#### Abstract

This paper describes applications of extensions of bivariate rank sum tests to the bilateral crossover

design to compare two treatments through four sequence groups. A randomized clinical trial in ophthalmology

provides motivating background for the discussion. The design for this study has four sequence groups T:T, T:P, P:T, and P:P respectively for T as test treatment or P as placebo treatment in the

corresponding order for the left and right eyes. With separate consideration of the left eye and the right eye, the Wilcoxon rank sum test is applicable to the comparison between T and P, but these two tests

are usually not independent because of the potentially strong correlation between the two eyes within the

respective patients. This paper describes how to use the average of the separate Wilcoxon rank sum tests for the left and right eyes for the overall comparison between T and P with the correlation between the two eyes taken into account. It additionally discusses extensions of rank sum tests to address underlying

assumptions concerning the absence of carryover effects of the treatment on one eye to the opposite eye as

well as the homogeneity of the sources of information from the four sequence groups for the comparison between T and P. With the invocation of constraints corresponding to the previously noted assumptions,

an extension of the average of the Wilcoxon rank sum tests for the left and right eyes can have better

sensitivity to potential differences between T and P through reduction of the applicable variance. The

methods summarized here are illustrated for the motivating clinical trial in ophthalmology.

KEY WORDS: Carryover effects; Contralateral and parallel design; Dermatology; Nonparametric covariance

adjustment; Ophthalmology.

#### Disciplines

Clinical Trials

#### Suggested Citation

Kawaguchi, Atsushi; Koch, Gary G.; and Ramaswamy, Ratna, "Applications of Extensions of Bivariate Rank Sum Tests to the Bilateral Crossover Design to Compare Two Treatments Through Four Sequence Groups" (December 2007). *The University of North Carolina at Chapel Hill Department of Biostatistics Technical Report Series.* Working Paper 4.

http://biostats.bepress.com/uncbiostat/art4