We have read with great interest the article by Kamiya and associates. The authors showed that eyes of older patients and eyes with longer axial length were more predisposed to have greater myopic regression after posterior chamber phakic intraocular lens (Visian ICL; STAAR Surgical) implantation. We are confident that the study was well designed, but we have the following comments from a statistical point of view.
First, they analyzed the results from 60 eyes from 35 patients. In other words, 10 eyes from 10 patients and 50 eyes from 25 patients were selected for the analysis in this study. The stepwise multiple regression analysis and Spearman rank correlation analysis, which were used in this study, are meaningful only under the assumption of independence of the data. To collect data from 1 or both eyes of a subject in ophthalmic statistics has been a main argument in terms of the dependence of observations. The use of measurements from only 1 eye for studies involving eye-specific outcomes is recommended, especially when the correlation between eyes is strong. We recommend that the between-eye correlation in the subjects should be estimated and 1 eye from 35 patients should be used for the final statistical analysis.
Second, the authors performed the Spearman rank correlation analysis, a nonparametric method, to assess the univariate relationship of myopic regression with other variables. When the variables are not normally distributed or the relationship between the variables is not linear, it may be more appropriate to use the Spearman rank correlation analysis. However, the multiple regression analysis, a parametric method, used in the same table can be feasible when the relationships between dependent variable and independent variables are linear and the dependent variable is normally distributed. Table 2 showed the results from the univariate and multivariate analyses with discrepant assumptions on the distribution of the same variables. Sixty eyes could be regarded as a sufficiently large number according to the central limit theory; it seems more appropriate to use the Pearson correlation coefficient, a parametric method, as a univariate version of the multiple regression analysis in Table 2.