{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T16:40:03Z","timestamp":1792600803576,"version":"4.5.0"},"reference-count":42,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:00:00Z","timestamp":1789516800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:00:00Z","timestamp":1789516800000},"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":["Biometrical J"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Researchers in biomedical research often analyze data that are subject to clustering. Development and validation of risk prediction models generally assumes independence of observations. For survival outcomes, the Cox proportional hazards (PH) regression model is commonly used to estimate an individual's risk at fixed time horizons. The stratified Cox PH and the shared gamma frailty Cox PH regression models are two common approaches to account for the presence of clustering in the data. The relative accuracy of the predictions of these two approaches has not been examined. We conducted a set of Monte Carlo simulations to assess the impact of the number of clusters, the size of the clusters, and the within\u2010cluster correlation in outcomes on the accuracy of the conditional predictions developed using the stratified and the shared gamma frailty Cox PH regression model. We compared the accuracy of the predictions in terms of discrimination, calibration, and overall performance metrics. We found that the stratified and the shared gamma frailty model had similar performance, especially for larger cluster size and higher number of clusters. For small cluster size, we observed slightly better discrimination and overall performance for the stratified model and better calibration for the shared gamma frailty model at shorter prediction horizons. The utility of the stratified Cox PH model for risk prediction is limited, especially for high within\u2010cluster correlation and when clusters are small, and at longer prediction horizons. Our results were accompanied with two applications using open\u2010source data on myelodysplastic syndrome and bladder cancer.<\/jats:p>","DOI":"10.1002\/bimj.70180","type":"journal-article","created":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T12:06:52Z","timestamp":1789560412000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Impact of the Number and the Size of Clusters on Prediction Performance of the Stratified and the Conditional Shared Gamma Frailty Cox Proportional Hazards Models"],"prefix":"10.1002","volume":"68","author":[{"given":"Daniele","family":"Giardiello","sequence":"first","affiliation":[{"name":"Bicocca Bioinformatics Biostatistics and Bioimaging B4 Center School of Medicine and Surgery University of Milano\u2010Bicocca  Monza Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edoardo","family":"Ratti","sequence":"additional","affiliation":[{"name":"Bicocca Bioinformatics Biostatistics and Bioimaging B4 Center School of Medicine and Surgery University of Milano\u2010Bicocca  Monza Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter C.","family":"Austin","sequence":"additional","affiliation":[{"name":"ICES  Toronto Ontario Canada"},{"name":"Institute of Health Policy, Management and Evaluation University of Toronto  Toronto Ontario Canada"},{"name":"Sunnybrook Research Institute  Toronto Ontario Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,16]]},"reference":[{"key":"e_1_2_14_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1972.tb00899.x"},{"key":"e_1_2_14_3_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471\u20102288\u201014\u20103"},{"key":"e_1_2_14_4_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874\u2010023\u201001836\u20105"},{"key":"e_1_2_14_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8570"},{"key":"e_1_2_14_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2059"},{"key":"e_1_2_14_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxy006"},{"key":"e_1_2_14_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7141"},{"key":"e_1_2_14_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.5732"},{"key":"e_1_2_14_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1384"},{"key":"e_1_2_14_11_1","volume-title":"The Frailty Model","author":"Duchateau L.","year":"2008"},{"key":"e_1_2_14_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201900075"},{"key":"e_1_2_14_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/s0140\u20106736(00)02137\u20101"},{"key":"e_1_2_14_14_1","volume-title":"Modelswith Ties to Machine Learning","author":"Gerds T. A.","year":"2022"},{"key":"e_1_2_14_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1599"},{"key":"e_1_2_14_16_1","doi-asserted-by":"publisher","DOI":"10.1182\/blood.V89.6.2079"},{"key":"e_1_2_14_17_1","doi-asserted-by":"publisher","DOI":"10.1182\/blood\u20102012\u201003\u2010420489"},{"key":"e_1_2_14_18_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-19425-7","volume-title":"Regression Model Strategies","author":"Harrell F. E.","year":"2015"},{"key":"e_1_2_14_19_1","doi-asserted-by":"publisher","DOI":"10.1038\/bmt.2008.101"},{"key":"e_1_2_14_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1304-8"},{"key":"e_1_2_14_21_1","doi-asserted-by":"publisher","DOI":"10.1186\/s41512\u2010018\u20100029\u20102"},{"key":"e_1_2_14_22_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1995.10476491"},{"key":"e_1_2_14_23_1","doi-asserted-by":"publisher","DOI":"10.1182\/blood\u20102004\u201010\u20103863"},{"key":"e_1_2_14_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bbmt.2015.03.020"},{"key":"e_1_2_14_25_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41409\u2010019\u20100748\u20101"},{"key":"e_1_2_14_26_1","doi-asserted-by":"publisher","DOI":"10.7326\/M22\u20100844"},{"key":"e_1_2_14_27_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.1612"},{"key":"e_1_2_14_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bbmt.2020.08.003"},{"key":"e_1_2_14_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68639-4"},{"key":"e_1_2_14_30_1","unstructured":"R Core Team.2005.R: A Language and Environment for Statistical Computing.R Foundation for Statistical Computing.https:\/\/www.R\u2010project.org\/."},{"key":"e_1_2_14_31_1","doi-asserted-by":"crossref","DOI":"10.1002\/9781119333784","volume-title":"Individual Participant Data Meta\u2010Analysis: A Handbook for Healthcare Research","author":"Riley R. D.","year":"2021"},{"key":"e_1_2_14_32_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1661"},{"key":"e_1_2_14_33_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119333784"},{"key":"e_1_2_14_34_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471\u20102288\u201014\u2010129"},{"key":"e_1_2_14_35_1","doi-asserted-by":"publisher","DOI":"10.1200\/JCO.2015.65.0515"},{"key":"e_1_2_14_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2015.04.005"},{"key":"e_1_2_14_37_1","doi-asserted-by":"crossref","unstructured":"Steyerberg E. W. A. J.Vickers N. R.Cook et\u00a0al.2010. \u201cAssessing the Performance of Prediction Models: A Framework for Traditional and Novel Measures.\u201dEpidemiology (Cambridge Mass.)21 no.1:128\u2013138.https:\/\/doi.org\/10.1097\/EDE.0b013e3181c30fb2.","DOI":"10.1097\/EDE.0b013e3181c30fb2"},{"key":"e_1_2_14_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eururo.2005.12.031"},{"key":"e_1_2_14_39_1","doi-asserted-by":"publisher","DOI":"10.1198\/1061860031365"},{"key":"e_1_2_14_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3294-8_9"},{"key":"e_1_2_14_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2015.12.005"},{"key":"e_1_2_14_42_1","volume-title":"Frailty Model in Survival Analysis (First)","author":"Wienke A.","year":"2011"},{"key":"e_1_2_14_43_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280216668555"}],"container-title":["Biometrical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70180","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/bimj.70180","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70180","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T15:50:38Z","timestamp":1792597838000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/bimj.70180"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,16]]},"references-count":42,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["10.1002\/bimj.70180"],"URL":"https:\/\/doi.org\/10.1002\/bimj.70180","archive":["Portico"],"relation":{},"ISSN":["0323-3847","1521-4036"],"issn-type":[{"value":"0323-3847","type":"print"},{"value":"1521-4036","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,16]]},"assertion":[{"value":"2026-02-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70180"}}