Cluster Analysis

Abstract

The issue of suitable similarity measures for a particular kind of genetic data - so called SNP data - arises, e.g., from the GENICA (The Interdisciplinary Study Group on Gene Environmental Interactions and Breast Cancer in Germany) case-control study of sporadic breast cancer. The GENICA study aims to investigate the influence and interaction of single nucleotide polymorphic (SNP) loci and exogenous risk factors. It is very unlikely that there exists one main effect, say only one polymorphism, being responsible for such a complex disease as sporadic breast cancer as the role of a single gene within the carcinogenic process is limited (Garte, 2001). Nevertheless, it is assumed that a number of interacting SNPs in combination with certain environmental risk factors increase the individual susceptibility. The search for SNP patterns in the present data set may be performed by a variety of clustering and classification approaches. Here we consider the problem of adequate similarity measures for variables or subjects as an indispensable basis for a further cluster analysis. The term ’similarity’ is still vague for SNP data. A main problem arises by the general structure of such data sets: the proportion of hetero- or homozygous SNPs is rather small compared with the homozygous reference sequence. Thus, the relevant information of combinations of genetic alterations is often masked by a huge amount of common occurrences of homozygous reference types. Therefore, we examine different similarity measures, conventional ones as well as new coefficients which we created especially for SNP data. Furthermore, we compare the resulting partitions with each other adapting the clustering of clustering methods of Rand (1971) for different similarity measures.