{
  "abstract": "The Bayesian optimal phase II (BOP2) design accommodates simple and complex endpoints but does not address biomarker-guided enrichment or multiplicity control across pooled and subgroup claims. We propose BOP2-ENR, which monitors biomarker-negative (NG) and biomarker-positive (PG) cohorts separately, permits interim enrichment to PG, and calibrates pooled and PG-restricted claims. Strong family-wise error rate (FWER) control is defined over a prespecified monotone-activity parameter space. Under the mixed configuration in which NG is inactive and PG is active, the probability of a false joint claim is bounded by the probability that NG survives futility monitoring. This exact single-cohort bound does not involve the final efficacy cutoff and also yields a ceiling on joint-claim power. For efficacy-toxicity monitoring, subgroup inactivity is defined by a union null and safety is established separately within each subgroup. Across the scenarios considered and binary, co-primary and efficacy-toxicity endpoints, all selected designs met the prespecified exact-bound and Monte Carlo verification criteria; in sensitivity analyses over odds ratios between component outcomes assumed independent in calibration, point estimates of the error-control quantities remained below the nominal level, although power was association-sensitive. The bound was nearly attained as PG efficacy approached the boundary of the nuisance space, whereas disabling enrichment produced mixed-configuration error rates near one. BOP2-ENR therefore extends the BOP2 framework to adaptive enrichment while clarifying that the NG futility gate governs the mixed-configuration component of strong error control and the attainable power of a joint claim.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38759",
  "author_total": 3,
  "authors": [
    {
      "name": "Kentaro Takeda"
    },
    {
      "name": "Belay B. Yimer"
    },
    {
      "name": "Masahiro Kojima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44jvg56fja87v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38759",
  "fulltext_url": null,
  "id": "44jvg56fja87v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38759",
  "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|Statistical Methods in Clinical Trials"
    ]
  ],
  "openalex": "W7215041045",
  "pdf_url": "https://arxiv.org/pdf/2609.38759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44jvg56fja87v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:58Z",
      "native_id": "2609.38759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "BOP2-ENR: a Bayesian optimal phase II design for adaptive enrichment with family-wise error rate control and a bound on joint-claim power",
  "title_text": "BOP2-ENR: a Bayesian optimal phase II design for adaptive enrichment with family-wise error rate control and a bound on joint-claim power",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/44jvg56fja87v",
  "venue": "arXiv",
  "versions": []
}