Improving the visualization, interpretation and analysis of two-sample summary data Mendelian randomization via the Radial plot and Radial regression

Abstract

BackgroundSummary data furnishing a two-sample Mendelian randomization (MR) study are often visualized with the aid of a scatter plot, in which single-nucleotide polymorphism (SNP)–outcome associations are plotted against the SNP–exposure associations to provide an immediate picture of the causal-effect estimate for each individual variant. It is also convenient to overlay the standard inverse-variance weighted (IVW) estimate of causal effect as a fitted slope, to see whether an individual SNP provides evidence that supports, or conflicts with, the overall consensus. Unfortunately, the traditional scatter plot is not the most appropriate means to achieve this aim whenever SNP–outcome associations are estimated with varying degrees of precision and this is reflected in the analysis.MethodsWe propose instead to use a small modification of the scatter plot—the Galbraith Radial plot—for the presentation of data and results from an MR study, which enjoys many advantages over the original method. On a practical level, it removes the need to recode the genetic data and enables a more straightforward detection of outliers and influential data points. Its use extends beyond the purely aesthetic, however, to suggest a more general modelling framework to operate within when conducting an MR study, including a new form of MR-Egger regression.ResultsWe illustrate the methods using data from a two-sample MR study to probe the causal effect of systolic blood pressure on coronary heart disease risk, allowing for the possible effects of pleiotropy. The Radial plot is shown to aid the detection of a single outlying variant that is responsible for large differences between IVW and MR-Egger regression estimates. Several additional plots are also proposed for informative data visualization.ConclusionsThe Radial plot should be considered in place of the scatter plot for visualizing, analysing and interpreting data from a two-sample summary data MR study. Software is provided to help facilitate its use.

MR-TRYX: A Mendelian randomization framework that exploits horizontal pleiotropy to infer novel causal pathways

“…The problem of instrumental variables being invalid due to horizontal pleiotropy has received much attention in MR analysis. Detecting and excluding such invalid instruments, based on whether they appear to be outliers in the analysis, is now a common strategy that exists in various forms 7,8,14,15,35 . We have shown here that outlier removal could, in some circumstances, compound rather than reduce bias, and misses an opportunity to better understand the traits under study.…”

“…Cook's distance), or most commonly the extent to which a SNP contributes to heterogeneity (e.g. Cochran's Q statistic, MR-PRESSO, and implicitly in median-and mode-based estimators) 7,8,14,15 . The philosophy of the latter two approaches is that proving horizontal pleiotropy is impossible, but that it should lead to outliers 9 .…”

“…We used the approach implemented in the RadialMR R package (https://github.com/WSpiller/RadialMR) to detect outliers. Full details are provided elsewhere 15 , but briefly, we used the so-called 'modified 2 nd order weighting' approach to estimate total Cochran's Q statistic as a measure of heterogeneity, as well as the individual contributions of each SNP, q i 15 . This has been shown to be comparable to the simulationbased approach in MR-PRESSO, providing a well-calibrated test statistic for outlier status whilst being computationally more efficient 14,20 .…”

“…Steiger filtering removes those SNPs that do not explain substantially more of the variance in the exposure trait than in the outcome, attempting to guard against using SNPs as instruments that are likely to be associated with the outcome through a pathway other than the exposure 12 . Finally, meta-analysis tools can be used to evaluate if a particular SNP contributes disproportionately to the heterogeneity between the estimates obtained from the set of instruments, and this has been adapted recently to detect outliers in MR analysis 13,14,15 . A potential limitation of heterogeneity-based outlier removal is that this practice could constitute a form of cherry picking 9,16 .…”

Bi-directional Mendelian randomization of epithelial ovarian cancer and schizophrenia and uni-directional Mendelian randomization of schizophrenia on circulating glycerophosphocholine metabolites

“…We applied IVW radial regression for each MR test. IVW radial regression uses the P-value from Cochran's Q-statistic (P[het]) to identify possible heterogeneity among an instrument's ratio estimates [22]. Heterogeneity can indicate pleiotropy.…”