Estimating relative risk functions in case-control studies using a nonparametric logistic regression.

The authors describe an approach to the analysis of case-control studies in which the exposure variables are continuous, i.e., quantitative variables, and one wishes neither to categorize levels of the exposure variable nor to assume a log-linear relation between level of exposure and disease risk. A dose-response association of an exposure variable with a disease outcome can be depicted by estimated relative risks at various exposure levels, and the functional relation between exposure dose and disease risk is here termed a relative risk function (RRF). A RRF takes values that are greater than zero: Values less than one imply lower risk; the value one implies no risk, and values greater than one imply increased risk, when compared with a reference value. The authors describe how a nonparametric logistic regression can be used to estimate and display these RRFs. Using data from a previously published case-control study of diet and colon cancer, RRFs for total energy, dietary fiber, and alcohol intakes are compared with the original results obtained from using categorized levels of exposure variables. For total energy and alcohol intakes, there were meaningful differences in study results based on the two analytic approaches. For energy, the nonparametric logistic regression detected a significant protective effect of low intakes, which was not found in the original analysis. For alcohol, the nonparametric logistic regression suggested that there were two underlying populations, non- or very light drinkers and moderate to heavy drinkers, with different relation of dose to disease risk. In contrast, the original analysis found a nonlinear increase in risk across intake categories and did not detect the complex, bimodal nature of the exposure distribution. These results demonstrate that nonparametric logistic regression can be a useful approach to displaying and interpreting results of case-control studies.