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Square contingency tables are a special case commonly used in various fields to analyze categorical data. Although several analysis methods have been developed to examine marginal homogeneity (MH) in these tables, existing measures are single-summary ones. To date, a visualization approach has yet to be proposed to intuitively depict the results of MH analysis. Current measures used to assess the degree of departure from MH are based on entropy such as the Kullback-Leibler divergence and do not satisfy distance postulates. Hence, the current measures are not conducive to visualization. Herein we present a measure utilizing the Matusita distance and introduce a visualization technique that employs sub-measures of categorical data. Through multiple examples, we demonstrate the meaningfulness of our visualization approach and validate its usefulness to provide insightful interpretations.

Retinitis pigmentosa (RP) and macular dystrophy (MD) are prevalent retinal degenerative diseases associated with gradual photoreceptor death. These diseases are often caused by genetic mutations that result in degeneration of the retina postnatally after it has fully developed. The Prominin-1 gene (Prom1) is a causative gene for RP and MD, and Prom1- knockout (KO) mice recapitulate key features of these diseases including light-dependent retinal degeneration and stenosis of retinal blood vessels. The mechanisms underlying progression of such degeneration have remained unknown, however. We here analysed early events associated with retinal degeneration in Prom1-KO mice. We found that photoreceptor cell death and glial cell activation occur between 2 and 3 weeks after birth. High-throughput analysis revealed that expression of the endothelin-2 gene (Edn2) was markedly up-regulated in the Prom1-deficient retina during this period. Expression of Edn2 was also induced by light stimulation in Prom1-KO mice that had been reared in the dark. Finally, treatment with endothelin receptor antagonists attenuated photoreceptor cell death, gliosis, and retinal vessel stenosis in Prom1-KO mice. Our findings suggest that inhibitors of endothelin signalling may delay the progression of RP and MD and therefore warrant further study as potential therapeutic agents for these diseases.