Statistical Evaluation of Correlated Measurement Data in Longitudinal Setting Based on Bilateral Corneal Cross-Linking
Abstract
Purpose In ophthalmology, data from both eyes of a person are frequently included in the statistical evaluation. This violates the requirement of data independence for classical statistical tests (e.g. t-Test or analysis of variance (ANOVA)) because it is correlated data.
Linear mixed models (LMM) were used as a possibility to include the data of both eyes in the statistical evaluation. Methods The LMM is available for a variety of statistical software such as SPSS or R.
The application was applied to a retrospective longitudinal analysis of an accelerated corneal cross-linking (ACXL (9*10)) treatment in progressive keratoconus (KC) with a follow-up period of 36 months. Forty eyes of 20 patients were included, whereas sequential bilateral CXL treatment was performed within 12 months.
LMM and ANOVA for repeated measurements were used for statistical evaluation of topographical and tomographical data measured by Pentacam (Oculus, Wetzlar, Germany). Results Both eyes were classified into a worse and better eye concerning corneal topography.
Visual acuity, keratometric values and minimal corneal thickness were statistically significant between them at baseline (p < 0.05). A significant correlation between worse and better eye was shown (p < 0.05).
Therefore, analyzing the data at each follow-up visit using ANOVA partially led to an overestimation of the statistical effect that could be avoided by using LMM. After 36 months, ACXL has significantly improved BCVA and flattened the cornea.
Conclusion The evaluation of data of both eyes without considering their correlation using classical statistical tests leads to an overestimation of the statistical effect, which can be avoided by using the LMM.