Designs combining instrumental variables with case-control: estimating principal strata causal effects.

The instrumental variables framework is commonly used for the estimation of causal effects from cohort samples. However, the combination of instrumental variables with more efficient designs such as case-control sampling requires new methodological consideration. For example, as the use of Mendelian randomization studies is increasing and the cost of genotyping and gene expression data can be high, the analysis of data gathered from more cost-effective sampling designs is of prime interest. We show that the standard instrumental variables analysis does not appropriately estimate the causal effects of interest when the instrumental variables design is combined with the case-control design. We also propose a method that can estimate the causal effects in such combined designs. We illustrate the method with a study in oncology.