{
  "abstract": "In longitudinal studies, repeated treatments may be followed by different sequences of mediators and time-varying covariates. We develop semiparametric inference for path-specific effects in this setting, allowing the number, type, and ordering of intermediate variables to vary across treatment occasions. Under consistency, positivity, edge consistency, and the cross-world restrictions of a nonparametric structural equation model with independent errors, path-specific means are identified by the edge g-formula. We derive two parameterizations of the efficient influence function of the identifying functional. The first follows the observed-data factorization and uses conditional intermediate-variable densities. The second uses sequential regressions to replace the corresponding integrations and Bayes' rule to express density ratios through treatment-history regressions, thereby avoiding direct estimation of intermediate-variable densities. Each yields a one-step estimator that permits flexible nuisance estimation. We establish product-rate conditions for asymptotic linearity and semiparametric efficiency. The density-based estimator has blockwise multiple robustness, generalizing triply robust estimation, while the regression-based estimator has sequential multiple robustness. We further develop a sensitivity analysis for selected violations of cross-world independence assumptions used to identify these effects. Simulations examine finite-sample performance and robustness to model misspecifications. An application to the Framingham Heart Study examines sustained-smoking effects on systolic blood pressure along pathways through repeated body mass index measurements. The proposed methods are implemented in the R package flexPaths on Gihub at xxou/flexPaths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34349",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaxian Ou"
    },
    {
      "name": "Xinwei He"
    },
    {
      "name": "Razieh Nabi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5w9w4wafjsmds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34349",
  "fulltext_url": null,
  "id": "5w9w4wafjsmds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34349",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7223987908",
  "pdf_url": "https://arxiv.org/pdf/2610.34349",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5w9w4wafjsmds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34349",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34349"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Inference for Causal Path-Specific Effects in Longitudinal Studies with Repeated Treatments and Multiple Mediators",
  "title_text": "Inference for Causal Path-Specific Effects in Longitudinal Studies with Repeated Treatments and Multiple Mediators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/5w9w4wafjsmds",
  "venue": "arXiv",
  "versions": []
}