Reappraising the role of instrumental inequalities for mendelian randomization studies in the mega Biobank era

• Objective: This commentary discusses the increasing relevance and power of instrumental inequalities (IIs)—mathematical constraints derived from the core assumptions of Instrumental Variables (IV)—as a tool for detecting bias in Mendelian Randomization (MR) studies using large-scale Biobank data.
• Instrumental Inequalities: IIs are a set of conditions that must be satisfied if the IV assumptions hold true. If the data violates these inequalities, it proves the instruments are invalid.
• Role in Mega-Biobanks: The authors argue that the large sample sizes of modern Biobanks provide the necessary statistical power to accurately detect subtle violations of the inequalities, making this tool highly effective for falsifying the validity of genetic instruments.
• Recommendation: IIs should be used as a complementary, stringent test alongside standard MR sensitivity analyses to enhance the statistical rigor of causal inference.

reviewing

PubMed: 37634227 DOI: 10.1007/s10654-023-01035-y Overview generated by: Gemini 2.5 Flash, 28/11/2025

Key Findings: Reappraisal of Instrumental Inequalities in MR

This commentary discusses the role and utility of instrumental inequalities (IIs)—a set of mathematical conditions that must hold true if the core Instrumental Variable (IV) assumptions of Mendelian Randomization (MR) are satisfied—especially in the context of the large datasets available in the “mega Biobank era.”

• Instrumental Inequalities as a Falsification Tool: Instrumental inequalities provide a valuable test of the validity of the instrumental variable (IV) assumptions. If the data violate the instrumental inequalities, it logically implies that at least one of the core IV assumptions is not met, and the instruments are therefore invalid.
• Increased Utility in Large Biobanks: The authors argue that the use of instrumental inequalities has become more relevant and powerful in the era of mega-Biobanks (like the UK Biobank), due to the massive increase in sample size.
  • Statistical Power: Large datasets provide the necessary statistical power to detect small violations of the inequalities, which may be missed in smaller studies. Detecting a violation strengthens the case for rejecting the IV assumptions.
• Limitations and Interpretation: The authors emphasize that while violating the inequalities proves the invalidity of the instruments, satisfying the inequalities does not prove validity (similar to how satisfying sensitivity analyses doesn’t guarantee the MR assumptions are met). However, IIs provide a unique way to flag potentially unreliable instruments.
• Complementary to Existing MR Methods: Instrumental inequalities should be viewed as a complementary tool to existing MR sensitivity analyses (like MR-Egger or MR-PRESSO). They offer an alternative perspective on bias detection, specifically testing the logical consequences of the IV assumptions themselves.

Study Design and Methods (Commentary)

This paper is a Commentary and does not report new empirical data but rather provides a methodological perspective on the role of existing statistical tools in modern genetic epidemiology.

Core Concepts

• MR Assumptions: MR relies on three core Instrumental Variable (IV) assumptions :
  1. Relevance: The genetic instrument (\(G\)) is associated with the exposure (\(X\)).
  2. Exclusion Restriction: The instrument affects the outcome (\(Y\)) only through the exposure (\(X\)).
  3. No Confounding: The instrument (\(G\)) is independent of all confounders of the exposure-outcome relationship.
• Instrumental Inequalities: Instrumental inequalities are a set of mathematical constraints on the observable correlations (or effects) between \(G\), \(X\), and \(Y\) that must be satisfied if the three IV assumptions hold true. Violation of these constraints is a definitive way to demonstrate that the IV assumptions are false.

Relevance in Mega-Biobanks

The commentary highlights that the ability to test IIs hinges on the power to accurately measure the associations between the instrument and the exposure, the instrument and the outcome, and the exposure and the outcome, which is significantly enhanced by the large sample sizes of modern Biobanks.

Conclusions and Recommendations

The authors recommend that researchers working with large datasets should reappraise and routinely incorporate the testing of instrumental inequalities into their Mendelian Randomization analyses.

• Enhanced Rigor: Testing instrumental inequalities adds a layer of statistical rigor by providing a formal test for falsifying the fundamental assumptions upon which MR is built.
• Cautionary Note: The authors caution that since IIs rely on observed data, a failure to reject the inequalities is not proof of instrument validity, and therefore, they should not replace robust sensitivity analyses. They are best used as an initial filter or a final check on the proposed instruments.