL bundles, based on ocular parameters. RESULTS A total of 6388 RNFL bundles were traced. The influence of ocular parameters could be evaluated for 33 out of 52 VF locations. The position of the ONH in relation to the fovea was the most prominent predictor for variations in the mapping of retinal locations to the ONH, followed by disc area, axial length, spherical equivalent, disc shape, disc orientation, and disc tilt. CONCLUSIONS Mapping of retinal locations to the optic nerve head varies between patients according to a given patients ocular parameters. By considering these parameters, patient-tailored, structure-function maps can be built and structural and functional measurements can be correlated more accurately. Individualized maps may assist clinicians detecting glaucoma and monitoring glaucomatous progression.

Predicting Visual Function from the Measurements of Retinal Nerve Fiber Layer Structure

PURPOSE To develop and validate a method of predicting visual function from retinal nerve fiber layer (RNFL) structure in glaucoma. METHODS RNFL thickness (RNFLT) measurements from scanning laser polarimetry (SLP) and visual field (VF) sensitivity from standard automated perimetry were made available for 535 eyes from three centers. In a training dataset, structure-function relationships were characterized by using linear regression and a type of neural network: radial basis function customized under a Bayesian framework (BRBF). These two models were used in a test dataset to (1) predict sensitivity at individual VF locations from RNFLT measurements and (2) predict the spatial relationship between VF locations and positions at a peripapillary RNFLT measurement annulus. Predicted spatial relationships were compared with a published anatomic structure-function map. RESULTS Compared with linear regression, BRBF yielded a nearly twofold improvement (P < 0.001; paired t-test) in performance of predicting VF sensitivity in the test dataset (mean absolute prediction error of 2.9 dB [SD 3.7] versus 4.9 dB [SD 4.0]). The predicted spatial structure-function relationship showed better agreement (P < 0.001; paired t-test) with anatomic prior knowledge when the BRBF was compared with the linear regression (median absolute angular difference of 15° vs. 62°). CONCLUSIONS The BRBF generates clinically useful relationships that relate topographical maps of RNFL measurement to VF locations and allows the VF sensitivity to be predicted from structural measurements. This method may allow clinicians to evaluate structural and functional measures in the same domain. It could also be generalized to use other structural measures.

Detecting Changes in Retinal Function: Analysis with Non-Stationary Weibull Error Regression and Spatial Enhancement (ANSWERS)

Visual fields measured with standard automated perimetry are a benchmark test for determining retinal function in ocular pathologies such as glaucoma. Their monitoring over time is crucial in detecting change in disease course and, therefore, in prompting clinical intervention and defining endpoints in clinical trials of new therapies. However, conventional change detection methods do not take into account non-stationary measurement variability or spatial correlation present in these measures. An inferential statistical model, denoted ‘Analysis with Non-Stationary Weibull Error Regression and Spatial enhancement’ (ANSWERS), was proposed. In contrast to commonly used ordinary linear regression models, which assume normally distributed errors, ANSWERS incorporates non-stationary variability modelled as a mixture of Weibull distributions. Spatial correlation of measurements was also included into the model using a Bayesian framework. It was evaluated using a large dataset of visual field measurements acquired from electronic health records, and was compared with other widely used methods for detecting deterioration in retinal function. ANSWERS was able to detect deterioration significantly earlier than conventional methods, at matched false positive rates. Statistical sensitivity in detecting deterioration was also significantly better, especially in short time series. Furthermore, the spatial correlation utilised in ANSWERS was shown to improve the ability to detect deterioration, compared to equivalent models without spatial correlation, especially in short follow-up series. ANSWERS is a new efficient method for detecting changes in retinal function. It allows for better detection of change, more efficient endpoints and can potentially shorten the time in clinical trials for new therapies.

