Causal inference in case-control studies

We investigate identification of causal parameters in case-control and related studies. The odds ratio in the sample is our main estimand of interest and we articulate its relationship with causal parameters under various scenarios. It turns out that the odds ratio is generally a sharp upper bound for counterfactual relative risk under some monotonicity assumptions, without resorting to strong ig-norability, nor to the rare-disease assumption. Further, we propose semparametrically efficient, easy-to-implement, machine-learning-friendly estimators of the aggregated (log) odds ratio by exploiting an explicit form of the efficient influence function. Using our new estimators, we develop methods for causal inference and illustrate the usefulness of our methods by a real-data example.