Linkage analysis using the derived measure of MSD as phenotype could increase power to detect shared risk loci due to pleiotropically severe affection, compared to analysis of an individual SD disorder, because each single SD does not fully reflect the clinical manifestation of these patients. The derived measure of MSD, which extracts the common component of the multiple phenotypes within each individual, reflects a more homogeneous trait corresponding to the underlying shared genetic risk loci. This measure was derived by fuzzy clustering. In comparison to hard clustering, fuzzy clustering preserves much more of the data structure and allows for diagnostic complexities often observed in real data. We pre-selected a solution with two clusters for the study based on the following considerations. First, if the two clusters could explain 100% of the five substance dependence traits, then the new clustering traits would be better phenotypes. For that reason, the key to selecting an appropriate number of clusters relied on the percentage of variation that the clusters could explain. In the exploratory stage, we observed over 60% variation in the five substance