What's on TV? Detecting age-related neurodegenerative eye disease using eye movement scanpaths

Purpose: We test the hypothesis that age-related neurodegenerative eye disease can be detected by examining patterns of eye movement recorded whilst a person naturally watches a movie. Methods: Thirty-two elderly people with healthy vision (median age: 70, interquartile range [IQR] 64–75 years) and 44 patients with a clinical diagnosis of glaucoma (median age: 69, IQR 63–77 years) had standard vision examinations including automated perimetry. Disease severity was measured using a standard clinical measure (visual field mean deviation; MD). All study participants viewed three unmodified TV and film clips on a computer set up incorporating the Eyelink 1000 eyetracker (SR Research, Ontario, Canada). Eye movement scanpaths were plotted using novel methods that first filtered the data and then generated saccade density maps. Maps were then subjected to a feature extraction analysis using kernel principal component analysis (KPCA). Features from the KPCA were then classified using a standard machine based classifier trained and tested by a 10-fold cross validation which was repeated 100 times to estimate the confidence interval (CI) of classification sensitivity and specificity. Results: Patients had a range of disease severity from early to advanced (median [IQR] right eye and left eye MD was −7 [−13 to −5] dB and −9 [−15 to −4] dB, respectively). Average sensitivity for correctly identifying a glaucoma patient at a fixed specificity of 90% was 79% (95% CI: 58–86%). The area under the Receiver Operating Characteristic curve was 0.84 (95% CI: 0.82–0.87). Conclusions: Huge data from scanpaths of eye movements recorded whilst people freely watch TV type films can be processed into maps that contain a signature of vision loss. In this proof of principle study we have demonstrated that a group of patients with age-related neurodegenerative eye disease can be reasonably well separated from a group of healthy peers by considering these eye movement signatures alone.

Quantifying discordance between structure and function measurements in the clinical assessment of glaucoma

OBJECTIVE To evaluate a new method of quantifying and visualizing discordance between structural and functional measurements in glaucomatous eyes by predicting the visual field (VF) from retinal nerve fiber layer thickness (RNFLT) using a bayesian radial basis function. METHODS Five GDx VCC RNFLT scans and 5 Humphrey 24-2 Swedish Interactive Thresholding Algorithm VF tests were performed for 50 glaucomatous eyes from 50 patients. A best-available estimate (BAE) of the true VF was calculated as the pointwise median of these 5 replications. This BAE VF was compared with every RNFLT-predicted VF from the bayesian radial basis function and every measured VF. Predictability of VFs from RNFLT was established from previous data. A structure-function pattern discordance map and a structure-function discordance index (scores of 0-1) were established from the predictability limits for each structure-function measurement pair to quantify and visualize the discordance between the structure-predicted and measured VFs. RESULTS The mean absolute difference between the structure-predicted and BAE VFs was 3.9 dB. The mean absolute difference between measured and BAE VFs was 2.6 dB. The mean (SD) structure-function discordance index score was 0.34 (0.11). Ninety-seven (39%) of the structure-predicted VFs showed significant discordance (structure-function discordance index score >0.3) from measured VFs. CONCLUSIONS On average, the bayesian radial basis function predicts the BAE VF from RNFLT slightly less well than a measured VF from the 5 VFs composing the BAE VF. The pattern discordance map highlights locations with structure-function discordance, with the structure-function discordance index providing a summary index. These tools may help clinicians trust the mutually confirmatory structure-function measurements with good concordance or identify unreliable ones with poor concordance.

More Accurate Modeling of Visual Field Progression in Glaucoma: ANSWERS

PURPOSE To validate a method for visual field (VF) progression analysis, called ANSWERS (Analysis with Non-Stationary Weibull Error Regression and Spatial Enhancement), which takes into account increasing measurement variability as glaucoma progresses and spatial correlation among test locations. METHODS ANSWERS outputs both a global index of progression and a pointwise estimate of rate of change at each VF location. ANSWERS was compared with linear regression of mean deviation (MD) and permutation of pointwise linear regression (PoPLR). Visual field series of up to 2 years from the United Kingdom Glaucoma Treatment Study were used. This consists of 9104 Swedish Interactive Thresholding Algorithm Standard 24-2 VFs. ANSWERS and PoPLR rate of change were used to predict the VF at the next visit using subseries that were within 7, 13, 18, or 22 months from the baseline. The comparison was carried out on the statistical sensitivity, specificity, and accuracy of predicting future VF. RESULTS Across all subseries, statistical sensitivity of ANSWERS in detecting VF deterioration was significantly better than the linear regression of MD and PoPLR, especially in short time series. Prediction accuracy of ANSWERS was better than PoPLR at all series lengths, and the improvement was particularly marked in shorter series. Seventy-five percent of VF series were better predicted by ANSWERS compared with PoPLR. The average prediction error of ANSWERS was 15% lower than that of PoPLR. CONCLUSIONS ANSWERS is more sensitive to detect VF progression and predicts future VF loss better than linear regression of MD and PoPLR, especially over short observation periods. (http://www.isrctn.com number, ISRCTN96423140.).

