{
  "abstract": "Large-scale molecular datasets have become increasingly important in bioinformatics, providing a foundation for prognostic modeling and the identification of biologically relevant genes. In survival analysis, however, censored observations and the high-dimensional nature of genomic data pose significant challenges for reliable prediction and variable selection. To address these challenges, we develop a Penalized Hierarchical Bayesian Cox (PHBC) modeling framework that extends hierarchical shrinkage and global–local prior formulations using Adaptive Gaussian Priors (AGP) and a modified Global–Local Gaussian–Inverse-Gamma Hyperprior (Gaussian–IGH) structure. The framework consists of two hierarchical components: (i) Adaptive Gaussian priors assigned to regression coefficients, with coefficient-specific variances updated from the data through an empirical-Bayes rule, and (ii) Inverse-Gamma hyperpriors on variance components to provide flexible and adaptive shrinkage. Inference is based on the Cox partial likelihood, yielding a partial-likelihood (pseudo-Bayesian) posterior. We derive the corresponding posterior kernels and construct scalable variational inference approximations, resulting in two computationally efficient procedures: AGP-VI and Global–Local Gaussian–IGH-VI. The methods are evaluated through extensive simulation studies and applications to six low- and high-dimensional genomic survival datasets. Performance is assessed using the concordance index (C-index), Integrated Brier Score, time-dependent AUC, and true/false positive rates for variable selection. A dedicated simulation study further examines sensitivity to multicollinearity under weak, moderate, and high predictor correlations, with the proposed methods remaining competitive across the different correlation levels. Across the real-data applications, no single method uniformly dominated all predictive criteria. The proposed variational methods showed strong but dataset-dependent performance, with Global–Local Gaussian–IGH-VI achieving the best overall predictive performance on one dataset and the best C-index on another, while AGP-VI achieved the best discrimination on two others. Classical penalized and Bayesian Cox approaches remained competitive, particularly in calibration. These results demonstrate the complementary strengths and trade-offs of the proposed methods in high-dimensional genomic survival analysis.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, Kwara State University, Malete, P.M.B. 1530, Ilorin 23431, Kwara State, Nigeria",
    "Department of Mathematics, University of Bergen, 5007 Bergen, Norway"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Bulus I. Doroh"
    },
    {
      "affs": [
        1
      ],
      "name": "Kazeem A. Dauda",
      "orcid": "0000-0002-4392-8592"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ef1zh4hfsf484.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203763",
  "fulltext_url": null,
  "id": "ef1zh4hfsf484",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3763",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7222712612",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/ef1zh4hfsf484.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203763",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3763"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Methods and Inference",
      "subfield": "statistics"
    }
  ],
  "title": "A Hierarchical Bayesian Cox Model with Variational Inference for High-Dimensional Survival Analysis",
  "title_text": "A Hierarchical Bayesian Cox Model with Variational Inference for High-Dimensional Survival Analysis",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/ef1zh4hfsf484",
  "venue": "Mathematics",
  "versions": []
}