Fig 1.
a, The causal directed graph represented by structural equations (1). b, The existence of a pleiotropic pathway 2 (purple) can result in multiple modes of the profile likelihood. c, Multi-modality of the profile likelihood can reflect causal direction. d, The work-flow with GRAPPLE.
Fig 2.
a, Estimation of β across selection p-value thresholds under no pleiotropy. Error bars show 95% Confidence intervals and the numbers are the number of independent SNPs obtained at each threshold. b, Estimation of β across three non-overlapping categories of SNPs: “strong”, “moderate” and “weak”. The numbers are the number of SNPs in each category. c, Identifying causal directions by multi-modality with MR reversely performed. The selection p-value threshold is kept at 10−4. d, three modes detected in the profile likelihood with selection p-value threshold 10−4 for CRP on CAD. Marker genes and GWAS traits (in parenthesis) are shown for each mode. e, estimation of the CRP effect β at different p-value selection threshold with each method. The numbers are the estimated , with * indicating p-value below 0.05 and ** indicating p-value below 0.01.
Fig 3.
a, Landscape of pleiotropic pathways on 25 diseases. The colors show average number of modes across 7 different selection p-value thresholds. The “+” sign shows a positive estimated effect and “−” indicates a negative estimated effect, with the p-value for each cell a combined p-value (see Materials and methods) of replicability across 7 thresholds using the single risk factor. These p-values are not multiple-testing adjusted across pairs. b, Multi-modality of the profile likelihood for effect of HDL-C on CAD at 2 different selection p-value threshold. Vertical bars are positions of marker SNPs (), labeled by their mapped genes (only unique gene names are shown). c, Multivariable MR for the effect of 5 risk factors on CAD. d, Multivariable MR for the effect of 4 risk factors on CAD. The Error bars are 95% confidence intervals.