Aligning Scan Acquisition Circles in Optical Coherence Tomography Images of The Retinal Nerve Fibre Layer

Optical coherence tomography (OCT) is widely used in the assessment of retinal nerve fibre layer thickness (RNFLT) in glaucoma. Images are typically acquired with a circular scan around the optic nerve head. Accurate registration of OCT scans is essential for measurement reproducibility and longitudinal examination. This study developed and evaluated a special image registration algorithm to align the location of the OCT scan circles to the vessel features in the retina using probabilistic modelling that was optimised by an expectation-maximization algorithm. Evaluation of the method on 18 patients undergoing large number of scans indicated improved data acquisition and better reproducibility of measured RNFLT when scanning circles were closely matched. The proposed method enables clinicians to consider the RNFLT measurement and its scan circle location on the retina in tandem, reducing RNFLT measurement variability and assisting detection of real change of RNFLT in the longitudinal assessment of glaucoma.

FloatingCanvas: quantification of 3D retinal structures from spectral-domain optical coherence tomography

Spectral-domain optical coherence tomography (SD-OCT) provides volumetric images of retinal structures with unprecedented detail. Accurate segmentation algorithms and feature quantification in these images, however, are needed to realize the full potential of SD-OCT. The fully automated segmentation algorithm, FloatingCanvas, serves this purpose and performs a volumetric segmentation of retinal tissue layers in three-dimensional image volume acquired around the optic nerve head without requiring any pre-processing. The reconstructed layers are analyzed to extract features such as blood vessels and retinal nerve fibre layer thickness. Findings from images obtained with the RTVue-100 SD-OCT (Optovue, Fremont, CA, USA) indicate that FloatingCanvas is computationally efficient and is robust to the noise and low contrast in the images. The FloatingCanvas segmentation demonstrated good agreement with the human manual grading. The retinal nerve fibre layer thickness maps obtained with this method are clinically realistic and highly reproducible compared with time-domain StratusOCT(TM).

The United Kingdom Diabetic Retinopathy Electronic Medical Record Users Group, Report 1: baseline characteristics and visual acuity outcomes in eyes treated with intravitreal injections of ranibizumab for diabetic macular oedema

Aims To describe baseline characteristics and visual outcome for eyes treated with ranibizumab for diabetic macular oedema (DMO) from a multicentre database. Methods Structured clinical data were anonymised and extracted from an electronic medical record from 19 participating UK centres: age at first injection, ETDRS visual acuity (VA), number of injections, ETDRS diabetic retinopathy (DR) and maculopathy grade at baseline and visits. The main outcomes were change in mean VA from baseline, number of injections and clinic visits and characteristics affecting VA change and DR grade. Results Data from 12 989 clinic visits was collated from baseline and follow-up for 3103 eyes. Mean age at first treatment was 66 years. Mean VA (letters) for eyes followed at least 2 years was 51.1 (SD=19.3) at baseline, 54.2 (SD: 18.6) and 52.5 (SD: 19.4) at 1 and 2 years, respectively. Mean visual gain was five letters. The proportion of eyes with VA of 72 letters or better was 25% (baseline) and 33% (1 year) for treatment naïve eyes. Eyes followed for at least 6 months received a mean of 3.3 injections over a mean of 6.9 outpatient visits in 1 year. Conclusions In a large cohort of eyes with DMO treated with ranibizumab injections in the UK, 33% of patients achieved better than or equal to 6/12 in the treated eye at 12 months compared with 25% at baseline. The mean visual gain was five letters. Eyes with excellent VA at baseline maintain good vision at 18 months.