Another problem with the use of many genetic variants is that of weak instruments. With many IVs in a one-sample setting (genetic variants, exposure and outcome measured in the same participants), IV estimates (particularly those from the TSLS method) are biased in the direction of the observational association between the exposure and the outcome.49 This bias depends on the strength of the association of the IVs with the exposure, and is typically small if there is one IV50 or if the IVs are strongly associated with the exposure, but the bias may be substantial for Mendelian randomization in realistic settings.36 In a two-sample setting, weak instrument bias is in the direction of the null, and hence is a less serious problem, as it will not lead to false-positive findings.37,39 One solution proposed for weak instrument bias is the use of allele scores, whereby the number of exposure-increasing alleles across multiple genetic variants is summed across individuals.9 The total number of alleles (possibly weighted according to their association with the exposure) is then used as a single IV, rather than the
