Valid Inference for Two Sample Summary Statistics Mendelian Randomization.
- 1Department of Biostatistics, University of Iowa, Iowa City, Iowa, USA.
- 2Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA.
Abstract
Mendelian randomization (MR) studies increasingly rely on summary statistics from genome-wide association studies (GWASs). However, current summary-data methods treat marginal GWAS effect estimates as independent across instrumental single-nucleotide polymorphisms (SNPs), which holds only when the SNPs have no effect. Without imposing this independence assumption, we derive expressions for the two-stage least squares (TSLS), two-sample TSLS (TSTSLS), and generalized method-of-moments estimators together with their variance estimators using only GWAS summary statistics, assuming the instrumental SNPs are in linkage equilibrium. We show that the widely used inverse-variance weighted (IVW) estimator is generally not equivalent to either TSLS or TSTSLS, contrary to a common claim in the MR literature. We further demonstrate that the conventional IVW standard error is generally inconsistent and provide a consistent alternative. Extensive simulations confirm the theoretical results and reveal that Wald confidence intervals based on summary statistics can be anti-conservative. An application to publicly available GWAS summary statistics on body mass index and systolic blood pressure illustrates the practical implications of the proposed methodology.
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BibTeX
@article{wang2026valid,
title = {{Valid Inference for Two Sample Summary Statistics Mendelian Randomization.}},
author = {Kai Wang and Grace Z Wang},
journal = {Statistics in medicine},
year = {2026},
month = oct,
doi = {10.1002/sim.70784},
url = {https://europepmc.org/article/MED/42893902},
note = {CC BY},
}
RIS
TY - JOUR
TI - Valid Inference for Two Sample Summary Statistics Mendelian Randomization.
AU - Kai Wang
AU - Grace Z Wang
PY - 2026
DA - 2026/10/01
JO - Statistics in medicine
DO - 10.1002/sim.70784
UR - https://europepmc.org/article/MED/42893902
AB - Mendelian randomization (MR) studies increasingly rely on summary statistics from genome-wide association studies (GWASs). However, current summary-data methods treat marginal GWAS effect estimates as independent across instrumental single-nucleotide polymorphisms (SNPs), which holds only when the SNPs have no effect. Without imposing this independence assumption, we derive expressions for the two-stage least squares (TSLS), two-sample TSLS (TSTSLS), and generalized method-of-moments estimators together with their variance estimators using only GWAS summary statistics, assuming the instrumental SNPs are in linkage equilibrium. We show that the widely used inverse-variance weighted (IVW) estimator is generally not equivalent to either TSLS or TSTSLS, contrary to a common claim in the MR literature. We further demonstrate that the conventional IVW standard error is generally inconsistent and provide a consistent alternative. Extensive simulations confirm the theoretical results and reveal that Wald confidence intervals based on summary statistics can be anti-conservative. An application to publicly available GWAS summary statistics on body mass index and systolic blood pressure illustrates the practical implications of the proposed methodology.
SN - 0277-6715
SN - 1097-0258
ER -