Habib, Malak (2025) A Clinically Applicable Bivariate Agreement Analysis of Astigmatism. Clinical and Experimental Ophthalmology, 53 (6). pp. 722-723.

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Abstract

[Extract] Congratulations to Feng et al. [1] for what is a large and comprehensive comparative accuracy study of four flagship biometers. Of note, I commend the authors for acknowledging the bivariate nature of astigmatism by additionally analysing its orthogonal power components (J0, J45).

However, I felt it relevant to comment on the statistical approach used to measure agreement, which involved a classic Bland–Altman analysis of the J0 and J45 Fourier components. Although component powers are a meridional composite of both magnitude and direction, analysing their agreement separately does not constitute a true bivariate analysis because it does not account for the extra error produced by changes in both components simultaneously. Further, knowing the agreement in component powers separately offers little clinical utility. In example, the MS-39 had a bias of +0.180 D for J0 and −0.062 D for J45 when compared to the Casia SS-1000. Though what does this mean clinically? The reader is left with two statistical parameters that indirectly represent one clinical entity. It is tempting to back-convert these powers into a hypotenuse magnitude, though this is flawed. The bivariate bias must be measured at the case level first and then aggregated at the cohort level [2].

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