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Why internal weights should be avoided (not only) in MR-Egger regression.

Germline genetic variants have been increasingly used as instrumental variables to strengthen causal inference in observational studies (i.e. Mendelian randomization). The field is also rapidly developing methodologically, with new estimators to overcome specific limitations featuring in the recent literature. However, it is important to understand the limitations and potential sources of bias for these approaches. Traditional Mendelian randomization studies depend on three critical assumptions: relevance, that the genetic variants associate with the risk factor of interest; the independence assumption, that the genetic variants do not associate with the potential confounders; and the exclusion restriction, that variants only affect the outcome via the risk factor of interest. It is impossible to prove that the exclusion restriction holds, and many genetic variants are thought to have pleiotropic effects which would violate this assumption. Bowden and colleagues recently proposed the MR-Egger regression method, which relaxes this final assumption. MR-Egger regression relies on the InSIDE assumption, that requires that instrument-exposure and instrument-outcome associations are independent. This estimator can be consistent even if all the instruments are invalid. Another advantage of MR-Egger is that it can efficiently use effect estimates from multiple samples. However, MR-Egger can suffer from ‘many weak instrument bias’. Many weak instrument bias occurs when a large number of instruments are used in an instrumental variable analysis, each of which explains only a very small portion of the variation in the exposure. Bowden and colleagues were successful in presenting and evaluating the method, and actually simulated both nonand fully-overlapping datasets to investigate the issue of weak instrument bias. However, one of their illustrated applications was based on instrument-height (exposure; in standard deviation units) and instrument-lung function [outcome; measured as forced vital capacity (FVC) in millilitres] estimated in 3631 adolescents in the ALSPAC cohort, without discussing the issue weak instrument bias towards the observational estimate. In this study, 180 height-associated variants were used as instruments based on a previous genome-wide association study (GWAS) (which made summary data available) in 183 727 individuals. Instrument-phenotype associations were identical to those used in Davies and colleagues, a methodological study of weak instrument bias in the single-sample setting. In the simulations performed by Davies and colleagues, two-stage least squares regression (2SLS) was biased, whereas the allele score, limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) methods were unbiased and had accurate falserejection rates when standard errors were corrected for the presence of many weak instruments. Figure 1 shows different estimates of the association of height on lung function (millilitre changes in FVC per 1-standard deviation increase in height). The conventional observational estimate was 0.67 [95% confidence interval (CI): 0.65; 0.70]. The CUE, LIML and allele score methods (more robust against weak instrument bias) presented consistent estimates of approximately 0.43, but the 2SLS estimate, which is known to be more prone to weak instrument bias, was biased towards the observational estimate [0.60 (95% CI: 0.52; 0.68)]. In Bowden and colleagues’ paper, the