Hypothesis testing in case-control studies

SUMMARY Prentice & Pyke (1979) have shown that valid estimators of the odds-ratio parameters in a logistic regression model may be obtained from case-control data by fitting the model as if the data had been obtained in a prospective study. The resulting estimates of standard errors are also valid asymptotically. We extend the Prentice-Pyke result to likelihood ratio tests obtained from fitting a prospective model. These tests are asymptotically exact if the hypothesis involves only the odds-ratio parameters and are asymptotically conservative if stratum effects are involved.