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

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.