ESTIMATING RELATIVE RISK FUNCTIONS IN CASE-CONTROL STUDIES USING A NONPARAMETRIC LOGISTIC-REGRESSION

The authors describe an approach to the analysis of case-control studi es in which ?he 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 exposur e and disease risk. A dose-response association of an exposure variabl e with a disease outcome can be depicted by estimated relative risks a t Various exposure levels, and the functional relation between exposur e 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 i mply lower risk; the Value one implies no risk, and values greater tha n one imply increased risk, when compared with a reference value, the authors describe how a nonparametric logistic regression can be used t o estimate and display these RRFs. Using data from a previously publis hed case-control study of diet and colon cancer, RRFs for total energy , dietary fiber, and alcohol intakes are compared with the original re sults obtained from using categorized levels of exposure variables. Fo r 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 e ffect of low intakes, which was not found in the original analysis. Fo r alcohol, the nonparametric logistic regression suggested that there were two underlying populations, non- or very light drinkers and moder ate to heavy drinkers, with different relation of dose to disease risk . In contrast, the original analysis found a nonlinear increase in ris k across intake categories and did not detect the complex, bimodal nat ure of the exposure distribution. These results demonstrate that nonpa rametric logistic regression can be a useful approach to displaying an d interpreting results of case-control studies.