Non-independence in network-structured Mendelian randomization: a permutation framework and six failure modes

Background. Protein Mendelian randomization (MR) is now routine, and a common inference treats an estimate built from a ligand's own cis protein quantitative trait locus (pQTL) and one built from its receptor's as evidence about the same pathway. That assumption has not been tested since it means comparing MR estimates across a network of interacting proteins, and network comparisons violate the independence that standard multiple-testing corrections assume. Methods. Using cis-pQTLs as instruments, we analyzed 660 of the 661 UK Biobank Pharma Proteomics Project proteins spanning 1,129 curated ligand–receptor pairs, and estimated effects on coronary artery disease in two genome-wide association studies (GWAS): Nikpay 2015 (60,801 cases, no UK Biobank overlap) and Aragam 2022 (181,522 cases, which include the Nikpay data). Discordance between ligand-level and receptor-level estimates was tested against a permutation null holding every protein's estimate and degree fixed and randomizing only the pairing. Estimates were followed up with Bayesian colocalization and with replication on a second proteomic platform. Results. Ligand and receptor estimates agreed no more than randomly paired proteins: 48.5% same-direction against a rewired null of 49.8% (p = 0.64) in Nikpay, and 47.0% against 50.0% (p = 0.20) in Aragam. Counts of significantly discordant pairs rose threefold with outcome power, from 10 to 31, and the null rose with them, from 9 to 30 (p = 0.85). Bonferroni correction across 476 deduplicated pairs built from 361 proteins reported ten discoveries that three proteins account for. A node-shuffling null gave p = 0.014 because protein degree correlates with effect size in Aragam (rho = + 0.133, p = 0.008). Flagging protein-altering instruments, a routine sensitivity analysis, flagged PCSK9 and showed no enrichment among causal proteins (Fisher p ≥ 0.44). Colocalization verdicts survived a change of outcome GWAS at only 11 of 14 loci (PP.H4 ≥ 0.8), mostly through outcome power; one locus reversed outright. Conclusions. Ligand-level and receptor-level MR are not interchangeable evidence about a pathway. More important, the naive analysis that appears to identify specific discordant pairs is reproducible. It returns ten pairs after correction, headed by one at p = 8.5 × 10 ^− 7 , and we show what removes them.