{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T12:02:06Z","timestamp":1784894526045,"version":"3.55.0"},"reference-count":24,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T00:00:00Z","timestamp":1781827200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T00:00:00Z","timestamp":1781827200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Pharmaceutical Statistics"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    Accurately distinguishing between healthy and diseased states is fundamental to clinical diagnostics. This paper introduces the Harmonic Fowlkes\u2010Mallows (\n                    <jats:italic>HFM<\/jats:italic>\n                    ) index, a novel and robust metric for assessing diagnostic accuracy and identifying optimal cut\u2010off points. The proposed\n                    <jats:italic>HFM<\/jats:italic>\n                    index integrates performance across both positive and negative classes by combining the traditional Fowlkes\u2010Mallows Index (\n                    <jats:italic>FM<\/jats:italic>\n                    ) with the proposed Negative Fowlkes\u2010Mallows Index (\n                    <jats:italic>NFM<\/jats:italic>\n                    ), using a weighted harmonic mean. Unlike conventional measures such as the F1\u2010score or Youden Index,\n                    <jats:italic>HFM<\/jats:italic>\n                    provides a more comprehensive evaluation of classification performance by simultaneously addressing sensitivity and specificity. Additionally, it incorporates a tunable\n                    <jats:italic>\u03b2<\/jats:italic>\n                    parameter to adjust for asymmetries in class importance. Through simulation studies, the\n                    <jats:italic>HFM<\/jats:italic>\n                    index demonstrates strong performance in binary classification tasks and proves effective in selecting optimal decision thresholds. To further demonstrate its practical utility, we apply the HFM index to real\u2010world breast cancer data and compare its performance with other diagnostic accuracy measures.\n                  <\/jats:p>","DOI":"10.1002\/pst.70104","type":"journal-article","created":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T04:27:19Z","timestamp":1781929639000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Harmonic Fowlkes\u2010Mallows Index for Medical Diagnostics Tests and Optimal Cut\u2010Off Point Selection of Binary Diseases"],"prefix":"10.1002","volume":"25","author":[{"given":"Parthkumar","family":"Rabari","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Environmental Health Sciences Jiann\u2010Ping Hsu College of Public Health, Georgia Southern University  Statesboro Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-5471-5551","authenticated-orcid":false,"given":"Purbasha","family":"Biswas","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Environmental Health Sciences Jiann\u2010Ping Hsu College of Public Health, Georgia Southern University  Statesboro Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7256-3978","authenticated-orcid":false,"given":"Jing X.","family":"Kersey","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Environmental Health Sciences Jiann\u2010Ping Hsu College of Public Health, Georgia Southern University  Statesboro Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3817-2249","authenticated-orcid":false,"given":"Hani","family":"Samawi","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Environmental Health Sciences Jiann\u2010Ping Hsu College of Public Health, Georgia Southern University  Statesboro Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,6,19]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198509844.001.0001"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470906514"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.2166"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.70016"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.2322"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.2413"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1093\/clinchem\/39.4.561"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1080\/10543406.2023.2169928"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/2288117"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-44892-y"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45167-9_14"},{"issue":"5","key":"e_1_2_12_14_1","first-page":"2942","article-title":"Determining the Quality of a Dataset in Clustering Terms Appl","volume":"13","author":"Rachwa\u0142 A.","year":"2023","journal-title":"Sciences"},{"key":"e_1_2_12_15_1","unstructured":"S. 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