The analysis of case-referent data can be based on a consideration of case and referent counts in various exposure categories as the realization of a set of binomial processes. After appropriate modeling of the binomial parameters, a joint likelihood function can be formed and maximized to obtain estimates of the parameters constituting the model elements. The procedure has been applied to the problem of additive and multiplicative models of disease incidence rates, as encountered in case-referent studies. Likelihood ratios can be used to compare models with equal numbers of parameters. These ratios do not lead to significance tests, but to estimate of the relative degree of corroboration of different hypotheses by the data at hand.