{
  "abstract": "Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such semi-continuous exposures, together with a two-stage estimation strategy. A two-part propensity structure is introduced for the semi-continuous exposure, with one component for exposure status (exposed vs unexposed) and another for the exposure level among those exposed, and incorporates both into a marginal structural model that disentangles the effects of exposure status and dose. The two-stage procedure sequentially targets the causal dose-response among exposed individuals and the causal effect of exposure status at a reference dose, allowing flexibility in the choice of propensity score methods in the second stage. We establish consistency and asymptotic normality for the resulting estimators, and characterize their limiting values under misspecification of the propensity score models. Simulation studies evaluate finite sample performance and robustness, and an application to a study of prenatal alcohol exposure and child cognition demonstrates how the proposed methods can be used to address a range of scientific questions about both exposure status and exposure intensity.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada.",
    "Department of Biostatistics, School of Medicine, Ankara University, Ankara, Turkey.",
    "Departments of Emergency Medicine and Pediatrics, Columbia University, New York, New York, USA.",
    "Department of Psychiatry and Behavioral Neurosciences, Wayne State University, Detroit, Michigan, USA.",
    "School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales, Australia."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 8,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xiaoya Wang",
      "orcid": "0009-0001-2759-5652"
    },
    {
      "affs": [
        0
      ],
      "name": "Richard J Cook",
      "orcid": "0000-0002-1414-4908"
    },
    {
      "affs": [
        0
      ],
      "name": "Yeying Zhu",
      "orcid": "0000-0002-9019-9716"
    },
    {
      "affs": [
        1
      ],
      "name": "Tugba Akkaya-Hocagil",
      "orcid": "0000-0003-3603-4491"
    },
    {
      "affs": [
        2
      ],
      "name": "R Colin Carter",
      "orcid": "0000-0003-1554-6914"
    },
    {
      "affs": [
        3
      ],
      "name": "Sandra W Jacobson"
    },
    {
      "affs": [
        3
      ],
      "name": "Joseph L Jacobson",
      "orcid": "0000-0001-8271-280X"
    },
    {
      "affs": [
        4
      ],
      "name": "Louise M Ryan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0tqg9zb20dd5n.bib",
  "cited_by": 0,
  "doi": "10.1002/sim.70800",
  "fulltext_url": "https://europepmc.org/articles/PMC13716696",
  "id": "0tqg9zb20dd5n",
  "issns": [
    "0277-6715",
    "1097-0258"
  ],
  "landing_url": "https://europepmc.org/article/MED/42951587",
  "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": [
    [
      "heading",
      "Research Article"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7224091023",
  "pdf_url": "https://europepmc.org/articles/PMC13716696?pdf=render",
  "pmcid": "PMC13716696",
  "pmid": "42951587",
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0tqg9zb20dd5n.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T00:20:33Z",
      "native_id": "MED:42951587",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42951587"
    },
    {
      "first_seen": "2026-11-01T12:23:55Z",
      "native_id": "PMC13716696",
      "source": "pmc",
      "url": "https://doi.org/10.1002/sim.70800"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Advanced Causal Inference Techniques",
      "subfield": "statistics"
    }
  ],
  "title": "Two-Stage Estimation for Causal Inference Involving Semi-Continuous Exposures.",
  "title_text": "Two-Stage Estimation for Causal Inference Involving Semi-Continuous Exposures.",
  "type": "peer-reviewed",
  "updated_at": "2026-11-02T12:21:09Z",
  "url": "https://research.draconitic.com/paper/0tqg9zb20dd5n",
  "venue": "Statistics in medicine",
  "versions": []
}