Prospective analysis of case-control data under general multiplicative-intercept risk models

We show that, under a general multiplicative-intercept model for risk, case-control data can be analyzed by maximum likelihood as if they had arisen prospectively, up to an unidentifiable multiplicative constant which depends on the relative sampling fractions. This generalizes earlier work of Anderson (1972, 1979), by showing that not only the point estimates but also the standard errors based on the observed information matrix are correct when the prospective likelihood is maximized. Likelihood ratio testing is also valid under this broad class of risk models. Data on disease status from a much larger cohort are shown to add no information to the estimation of the covariate-related parameters.