The method of multivariable Mendelian randomization uses genetic variants to instrument multiple exposures, to estimate the effect that a given exposure has on an outcome conditional on all other exposures included in a linear model. Unfortunately, the inclusion of every additional exposure makes a weak instruments problem more likely, because we require conditionally strong genetic predictors of each exposure. This issue is well appreciated in practice, with different versions of F-statistics routinely reported as measures of instument strength. Less transparently, however, these F-statistics are sometimes used to guide instrument selection, and even to decide whether to report empirical results. Rather than discarding findings with low F-statistics, weak instrument-robust methods can provide valid inference under weak instruments. For multivariable Mendelian randomization with two-sample summary data, we encourage use of the inference strategy of Andrews (2018) that reports both robust and non-robust confidence sets, along with a statistic that measures how reliable the non-robust confidence set is in terms of coverage. We also propose a novel adjusted-Kleibergen statistic that corrects for overdispersion heterogeneity in genetic associations with the outcome.

翻译：多变量孟德尔随机化方法利用遗传变异作为多个暴露变量的工具变量，以估计在包含所有其他暴露的线性模型中，某一给定暴露对结局的条件性效应。然而，每增加一个暴露变量都会加剧弱工具变量问题，因为我们需要每个暴露变量都具有条件性强的遗传预测因子。实践中这一问题已得到充分重视，通常报告不同版本的F统计量作为工具变量强度的度量。但较不透明的是，这些F统计量有时被用于指导工具变量选择，甚至决定是否报告实证结果。与其直接舍弃F统计量较低的研究结果，采用弱工具变量稳健方法可以在弱工具变量条件下提供有效的统计推断。针对基于两样本汇总数据的多变量孟德尔随机化，我们推荐采用Andrews（2018）的推断策略，该策略同时报告稳健与非稳健置信集，并提供一个统计量来衡量非稳健置信集在覆盖率方面的可靠性。此外，我们提出了一种新颖的调整型Kleibergen统计量，用于校正遗传与结局关联中的过度离散异质性。