The instrumental variable framework is commonly used in the estimation of causal effects from cohort samples. In the case of more efficient designs such as the case-control study, however, the combination of the instrumental variable and complex sampling designs requires new methodological consideration. As the prevalence of Mendelian randomization studies is increasing and the cost of genotyping and 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 variable analysis is not applicable to the case-control design and can lead to erroneous estimation and inference. We also propose a method based on principal stratification for the analysis of data arising from the combination of case-control sampling and instrumental variable design and illustrate it with a study in oncology.
Shinohara, Russell T.; Frangakis, Constantine E.; Platz, Elizabeth; and Tsilidis, Konstantinos, "Estimating effects by combining instrumental variables with case-control designs: the role of principal stratification" (September 2009). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 198.