Minelli, C. | bioRxiv Science

bioRxiv2017

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

BackgroundSummary data furnishing a two-sample Mendelian randomization 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.\n\nMethodsWe 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.\n\nResultsWe illustrate the methods using data from a two-sample Mendelian randomization 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 which is responsible for large differences between IVW and MR-Egger regression estimates. Several additional plots are also proposed for informative data visualisation.\n\nConclusionThe radial plot should be considered in place of the scatter plot for visualising, analysing and interpreting data from a two-sample summary data MR study. Software is provided to help facilitate its use.

epidemiology↗

bioRxiv2017

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

BackgroundTwo-sample summary data Mendelian randomization (MR) incorporating multiple genetic variants within a meta-analysis framework is a popular technique for assessing causality in epidemiology. If all genetic variants satisfy the instrumental variable (IV) and necessary modelling assumptions, then their individual ratio estimates of causal effect should be homogeneous. Observed heterogeneity signals that one or more of these assumptions could have been violated.\n\nMethodsCausal estimation and heterogeneity assessment in MR requires an approximation for the variance, or equivalently the inverse-variance weight, of each ratio estimate. We show that the most popular 1st order weights can lead to an inflation in the chances of detecting heterogeneity when in fact it is not present. Conversely, ostensibly more accurate 2nd order weights can dramatically increase the chances of failing to detect heterogeneity, when it is truly present. We derive modified weights to mitigate both of these adverse effects.\n\nResultsUsing Monte Carlo simulations, we show that the modified weights outperform 1st and 2nd order weights in terms of heterogeneity quantification. Modified weights are also shown to remove the phenomenon of regression dilution bias in MR estimates obtained from weak instruments, unlike those obtained using 1st and 2nd order weights. However, with small numbers of weak instruments, this comes at the cost of a reduction in estimate precision and power to detect a causal effect compared to 1st order weighting. Moreover, 1st order weights always furnish unbiased estimates and preserve the type I error rate under the causal null. We illustrate the utility of the new method using data from a recent two-sample summary data MR analysis to assess the causal role of systolic blood pressure on coronary heart disease risk.\n\nConclusionsWe propose the use of modified weights within two-sample summary data MR studies for accurately quantifying heterogeneity and detecting outliers in the presence of weak instruments. Modified weights also have an important role to play in terms of causal estimation (in tandem with 1st order weights) but further research is required to understand their strengths and weaknesses in specific settings.

epidemiology↗