Synthetic cancer variables and the construction and testing of synthetic risk maps

Cancer cluster investigations are usually univariate in nature; they focus on a particular cancer, such as leukaemia, and attempt to determine whether excess risk is associated with a suspected cancer-causing agent. Although several causes of death (such as leukaemia, lymphoma, Hodgkin's) may be considered, the approach is univariate because the causes of death are analysed sequentially and independently of one another. This approach is consistent with a one-cause one-effect model. Rarely, however, is the action of a carcinogen manifested at only one body site, and correlations among causes of death are the norm rather than the exception. A multiple effects model is therefore appropriate, and the multivariate nature of cancer mortality data should be exploited when exploring geographic pattern in cancer risks. This paper describes such an approach. We construct maps based on a principal components analysis of cancer mortality rates from different geographic areas. The resulting principal components are called synthetic cancer variables (SCVs), and maps of the SCV scores are synthetic risk maps (SRMs). These maps quantify geographic variation in cancer risk at several body sites simultaneously, and may be analysed for (1) spatial structure and (2) geographic association with potential risk factors. As an example, we use synthetic risk maps to determine whether high-risk counties in Illinois cluster near nuclear facilities. Much work remains to be done, but synthetic cancer risk maps appear to be a useful tool for quantifying geographic pattern and multivariate structure in cancer mortality.