Commentary: Can 'many weak' instruments ever be 'strong'?

Investigations into the aetiology of common complex diseases based on observational data should make use of any opportunity to reduce bias due to unobserved confounding. In this context, it has become popular to exploit instrumental variable (IV) methods via Mendelian randomization but the key to success lies in finding suitable genetic instruments. Genome-wide association studies are increasingly yielding large numbers of biomarkers and the understanding of the functionality of these variants is continually improving. However, genetic instruments typically explain only a small proportion of the overall variation in a given exposure and are therefore loosely regarded as ‘weak’ instruments. Combining several instruments intuitively seems like a plausible approach to improving overall instrument strength. Given the likely availability of ever more genetic instruments in the foreseeable future, an investigation into the power and instrument strength requirements of Mendelian randomization analyses with multiple instruments, as proposed by Pierce et al. 1 , is both relevant and timely. In a Mendelian randomization study, the typical target of inference is the effect of an exposure X on a disease outcome Y in the presence of unmeasured confounding factors, U, using one or a combination of several genetic variant(s), G, as an IV. It is often assumed that X and Y are continuous and that all relationships are linear with no interactions, as in