Assessing the suitability of summary data for two-sample Mendelian randomization analyses using MR-Egger regression: the role of the I2 statistic

Abstract

BackgroundMR-Egger regression has recently been proposed as a method for Mendelian randomization (MR) analyses incorporating summary data estimates of causal effect from multiple individual variants, which is robust to invalid instruments. It can be used to test for directional pleiotropy and provides an estimate of the causal effect adjusted for its presence. MR-Egger regression provides a useful additional sensitivity analysis to the standard inverse variance weighted (IVW) approach that assumes all variants are valid instruments. Both methods use weights that consider the single nucleotide polymorphism (SNP)-exposure associations to be known, rather than estimated. We call this the `NO Measurement Error’ (NOME) assumption. Causal effect estimates from the IVW approach exhibit weak instrument bias whenever the genetic variants utilized violate the NOME assumption, which can be reliably measured using the F-statistic. The effect of NOME violation on MR-Egger regression has yet to be studied.MethodsAn adaptation of the I2 statistic from the field of meta-analysis is proposed to quantify the strength of NOME violation for MR-Egger. It lies between 0 and 1, and indicates the expected relative bias (or dilution) of the MR-Egger causal estimate in the two-sample MR context. We call it IGX2. The method of simulation extrapolation is also explored to counteract the dilution. Their joint utility is evaluated using simulated data and applied to a real MR example.ResultsIn simulated two-sample MR analyses we show that, when a causal effect exists, the MR-Egger estimate of causal effect is biased towards the null when NOME is violated, and the stronger the violation (as indicated by lower values of IGX2), the stronger the dilution. When additionally all genetic variants are valid instruments, the type I error rate of the MR-Egger test for pleiotropy is inflated and the causal effect underestimated. Simulation extrapolation is shown to substantially mitigate these adverse effects. We demonstrate our proposed approach for a two-sample summary data MR analysis to estimate the causal effect of low-density lipoprotein on heart disease risk. A high value of IGX2 close to 1 indicates that dilution does not materially affect the standard MR-Egger analyses for these data.ConclusionsCare must be taken to assess the NOME assumption via the IGX2 statistic before implementing standard MR-Egger regression in the two-sample summary data context. If IGX2 is sufficiently low (less than 90%), inferences from the method should be interpreted with caution and adjustment methods considered.

Improving the accuracy of two-sample summary data Mendelian randomization: moving beyond the NOME assumption

“…Choice of weights and the NOME assumption 1st order weights ignore uncertainty in the denominator of the ratio estimate, which is equivalent to making the 'NO Measurement Error' (NOME) assumption, as defined by Bowden et al [19] within the context of a two-sample MR analysis. The NOME assumption reminds the practitioner that the SNP-exposure association estimates, γ j , which play the role of the explanatory variable in both the IVW and MR-Egger regression models, are only equal to the true associations, γ j , when measured with infinite precision.…”

“…The NOME assumption reminds the practitioner that the SNP-exposure association estimates, γ j , which play the role of the explanatory variable in both the IVW and MR-Egger regression models, are only equal to the true associations, γ j , when measured with infinite precision. In practice, therefore, NOME is always violated, and soγ j can be viewed as the association, γ j , plus some uncertainty or error, with mean zero and variance σ the measurement error literature, such as Simulation Extrapolation [3,19,20].…”

“…The IVW estimate is known to suffer from regression dilution bias towards zero by an amount approximately proportional to the inverse of the mean F -statistic. This dilution can be mitigated by applying bias adjustment techniques from the measurement error literature, such as simulation extrapolation [3,19,20]. For brevity, we do not additionally assess SIMEX correction here.…”

Cannabis use and risk of schizophrenia: a Mendelian randomization study

“…As a sensitivity analysis, we measured the relative bias in the MR-Egger causal effect estimate because of the variance of the estimates of the SNP-cannabis association. 25 Indeed, all MR analyses rely on the assumption that the SNP-exposure association is true (NO Measurement Error (NOME) assumption), 25 but whenever the SNP-exposure association estimates are imprecise, weak instrument bias can distort the causal effect estimate. The I 2 statistic, quantifying weak instrument bias in the context of MR-Egger, was moderate (I 2 = 67%; potential bias of 43%).…”

“…The I 2 statistic, quantifying weak instrument bias in the context of MR-Egger, was moderate (I 2 = 67%; potential bias of 43%). As described by Bowden et al, 25 we then applied simulation extrapolation (implemented in R using the simex package) to adjust the MR-Egger causal estimates to account for a potential NOME violation.…”