Comparison of case-control to full cohort analyses under model misspecification

We investigate the question of whether or not estimates of relative risk fr om matched case-control studies well represent the population from which th ey were drawn. We derive the formula for the asymptotic maximum partial lik elihood estimators from nested case-control studies when the Cox proportion al hazards model is misspecified and compare these to the corresponding ful l cohort values under various types of model misspecification, such as cova riate omission, mismodelling available measurements and covariates measured with error. We found that lack of covariate information, as in covariate o mission and measurement error, cannot per se result in differences in case- control and cohort estimates. Differences can only occur when the covariate s used in the presumed model are mismodelled and we find that the magnitude of the misspecification must be unreasonably large in order to produce dif ferences of,practical importance.