Conventional Mendelian randomization uses genetic markers known to be associated with a modifiable exposure of interest, for which there is also a known observational association between the modifiable exposure and an outcome of interest. In an ideal situation, the association of the genotype with the outcome can be tested across strata of individuals who are positive or negative for the putative mediating exposure (e.g., ever-smokers versus never-smokers). If there is a causal effect of the exposure (e.g., smoking heaviness) that is being captured by the genotype, then an association of the genotype with the outcome should only be seen in the exposed group and not the unexposed group (see Fig 1) [9]. This is a special case of gene × environment (G × E) interaction, where both G and E are known, although it will not always be possible to stratify on the exposure, and stratification (which can be considered a form of statistical adjustment) can introduce other potential biases in certain circumstances (see Box 3) [10]. Nevertheless, if differences in the magnitude of association observed in exposed and unexposed
