Validity of a method for identifying disease subtypes that are etiologically heterogeneous

A focus of cancer epidemiologic research has become the identification of risk factors that influence specific subtypes of disease, a phenomenon known as etiologic heterogeneity. In previous work we developed a novel strategy to cluster tumor markers and identify disease subtypes that differ maximally with respect to known risk factors for use in the context of case-control studies. The method relies on the premise that unsupervised k-means clustering will find candidate solutions that are closely aligned with the sought-after etiologically distinct clusters, which may not be true in the presence of clusters of tumor markers that are not related to risk of disease. In this article, we investigate in detail the ability of the method to identify the "true" clusters in the presence of clusters that are unrelated to risk factors, what we term "counterfeit" clusters. We find that our method works when the strength of structure is larger in the clusters that truly represent etiologic heterogeneity than in the counterfeit clusters, but when this condition is not met, or when there are many tumor markers that simply represent noise, the method will not find the correct solution without first performing variable selection to identify the tumor markers most strongly related to the risk factors. We illustrate the results using data from a breast cancer case-control study.