A Nonparametric Test for Observational Non-Normally Distributed Ophthalmic Data with Eye-Specific Exposures and Outcomes

Abstract

Purpose: To extend the Wilcoxon rank sum test to the analysis of clustered observational data with a binary exposure variable where not all cluster members (or subunits) have the same exposure status, as in ophthalmologic data where fellow eyes may differ in exposure status. Methods: The Wilcoxon rank sum test statistic (Wc) is defined as the sum of ranks of all exposed subunits over all clusters. The large sample distribution of Wc is derived based on a two-stage permutation distribution approach which maintains the clustering structure of the exposure distribution in the original data. The procedure is applied to data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy (WESDR) for assessing differences in retinopathy grade between eyes with high vs. low intraocular pressure (IOP). Results: Data analyses based on the WESDR data indicate significant positive associations between IOP and retinopathy grade as assessed by the clustered Wilcoxon test (p = 0.019), but non-significant effects with mixed model procedures based on raw scores (p = 0.30). Conclusions: The clustered Wilcoxon procedure is an effective approach for analyzing clustered non-normal outcome data with a binary eye-specific exposure which may vary in 2 eyes of an individual.