{
  "abstract": "Cluster randomized trials (CRTs) can exhibit informative cluster sizes (ICS) where cluster size is associated with outcomes and/or treatment effects. Under ICS, the individual and cluster-average treatment effects (iATE, cATE) can diverge, and the conventional linear mixed-effects model (LMM) and generalized estimating equation (GEE) with an exchangeable working correlation can produce data-dependent weighted contrasts that are not consistent for either estimand. In these settings with ICS, we propose easy to implement \"cluster-size saturated models with g-computation\" (CS-g), which employ a simple two-step adjustment to standard practice: (1.) augment the appropriately weighted working LMM or GEE with a saturated continuous cluster-size main effect and treatment x cluster-size interaction, and (2.) apply g-computation to target an interpretable marginal estimand. We prove that the appropriately weighted cluster-size saturated LMM with g-computation and more general cluster-size saturated GEE with g-computation can consistently target the iATE and cATE, among a broad class of interpretable estimands, while allowing for ICS. Crucially, this consistency holds under arbitrary misspecification of other model components, including the functional form of the saturated cluster-size terms. Furthermore, we demonstrate exact finite-sample equivalence between these consistent CS-g estimators and their model-robust standardization counterparts. Across simulations with continuous and binary outcomes, the proposed CS-g estimators were unbiased, more efficient than other consistent estimators, and returned greater power to detect ICS. A re-analysis of the PPACT P-CRT further illustrates the approach. Altogether, CS-g offers a simple, robust, and efficient route to target interpretable marginal effects in P-CRTs with ICS.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28943",
  "author_total": 3,
  "authors": [
    {
      "name": "Kenneth M. Lee"
    },
    {
      "name": "Michael O. Harhay"
    },
    {
      "name": "Fan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68tzrj0ts1kmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28943",
  "fulltext_url": null,
  "id": "68tzrj0ts1kmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28943",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7204927733",
  "pdf_url": "https://arxiv.org/pdf/2608.28943",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68tzrj0ts1kmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "2608.28943",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28943"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Saturation in G: simple & robust causal inference in cluster randomized trials with informative cluster sizes",
  "title_text": "Saturation in G: simple & robust causal inference in cluster randomized trials with informative cluster sizes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/68tzrj0ts1kmj",
  "venue": "arXiv",
  "versions": []
}