variants tended towards different values, it would not be possible to distinguish which of those values is the causal effect. A similar approach is simply to calculate the causal estimates using each genetic variant individually, rank the estimates in order of magnitude and take the median estimate.42 Again, this is guaranteed to give a consistent causal estimate if at least half of the genetic variants are valid IVs, although at the cost of a considerable reduction in precision of the causal estimate. Kolesár et al.25 also propose a consistent causal estimator under the same conditions as considered in this paper. This is based on a modified version of the bias-corrected TSLS estimator, which is part of the wider group of k-class estimators, a group that also includes the TSLS, bias-corrected TSLS and limited information maximum likelihood estimators.43 Further theoretical work is needed to compare the statistical properties of this estimator with the MR-Egger estimator proposed in this paper.
