{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Biostatistics, University of Iowa, Iowa City, Iowa, USA.",
    "Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Kai Wang",
      "orcid": "0000-0002-3229-9866"
    },
    {
      "affs": [
        1
      ],
      "name": "Grace Z Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mxfgnw36phh9.bib",
  "cited_by": 0,
  "doi": "10.1002/sim.70784",
  "fulltext_url": "https://europepmc.org/articles/PMC13677446",
  "id": "7mxfgnw36phh9",
  "issns": [
    "0277-6715",
    "1097-0258"
  ],
  "landing_url": "https://europepmc.org/article/MED/42893902",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1311|Genetic Associations and Epidemiology"
    ]
  ],
  "openalex": "W7222897981",
  "pdf_url": "https://europepmc.org/articles/PMC13677446?pdf=render",
  "pmcid": "PMC13677446",
  "pmid": "42893902",
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mxfgnw36phh9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:00Z",
      "native_id": "MED:42893902",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42893902"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "openalex:1311|Genetic Associations and Epidemiology",
      "subfield": "genetics-genomics"
    }
  ],
  "title": "Valid Inference for Two Sample Summary Statistics Mendelian Randomization.",
  "title_text": "Valid Inference for Two Sample Summary Statistics Mendelian Randomization.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:19:00Z",
  "url": "https://research.draconitic.com/paper/7mxfgnw36phh9",
  "venue": "Statistics in medicine",
  "versions": []
}