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Statistics in Medicine
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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PubMed Central
Article . 2025
License: CC BY
Data sources: PubMed Central
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A Modification to Two‐Stage Least Squares With Genetic Applications

Authors: Lei Fang; Wei Pan;

A Modification to Two‐Stage Least Squares With Genetic Applications

Abstract

ABSTRACT Two‐stage least squares (2SLS) is by default applied to infer a putative causal association between an exposure, such as a gene or a protein, with an outcome such as a complex disease or trait, in transcriptome‐ or proteome‐wide association studies (TWAS/PWAS). In a typical two‐sample setting for TWAS/PWAS, the stage 1 sample size is much smaller than that of stage 2. To reduce the resulting attenuation bias and estimation uncertainty in stage 1 and boost the statistical power of the conventional TWAS, we propose a new method, called reverse two‐stage least squares (r2SLS): Instead of imputing a gene's expression (using genetic variants as instrumental variables, IVs) in stage 1 and then testing the association between the imputed expression and the observed outcome in stage 2 in the conventional 2SLS approach, we propose predicting the outcome (using IVs) and testing the association between the predicted outcome and the observed gene expression. Theoretically, we establish that the r2SLS estimator is asymptotically unbiased with a normal distribution. We also show theoretically when 2SLS and r2SLS are asymptotically equivalent and when r2SLS is asymptotically more efficient than 2SLS. We also consider the practical issue of how to select invalid IVs. We use simulations and three real data examples based on the GTEx gene expression data, UKB‐PPP proteomic data, and several GWAS summary datasets to demonstrate some advantages of r2SLS over 2SLS, including possibly better type I error control, higher statistical power and robustness to weak IVs.

Related Organizations
Keywords

Models, Statistical, Sample Size, Humans, Computer Simulation, Least-Squares Analysis, Transcriptome, Research Article, Genome-Wide Association Study

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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