Estimation based on case-control designs with known prevalence probability.

Regular case-control sampling is an extremely common design used to generate data to estimate effects of exposures or treatments on a binary outcome of interest when the proportion of cases (i.e., binary outcome equal to 1) in the population of interest is low. Case-control sampling represents a biased sample of a target population of interest by sampling a disproportional number of cases. Case-control studies are also commonly employed to estimate the effects of genetic markers or biomarkers on binary phenotypes. In this article we present a general method of estimation relying on knowing the prevalence probability, conditional on the matching variable if matching is used. Our general proposed methodology, involving a simple weighting scheme of cases and controls, maps any estimation method for a parameter developed for prospective sampling from the population of interest into an estimation method based on case-control sampling from this population. We show that this case-control weighting of an efficient estimator for a prospective sample from the target population of interest maps into an efficient estimator for matched and unmatched case-control sampling. In particular, we show how application of this generic methodology provides us with double robust locally efficient targeted maximum likelihood estimators of the causal relative risk and causal odds ratio for regular case control sampling and matched case control sampling. Various extensions and generalizations of our methods are discussed.