The many weak instruments problem and Mendelian randomization

Abstract

Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation study demonstrates that, using many weak individual variants, two-stage least squares (2SLS) is biased, whereas the limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak instruments. Our illustrative empirical example uses data on 3631 children from England. We used 180 genetic variants as instruments and compared conventional ordinary least squares estimates with results for the 2SLS, LIML, and CUE instrumental variable estimators using the individual height variants. We further compare these with instrumental variable estimates using an unweighted or weighted allele score as single instruments. In conclusion, the allele scores and CUE gave consistent estimates of the causal effect. In our empirical example, estimates using the allele score were more efficient. CUE with corrected standard errors, however, provides a useful additional statistical tool in applications with many weak instruments. The CUE may be preferred over an allele score if the population weights for the allele score are unknown or when the causal effects of multiple risk factors are estimated jointly. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Genetic Obesity and the Risk of Atrial Fibrillation

“…68 The use of a weighted genetic score, as employed in our study, mitigated both of these risks. 27 Fourth, additional SNPs not included in our gene score have been recently associated with BMI in GWAS. 69 Given the reported per allele effect estimates, we would estimate that these SNPs in toto would account for no more than 0.6% of the variance in BMI (assuming an additive contribution) and therefore inclusion of these identified gene variants would be unlikely to alter the findings of our study.…”

“…24,26 A weighted genetic score (BMI gene score) comprised of these 39 SNPs was constructed for each individual by summing the number of inherited BMI-increasing alleles of each SNP weighted by their effect size. 27 …”

Power calculator for instrumental variable analysis in pharmacoepidemiology

“…8,11 Weak instruments will result in low power to detect a causal effect. [12][13][14] They are also known to induce bias, as such instruments may explain only a small proportion of the association between the exposure and outcome. Therefore, although pharmacoepidemiological studies are likely to have stronger instruments than other forms of instrumental variable analysis such as Mendelian randomization, researchers should remain mindful of their choice of instrument and whether it is appropriate for the research question they wish to study.…”

Predicting the Direction of Causal Effect Based on an Instrumental Variable Analysis: A Cautionary Tale

“…If the genetic variants are all instrumental variables, then the score will be an instrumental variable. The use of allele scores is motivated by the desire to avoid bias from weak instruments that can lead to misleading findings if the genetic variants do not explain much variation in the exposure [34]. As genetic variants will generally have different magnitudes of association with the exposure, the monotonicity assumption is likely to be violated for an unweighted score as greater values of the score will not necessarily correspond to greater expected values of the exposure.…”