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).1,2 The field is also rapidly developing methodologically, with new estimators to overcome specific limitations featuring in the recent literature.2–5 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,5 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.5 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 non- and 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.6 Instrument-phenotype associations were identical to those used in Davies and colleagues,7 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 false-rejection rates when standard errors were corrected for the presence of many weak instruments. Linear regression coefficients and 95% confidence intervals of changes in millilitres of forced vital capacity (FVC) per 1-standard deviation (SD) increase in height in adolescents in the ALSPAC cohort using different estimators. The dashed line corresponds to a null effect. 2SLS: 2-stage least squares regression. LIML: limited information maximum likelihood (with corrected standard errors). CUE: continuously updating estimator (with corrected standard errors). IVW: inverse-variance weighted. Internal weights: both instrument-height and instrument-lung function associations estimated in the ALSPAC cohort (result extracted from Bowden et al.5). External weights: instrument-height associations estimated in the latest height GWAS,9 and instrument-lung function associations estimated in the ALSPAC cohort. Thus MR-Egger can suffer from weak instrument bias towards the (potentially confounded) observational estimate in the singl- sample setting. One potential solution for estimating MR-Egger in a single sample is to use a split-sample approach. However, there is a danger that empirical researchers will apply MR-Egger in single samples without correcting for the bias. For example, in a recent paper in the International Journal of Epidemiology, Kemp and colleagues used Mendelian randomization to assess if adiposity affected bone mineral density (BMD). They used data from children participating in the Avon Longitudinal Study of Parents and Children (ALSPAC).10 The authors acknowledged the possibility of weak instrument bias in their paper, and performed a range of sensitivity analyses unlikely to be affected by this bias in order to test the robustness of their results including using only genetic variants strongly associated with BMI (i.e. partial F statistics > 10) in two-stage least squares analysis, and performing a range of analyses involving strong instruments consisting of allelic scores. In their MR-Egger analysis, they estimated the instrument-adiposity and instrument-BMD associations in a single sample using 32 variants, some of which were weakly associated with the exposure. The analyses were performed in up to 5221 children, and the adjusted R² of the associations of most variants with adiposity measures were low: mean (standard deviation) and median (10th; 90th percentiles) were 0.12% (0.17%) and 0.05% (0.00%; 0.38%), respectively, after setting negative adjusted R² values to zero. As a consequence, the partial F statistics were generally low: mean (standard deviation) and median (10th; 90th percentiles) were 7.01 (9.08) and 3.55 (0.05; 21.25), respectively. The authors acknowledged this issue and performed simulations to investigate the potential impact of weak instrument bias on their MR-Egger estimates. However, another strategy would have been to use external weights for BMI from published GWAS,11 which may have resulted in a smaller bias that acts towards the null.12 Doing so may have also increased statistical power to detect a causal effect, because instrument-BMI associations are more precise since the BMI GWAS included > 300 000 participants (assuming of course that results from a GWAS of adult BMI truly reflect the associations of these variants with BMI in children). Fortunately, none of Kemp and colleagues’ key conclusions depends solely on the MR-Egger results, which was just one of many techniques used to investigate the robustness of their main conclusions. However, other studies may depend more heavily on the results from MR-Egger, and so it is important that researchers be aware that MR-Egger can suffer from many weak instrument bias and take steps to rectify this situation if possible, for example by using external weights. In conclusion, Mendelian randomization is a useful strategy to interrogate causal hypotheses using observational data. MR-Egger regression is a useful sensitivity analysis, but it is prone to weak instrument bias. If instrument-exposure and instrument-outcome associations are estimated in the same or partially overlapping datasets, it can have falsely inflated rejection rates. This issue could be avoided in many cases given the increasing availability of summary data from large GWAS meta-analysis of different phenotypes.13 The promise of sophisticated methods, like MR-Egger regression, will only be realized if investigators are aware of potential pitfalls and sources of bias. The Medical Research Council (MRC) and the University of Bristol fund the MRC Integrative Epidemiology Unit [MC_UU_12013/1, MC_UU_12013/9]. NMD is supported by the Economics and Social Research Council (ESRC) via a Future Research Leaders Fellowship [ES/N000757/1].