Dioptric power and refractive behaviour: a review of methods and applications

Abstract

Myopia is a global healthcare concern and effective analyses of dioptric power are important in evaluating potential treatments involving surgery, orthokeratology, drugs such as low-dose (0.05%) atropine and gene therapy. This paper considers issues of concern when analysing refractive state such as data normality, transformations, outliers and anisometropia. A brief review of methods for analysing and representing dioptric power is included but the emphasis is on the optimal approach to understanding refractive state (and its variation) in addressing pertinent clinical and research questions.Although there have been significant improvements in the analysis of refractive state, areas for critical consideration remain and the use of power matrices as opposed to power vectors is one such area. Another is effective identification of outliers in refractive data. The type of multivariate distribution present with samples of dioptric power is often not considered. Similarly, transformations of samples (of dioptric power) towards normality and the effects of such transformations are not thoroughly explored. These areas (outliers, normality and transformations) need further investigation for greater efficacy and proper inferences regarding refractive error. Although power vectors are better known, power matrices are accentuated herein due to potential advantages for statistical analyses of dioptric power such as greater simplicity, completeness, and improved facility for quantitative and graphical representation of refractive state.

Standardised approach to the reporting and presentation of refractive data: electronic patient record

“…Rubin et al , 25 have reviewed issues which affect the analysis of refractive state such as data normality, transformations, outliers and anisometropia. They provide a review of the methods needed for analysing and representing dioptric power and concentrate on the optimal approach to understanding refractive state in addressing pertinent clinical and research questions.…”

Multivariate analysis of repeatability for the Near Eye Tool for Refractive Assessment (NETRA)

“…In the past, most studies involving refractive state treated refractive error components (sphere and cylinder powers and cylinder axes) as independent and univariate entities, whereas they should be evaluated with linear algebra and multivariate statistics 1 14–28. Therefore spheres, cylinders and their axes are first transformed from conventional or clinical terms to a vector representation (f or t)1 8 14–16 26 or to the dioptric power matrix, F 14–16.…”

“…Analysis of refractive states in clinical notation ( F s F c A ) from NETRA is performed using symmetrical dioptric power matrices, F and vector f :8 14–27…”

“…Multivariate statistical analysis includes stereo-pair scatterplots with comets8 26 27 and 95% distribution ellipsoids,21 and hypothesis testing of variances and covariances 20 21. A comet is simply a line plotted between two points here to link repeated measurements for an eye.…”

“…Vision impairment (VI) due to uncompensated refractive error (URE) such as with myopia is a global health concern and inexpensive and portable technology to address the unmet needs of patients with mild to severe VI due to URE is important and the repeatability2 of an example of such technology2–9 is addressed here. The necessary analytical methods1–27 to effectively explore refractive error obtained via such technology are also demonstrated.…”