While multiplicative (log-linear and logistic) models have a firmly established place in epidemiologic methodology, additive and other more general model structures are needed also. The authors propose a parametric family of relative risk functions ranging from subadditive to supramultiplicative that is generated by varying the exponent in a power transform for the log relative risk. The choice of model is facilitated by graphic analysis of goodness-of-fit statistics computed for various values of the exponent. Intermediate quantities available as by-products of the fit are useful for checking the influence of particular observations on the estimated regression coefficients. Three examples illustrate the applications of these methods to random, stratified, and matched samples of cases and controls. Computer software is available for each of these situations. Even though different relative risk models may have markedly different implications for the multifactorial nature of the disease process, it may be difficult to distinguish between them unless the data are quite extensive.