Abstract
We develop purely nonparametric methods for the analysis of repeated measures designs with missing values. Hypotheses are formulated in terms of purely nonparametric treatment effects. In particular, data can have different shapes even under the null hypothesis and therefore, a solution to the nonparametric Behrens-Fisher problem in repeated measures designs will be presented. Moreover, global testing and multiple contrast test procedures as well as simultaneous confidence intervals for the treatment effects of interest will be developed. All methods can be applied for the analysis of metric, discrete, ordinal, and even binary data in a unified way. Extensive simulation studies indicate a satisfactory control of the nominal type-I error rate, even for small sample sizes and a high amount of missing data (up to 30%). We apply the newly developed methodology to a real data set, demonstrating its application and interpretation.
Highlights
Repeated measures (RM) designs are commonly used in various research areas and especially in biomedicine
In RM designs with missing values, the application of existing ranking methods has some disadvantages, which are all motivated from a practical point of view: 1. The procedures can only be used to test global null hypotheses formulated in terms of the distribution functions
We propose a solution to the nonparametric Behrens-Fisher problem in RM designs with missing data
Summary
Repeated measures (RM) designs are commonly used in various research areas and especially in biomedicine. Brunner et al.[2] and Domhof et al.[3] propose purely nonparametric rank-based methods, which do not rely on any distributional assumption and can be used for analyzing metric, discrete or even ordinal data in a unified way. While these ranking methods assume MCAR data, Akritas et al.[4] propose a generalized approach for bivariate data that is valid under a mixture of MCAR and MAR observations. The methods are known to be powerful and robust (with respect to data distributional shapes) and, in particular, they are invariant
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