Combining Mendelian randomization with the sibling comparison design

Mendelian randomization (MR) is a popular epidemiologic study design that uses genetic variants as instrumental variables (IVs) to estimate causal effects, while accounting for unmeasured confounding. The validity of the MR design hinges on certain IV assumptions, which may sometimes be violated due to dynastic effects, population stratification, or assortative mating. Since these mechanisms act through parental factors it was recently suggested that the bias resulting from violations of the IV assumptions can be reduced by combing the MR design with the sibling comparison design, which implicitly controls for all factors that are constant within families. In this article, we provide a formal discussion of this combined MR-sibling design. We derive conditions under which the MR-sibling design is unbiased, and we relate these to the corresponding conditions for the standard MR and sibling comparison designs. We proceed by considering scenarios where all three designs are biased to some extent, and discuss under which conditions the MR-sibling design can be expected to have less bias than the other two designs. We finally illustrate the theoretical results and conclusions with an application to real data, in a study of low-density lipoprotein and diastolic blood pressure using data from the Swedish Twin Registry.