Robust non-parametric tests for complex-repeated measures problems in ophthalmology

Abstract

The NonParametric Combination methodology (NPC) of dependent permutation tests allows the experimenter to face many complex multivariate testing problems and represents a convincing and powerful alternative to standard parametric methods. The main advantage of this approach lies in its flexibility in handling any type of variable (categorical and quantitative, with or without missing values) while at the same time taking dependencies among those variables into account without the need of modelling them. NPC methodology enables to deal with repeated measures, paired data, restricted alternative hypotheses, missing data (completely at random or not), high-dimensional and small sample size data. Hence, NPC methodology can offer a significant contribution to successful research in biomedical studies with several endpoints, since it provides reasonably efficient solutions and clear interpretations of inferential results. Pesarin F. Multivariate permutation tests: with application in biostatistics. Chichester-New York: John Wiley &Sons, 2001; Pesarin F, Salmaso L. Permutation tests for complex data: theory, applications and software. Chichester, UK: John Wiley &Sons, 2010. We focus on non-parametric permutation solutions to two real-case studies in ophthalmology, concerning complex-repeated measures problems. For each data set, different analyses are presented, thus highlighting characteristic aspects of the data structure itself. Our goal is to present different solutions to multivariate complex case studies, guiding researchers/readers to choose, from various possible interpretations of a problem, the one that has the highest flexibility and statistical power under a set of less stringent assumptions. MATLAB code has been implemented to carry out the analyses.