Nonparametric correlation-based methods with biomedical applications

Abstract

This cumulative dissertation consists of three manuscripts on nonparametric methodology, i.e., Simultaneous inference for Kendall’s tau, Group sequential methods for the Mann-Whitney parameter, and The nonparametric Behrens-Fisher problem in small samples. The manuscript on Kendall’s τ fully develops a nonparametric estimation theory for multiple rank correlation coefficients in terms of Kendall’s τA and τB, Somers’ D, as well as Kruskal and Goodman’s γ, necessitating joint estimation of both the probabilities of ties occurring and the probability of concordance minus discordance. As for the second manuscript, I review and further develop group sequential methodology for the Mann-Whitney parameter. With the aid of data from a clinical trial in patients with relapse-remitting multiple sclerosis, I demonstrate how one could repeatedly estimate the Mann-Whitney parameter during an ongoing trial together with repeated confidence intervals obtained by test inversion. In addition, I give simple approximate power formulas for this group sequential setting. The last manuscript further explores how best to approximate the sampling distribution of the Mann-Whitney parameter in terms of the nonparametric Behrens-Fisher problem, an issue that has arisen from the preceding manuscript. In that regard, I explore different variance estimators and a permutation approach that have been proposed in the literature and examine some slightly modified ways as regards a small sample t approximation as well. In all three manuscripts, I carried out simulations for various settings to assess the adequacy of the proposed methods.