gms | German Medical Science

While, over the past decade, a plethora of methods has been developed to address the detection of global effects with regard to high-dimensional groups of metric variables such as gene sets, less effort has been invested in the case when the variables of interest are categorical. For the former, the construction of a global test statistic as the sum of (transformed) univariate test statistics has amply been discussed, see Ackermann and Strimmer [1] for an extensive review. The rationale behind these so-called summary statistics is a straightforward construction of global tests both addressing arbitrary dimension and exploiting the multiplicity of well investigated univariate tests, each assessing marginal effects. By computing permutation-based p-values, global tests which are obtained through this approach can account for possible correlations within the summary statistics. A first model-based attempt to two sample summary statistics addressing binary variables was made by Mansmann and Meister [2] who employ a deviance summary statistic. In our work, we propose further summary statistics for categorical (i.e. nominal and ordinal) variables and thus extend their range of application from metric to arbitrary scales of measurement. Unlike Mansmann and Meister [2], we do not pursue model-based approaches, but focus on established two sample tests such as the chi-square test for homogeneity. We examine the properties of these summary statistics by means of simulated data and demonstrate their potential usefulness for analyzing International Classication of Functioning (ICF) Core Sets where a lot of ordinal covariates are usually collected [3]. Beyond, Single Nucleotide Polymorphisms arising in Genome-Wide Association Studies are another relevant scope of application for the approach we present. In case of hierarchically structured data such as the ICF Core Sets, we illustrate how the proposed summary statistics might be used in order to reveal significant subsets according to the hierarchical testing approach introduced by Meinshausen [4]. Our analysis of ICF Core Sets for stroke patients [5] suggests strong differences between the functional profiles of patients where the stroke is located in the right versus the left brain hemisphere. Applying the hierarchical testing procedure allowed to assign significant differences to subsets concerning specific mental functions, the ability of applying knowledge and communication devices.