Bias and mean squared error in Mendelian randomization with invalid instrumental variables

Area of Science:

• Genetics
• Epidemiology
• Biostatistics

Background:

• Mendelian randomization (MR) is a popular causal inference method using genetic variants as instrumental variables (IVs).
• MR relies on numerous single nucleotide polymorphisms (SNPs) as IVs for statistical power, but invalid IVs can bias results.
• Invalid IVs, due to pleiotropy or confounding, inflate the mean squared error (MSE) of causal effect estimates.

Purpose of the Study:

• To derive formulas for bias and MSE in two-stage least squares (2SLS) MR when using invalid IVs.
• To identify conditions for unbiased 2SLS estimates and analyze the impact of pleiotropic effects on accuracy and precision.
• To validate derived formulas via simulations and apply them to a real-world MR study.

Main Methods:

• Derivation of analytical formulas for bias and MSE of 2SLS estimates with invalid IVs.
• Extensive simulation studies to validate the derived formulas under various scenarios.
• Application of the formulas in a Mendelian randomization study investigating the causal effect of waist-to-hip ratio on sleep patterns.

Main Results:

• Formulas quantifying bias and MSE for 2SLS in the presence of invalid IVs were derived.
• Conditions for unbiased 2SLS estimates were identified, clarifying the influence of pleiotropic effects.
• Simulation studies confirmed the accuracy of the derived formulas, and the application demonstrated their utility in a real-world MR analysis.

Conclusions:

• The derived formulas provide a theoretical framework for understanding bias and precision in 2SLS MR with invalid IVs.
• These results aid in designing more robust MR studies and offer benchmarks for evaluating advanced MR methodologies.
• The study enhances the reliability of causal inference in genetic epidemiology by addressing the challenge of invalid instrumental variables.