Collinear nutrients and the risk of colon cancer

The relationship between colon cancer risk and the relative contributions of fat and caloric intake are assessed. A lack of consensus exists regarding the role of each of these dietary factors in the development of colon cancer. This lack of agreement originates from the high correlations between the nutrients, as well as the manner in which researchers treat these dietary variables in their analyses. Four proposed methods are evaluated which attempt to address the collinearity problem in nutritional epidemiology: (1) exclude one or more collinear variables, (2) use the proportion of calories consumed attributable to each dietary component, (3) use a regression-adjustment approach to purge the collinearity correlated nutrients, and (4) ridge regression. Diagnostic tests are reported which assess the degree of collinearity on data collected for a case-control study of colon cancer conducted in Utah between 1979 and 1983. Using logistic regression analyses, we apply each of these methods to case-control data. We find that the risks associated with fat and caloric consumption are extremely sensitive to a priori analytic decisions made by epidemiologist about the underlying collinearity problem.