Standards for analyzing astigmatic outcomes: Part II: Recommended statistical methods

Surgically induced astigmatism (SIA) is the astigmatic component of the surgically induced refractive change. Vector prediction error (PE) is the key expression for evaluating refractive surgery, defined as the vector difference between the postoperatively observed refractive astigmatism and the refractive astigmatism predicted from the preoperative measurements. Astigmatic analysis of the SIA and PE includes both univariate and bivariate analyses. The magnitude of the refractive astigmatism is a predictor of visual function and a valuable component of astigmatic reporting. For vector metrics from bivariate analysis, data should be analyzed and displayed with double-angle plots. Vector calculations can be performed independent of or relative to a reference meridian or axis. Double-angle plots with convex polygons and statistical analysis for astigmatism data can be obtained easily with the wrap-up functions from the Wilcox-Holladay-Wang-Koch Statistical Software using the free software R Project for Statistical Computing or with Eyetemis software, which is also available online.