{
  "abstract": "Competing-risk cure models describe time-to-event populations with individuals immune to all event types or an event of interest, yet literature is fragmented across model families. We review 26 papers across five axes: cure definition/scope; decomposition/cure mechanism; latency; dependence, censoring, and masked causes; and estimation. We distinguish global from cause-specific cure and incidence--latency mixtures from vertical susceptibility factorizations, latent competing-causes/zero-count constructions, defective-survival models, and zero-inflated mixture or cumulative incidence function (CIF) formulations. We compare parametric, piecewise-constant, PH, AFT, transformation, CIF-based, nonparametric, and partially specified latency models for right/interval censoring, clustering, and masked causes. Mixture formulations dominate, but similar names can mask different estimands, cure mechanisms, latent-risk/censoring assumptions, and regression interpretations. Latent-failure dependence is modeled less often than cure or latency; failure--censoring dependence, within-cluster association, and masked causes occur in smaller subsets. Estimation spans likelihood and expectation-maximization (EM), including neural-network M-steps, estimating equations, inverse-probability-of-censoring weighting, Bayesian computation, and copula-graphic estimation. A reproducible defective-Gompertz analysis of public bone-marrow-transplant data shows that fitted tail probabilities require model- and endpoint-specific interpretation, not all-method comparison. Reproducibility remains limited: most implementations use custom code, few offer repository access, and no widely adopted, clearly licensed R/Python framework unifies the constructions. This taxonomy supports transparent model selection/reporting, estimation-method comparison, and needs for theory, software, benchmarking, and reproducible applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15455",
  "author_total": 1,
  "authors": [
    {
      "name": "Nilotpal Sanyal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3cdw1ngtcmad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15455",
  "fulltext_url": null,
  "id": "b3cdw1ngtcmad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15455",
  "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 Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7203708700",
  "pdf_url": "https://arxiv.org/pdf/2608.15455",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3cdw1ngtcmad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:10Z",
      "native_id": "2608.15455",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15455"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Competing-Risk Cure Models: A Comprehensive Systematic Review of Methodological Literature",
  "title_text": "Competing-Risk Cure Models: A Comprehensive Systematic Review of Methodological Literature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:10Z",
  "url": "https://research.draconitic.com/paper/b3cdw1ngtcmad",
  "venue": "arXiv",
  "versions": []
}