Regression Methods for Estimating Attributable Risk in Population-based Case-control Studies: a Comparison of Additive and Multiplicative Models

A regression method that utilizes an additive model is proposed for the estimation of attributable risk in case-control studies carried out in defined populations. In contrast to previous multivariate procedures for the estimation of attributable risk, which have utilized logistic regression techniques to adjust for confounding factors, the model assumes an additive relation between the covariates included in the regression equation. As an empirical example, additive and logistic models were fitted to matched case-control data from a population-based study of childhood astrocytoma brain tumors. Although both models fitted the data well, the additive model provided a more satisfactory estimate of the risk attributable to multiple exposures, in the absence of significant additive interaction. In contrast to the results from the logistic model, the adjusted estimates of the risk attributable to each factor included in the additive model summed to the overall estimate for all of the factors considered jointly. Thus, the additive approach provides a useful alternative to existing procedures for the multivariate estimation of attributable risk when the additive model is determined to be appropriate on the basis of goodness-of-fit.