Evaluation of Statistical Methods for Clustered Eye Data with Skewed Distribution

To evaluate the performance of various analysis approaches for skewed correlated eye data from 2 eyes of a subject in the same comparison group, which is common in ophthalmology and vision research.

Simulation study and real data analysis.

Simulated subjects and participants of the Dry Eye Assessment and Management (DREAM) study.

We simulated skewed correlated data using (skewness, kurtosis) = (27, 50) and (0.06, 5.9), intereye correlation (ρ = 0, 0.25, 0.50, and 0.75), sample sizes (n = 20, 50, 100, and 200), and mean differences between 2 groups (0 for type 1 error rate, 0.2 for statistical power). Each simulated data set was analyzed without and with applying rank-based normalization: (1) 2-sample t test of 2 eye data; (2) 2-sample t test of random eye data; (3) Wald test from generalized estimating equations (GEE Wald); (4) GEE score test (GEE score); (5) F-test from linear mixed effects model (LMM); (6) clustered Wilcoxon test of Rosner, Glynn, and Lee; (7) clustered Wilcoxon test of Datta and Satten; (8) Wilcoxon rank sum test of 2 eyes ignoring intereye correlation; and (9) Wilcoxon rank sum test on average of 2 eyes. We demonstrated analysis of skewed tear break-up time (TBUT) data from the DREAM study.

Type 1 error rate and statistical power.

T test and Wilcoxon test on 2 eye data without accounting for intereye correlation inflated type 1 error rate up to 0.13, and GEE Wald inflated type 1 error rate to 0.08 when sample size is small, whereas all other tests maintained type 1 error rate close to 0.05. For skewed data without normalization, t test of random eye, GEE Wald, GEE score, and LMM had substantially lower power than clustered Wilcoxon methods. After normalization, GEE score and LMM achieved similar or slightly higher power than clustered Wilcoxon methods. Results from analysis of TBUT are consistent with simulation findings.

When comparing skewed correlated eye measures between 2 groups of subjects with their 2 eyes in the same comparison group, clustered Wilcoxon methods can be used. Alternatively, skewed data can be normalized before applying GEE score or LMM, which may achieve slightly higher statistical power than clustered Wilcoxon methods and offers flexibility to adjust for other covariates.

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