Nonparametric tests for comparing two treatments by using ordinal data
Abstract: This thesis concerns four nonparametric tests for comparing two treatments in a randomized controlled clinical trial when the main response variable generates discrete or continuous ordinal data and measurements are made at baseline and follow-up.In the Wilcoxon-Mann-Whitney test (WMW) the baseline values are not taken into account at all, but in the other three tests both baseline and follow-up values are used. In the stratified WMW test (SWMW) the baseline variable is used as a stratification variable; thus the baseline and follow-up values are used in an asymmetric way. Also in a test which is a modified version of one part of the method for analysing paired ordinal data proposed by Svensson (S) and a test which is based on a statistic proposed by Lanke and Svensson (LS) both variables are used, but in more symmetric fashions.The four tests are considered mainly concerning their powers to detect differences between the treatments and regarding the impact of the strength of association between the responses at baseline and follow-up on the efficiencies of the tests. The thesis consists of an introductory part and three papers. In the first paper, large-sample aspects of WMW, SWMW, and S are considered when applied to discrete ordinal data, i.e. ordered categorical data. Known asymptotic distribution results for the test statistics used in WMW and SWMW are given together with derivations of corresponding results for the test statistic used in S. Furthermore, results from a simulation study of actual significance levels of the tests are presented. Pitman efficiencies are derived and some numerical examples are given.The second paper concerns small-sample aspects of WMW, SWMW, and S when they are performed as permutation tests and applied to ordered categorical data. A method for estimating the power of such tests in a Monte Carlo study is developed further and implemented on some artificial distributions.Finally, the third paper deals with the tests WMW, S, and LS when applied to continuous ordinal data, i.e. data which for example are assessments on a visual analogue scale. As in the second paper, the tests are performed as permutation tests and the method for estimating the power of such tests in a Monte Carlo study is used on logistic-normal distributions.
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