[Statistical analysis of correlated measurement data in ophthalmology : Tutorial for the application of the linear...

In ophthalmology data from both eyes of a person are frequently included in statistical analyses. As correlated data are used this procedure contradicts the independency principle for classical statistical tests, such as Student's t‑test and analysis of variance (ANOVA). In this tutorial a new possibility is presented in which data from both eyes can be used for statistical analysis.

The statistical approach of linear mixed models (LMM) was used to take correlated data of both eyes of patients into account.

The LMM is available in several statistical software packages, e.g. SPSS and R, and allows the inclusion of measurement data from both eyes of a person in the statistical analysis. The application was tested on data from a biomechanical characterization of the cornea from healthy participants assessed with the dynamic Scheimpflug analyzer (Corvis ST; Oculus, Wetzlar, Germany).

A total of 158 eyes from 79 healthy participants were included. A strong correlation between the right and left eyes of the participants could be observed with respect to the analyzed parameters. Comparison of the biomechanical parameters between the different age groups showed that P-values were increased when using the LMM compared to the ANOVA. Older participants (56-79 years) showed a significantly shorter time to the second applanation (P = 0.002), a significantly increased eyeball movement during the deformation (P = 0.001) and a significantly higher stiffness at the first applanation (P = 0.006) compared to younger participants (18-35 years).

The analysis of measurement data from both eyes using classical statistical tests, without the consideration of the correlation, leads to an overestimation of the statistical power. This can be avoided by implementation of the LMM.