{
  "abstract": "Small sample sizes in clinical studies arise from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the normal distribution approximation. In this paper, we employ a quadratic-form-based statistic, from which we derive more accurate confidence intervals, particularly for data with small sample sizes or proportions. Based on the study, we suggest reasonable values of sample sizes and proportions for the application of the quadratic method. Consequently, this method enhances the reliability of statistical inferences. We illustrate this method with real medical data from clinical trials.",
  "abstract_shown": true,
  "affiliations": [
    "University of Chicago Laboratory High School, Chicago, IL, 60637 USA.",
    "School of Data, Mathematical, and Statistical Sciences, College of Sciences, University of Central Florida, Orlando, FL 32816 USA.",
    "Office of Biostatistics Research, Division of Intramural Research, National Heart, Lung, and Blood Institute, NIH, Bethesda, Maryland, USA."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mulan Wu"
    },
    {
      "affs": [
        1
      ],
      "name": "Mengyu Xu"
    },
    {
      "affs": [
        2
      ],
      "name": "Dong-yun Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fgnmw6rvy5c6.bib",
  "cited_by": 0,
  "doi": "10.1007/s42519-026-00579-y",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13730110/",
  "id": "2fgnmw6rvy5c6",
  "issns": [
    "1559-8608",
    "1559-8616"
  ],
  "landing_url": "https://doi.org/10.1007/s42519-026-00579-y",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Article"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7165191185",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s42519-026-00579-y.pdf",
  "pmcid": "PMC13730110",
  "pmid": "42979530",
  "published": "2026-06-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fgnmw6rvy5c6.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:22:44Z",
      "native_id": "PMC13730110",
      "source": "pmc",
      "url": "https://doi.org/10.1007/s42519-026-00579-y"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Probability and Statistical Research",
      "subfield": "statistics"
    }
  ],
  "title": "Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine",
  "title_text": "Confidence Intervals Based on the Modified Chi-Squared Distribution and Its Applications in Medicine",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T12:22:44Z",
  "url": "https://research.draconitic.com/paper/2fgnmw6rvy5c6",
  "venue": "Journal of statistical theory and practice",
  "versions": []
}