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Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments
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Identifies conditions under which valid IV sets and causal directions are identifiable in one-sample bi-directional Mendelian randomization with invalid IVs, and proposes the PReBiM cluster-fusion-style algorithm that recovers both bi-directional causal effects from simulated data.
Problem
Estimating bi-directional causal effects between a treatment and outcome from one-sample observational data where some genetic instruments are invalid (horizontal pleiotropy) and unmeasured confounding exists, without prior knowledge of which IVs are valid or of the causal direction.
Approach
Uses pseudo-residuals (Y minus X times the TSLS estimate from a subset of IVs) and tests whether they are uncorrelated with the held-out candidate IV; valid IV sets satisfy this zero-correlation condition, and a magnitude ratio of corr(G,Y)/corr(G,X) identifies the causal direction, enabling a cluster-fusion search for valid IV sets.
Key results
- On bi-directional simulations with n=10k, PReBiM achieves CSR of 0.95 (X→Y) and 0.93 (Y→X) in S(2,2,6) with MSE 0.044 and 0.018, outperforming all baselines.
- Baseline TSHT achieves CSR of at most about 0.12 and IV-TETRAD around 0.6 in the same bi-directional settings.
- NAIVE regression MSE stays near 0.3-0.37 regardless of sample size, indicating persistent bias from unmeasured confounding.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PReBiM instead of the comparison methods | Bi-directional MR estimation · Bi-directional MR simulations, all reported sample sizes and IV scenarios | CSR | Helped |
| Use PReBiM instead of the comparison methods | Bi-directional MR estimation · Bi-directional MR simulations, all reported sample sizes and IV scenarios | MSE | Helped |
| Estimate with NAIVE least-squares regression without accounting for unobserved confounding | Bi-directional MR estimation · Bi-directional MR simulations | MSE | Hurt |
| Estimate MR-Egger using all instrumental variables | Bi-directional MR estimation · Bi-directional MR simulations | MSE | Hurt |
Surprising findings
- Valid IV sets can be identified even when some candidate IVs are correlated with each other in certain subgraphs, suggesting the results partly tolerate dependence among genetic variants.
Limitations
- Assumes genetic variants are mutually independent (randomized); dependence is left to future work.
- Restricted to linear causal relationships.
- Identifiability relies on generic-identifiability and variance-ratio assumptions and infinite-sample limits; finite-sample tests can be unreliable.
Experimental setup
Datasets: synthetic SNP-based simulated data
Benchmarks: synthetic bi-directional MR simulations S(2,2,6), S(3,3,8), S(4,4,10)
Metrics: Correct-Selecting Rate Mean Squared Error
Baselines: NAIVE MR-Egger sisVIVE IV-TETRAD TSHT
Builds on: two-stage least squares MR-Egger sisVIVE IV-TETRAD TSHT
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