Approximation of bias and mean-squared error in two-sample Mendelian randomization analyses.

Area of Science:

• Biostatistics
• Genetic Epidemiology
• Causal Inference

Background:

• Mendelian randomization (MR) employs genetic variants as instrumental variables (IVs) to infer causal relationships between risk factors and outcomes.
• Traditional MR analyses often assume a one-sample setting, where all data are available from a single cohort.
• Modern MR commonly utilizes a two-sample setting, combining data from independent or partially overlapping genetic association studies.

Purpose of the Study:

• To investigate the performance of two-stage least squares (2SLS) in two-sample MR when genetic variants (IVs) have weak associations with the risk factor.
• To derive analytical formulas for bias and mean squared error (MSE) of the 2SLS estimator in this scenario.
• To compare the one-sample and two-sample MR settings and evaluate the effect of sample overlap.

Main Methods:

• Derivation of closed-form formulas for bias and MSE of the 2SLS estimator in two-sample MR with weak instruments.
• Validation of derived formulas through numerical simulations under realistic conditions.
• Development and validation of a bias-corrected estimator for causal effects.

Main Results:

• Analytical formulas quantify the bias and MSE of 2SLS in two-sample MR with weak instruments.
• The study elucidates the trade-offs between one-sample and two-sample MR settings.
• The proposed bias-corrected estimator demonstrates improved accuracy in estimating causal effects.

Conclusions:

• Two-stage least squares (2SLS) in two-sample Mendelian randomization (MR) is susceptible to bias when using weak instruments.
• Understanding the impact of sample overlap is crucial for accurate causal inference in MR.
• The developed bias-corrected estimator offers a more reliable approach for estimating causal effects in two-sample MR settings.