{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T09:06:39Z","timestamp":1773738399225,"version":"3.50.1"},"reference-count":17,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Multi-stage models for cohort data are popular statistical models in several fields such as disease progressions, biological development of plants and animals, and laboratory studies of life cycle development.\nA Bayesian approach on adopting deterministic transformations in the Metropolis\u2013Hastings (MH) algorithm was used to estimate parameters for these stage structured models.\nHowever, the biases in later stages are limitations of this methodology, especially the accuracy of estimates for the models having more than three stages.\nThe main aim of this paper is to reduce these biases in parameter estimation.\nIn particular, we conjoin insignificant previous stages or negligible later stages to estimate parameters of a desired stage, while an adjusted MH algorithm based on deterministic transformations is applied for the non-hazard rate models.\nThis means that current stage parameters are estimated separately from the information of its later stages.\nThis proposed method is validated in simulation studies and applied for a case study of the incubation period of COVID-19.\nThe results show that the proposed methods could reduce the biases in later stages for estimates in stage structured models, and the results of the case study can be regarded as a valuable continuation of pandemic prevention.<\/jats:p>","DOI":"10.1515\/mcma-2024-2001","type":"journal-article","created":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T19:10:52Z","timestamp":1706641852000},"page":"205-216","source":"Crossref","is-referenced-by-count":1,"title":["On bias reduction in parametric estimation in stage structured development models"],"prefix":"10.1515","volume":"30","author":[{"given":"Hoa","family":"Pham","sequence":"first","affiliation":[{"name":"Mathematical Department , An Giang University , Long Xuy\u00ean ; and Vietnam National University, Ho Chi Minh City , Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huong T.\u2009T.","family":"Pham","sequence":"additional","affiliation":[{"name":"Mathematical Department , An Giang University , Long Xuy\u00ean ; and Vietnam National University, Ho Chi Minh City , Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai Siong","family":"Yow","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , Faculty of Science , Universiti Putra Malaysia , UPM Serdang , Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"2024052809495401950_j_mcma-2024-2001_ref_001","doi-asserted-by":"crossref","unstructured":"J. A. Backer, D. Klinkenberg and W. Jacco,\nIncubation period of 2019 novel coronavirus (2019-ncov) infections among travellers from Wuhan,\nEuro Surveill. 25 (2020), no. 5, Article ID 2000062.","DOI":"10.2807\/1560-7917.ES.2020.25.5.2000062"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_002","doi-asserted-by":"crossref","unstructured":"S. Brooks, A. Gelman, G. L. Jones and X.-L. Meng\nHandbook of Markov Chain Monte Carlo,\nChapman & Hall\/CRC Handb. Mod. Stat. Methods,\nCRC Press, Boca Raton, 2011.","DOI":"10.1201\/b10905"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_003","doi-asserted-by":"crossref","unstructured":"P. de Valpine and J. Knape,\nEstimation of general multistage models from cohort data,\nJ. Agric. Biol. Environ. Stat. 20 (2015), no. 1, 140\u2013155.","DOI":"10.1007\/s13253-014-0189-7"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_004","doi-asserted-by":"crossref","unstructured":"K. Goel and A. Kumar,\nNonlinear dynamics of a time-delayed epidemic model with two explicit aware classes, saturated incidences, and treatment,\nNonlinear Dyn. 101 (2020), 1693\u20131715.","DOI":"10.1007\/s11071-020-05762-9"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_005","doi-asserted-by":"crossref","unstructured":"J. A. Hoeting, R. L. Tweedie and C. S. Olver,\nTransform estimation of parameters for stage-frequency data,\nJ. Amer. Statist. Assoc. 98 (2003), no. 463, 503\u2013514.","DOI":"10.1198\/016214503000000288"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_006","doi-asserted-by":"crossref","unstructured":"J. Knape, K. M. Daane and P. De Valpine,\nEstimation of stage duration distributions and mortality under repeated cohort censuses,\nBiometrics 70 (2014), no. 2, 346\u2013355.","DOI":"10.1111\/biom.12138"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_007","doi-asserted-by":"crossref","unstructured":"J. Knape and P. De Valpine,\nMonte Carlo estimation of stage structured development from cohort data,\nEcology 97 (2016), no. 4, 992\u20131002.","DOI":"10.1890\/15-0942.1"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_008","doi-asserted-by":"crossref","unstructured":"H. Pham and A. Branford,\nExploring parameter relations for multi-stage models in stage-wise constant and time dependent hazard rates,\nAust. N. Z. J. Stat. 58 (2016), no. 3, 357\u2013376.","DOI":"10.1111\/anzs.12164"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_009","doi-asserted-by":"crossref","unstructured":"H. Pham, D. Nur, H. T. T. Pham and A. Branford,\nA Bayesian approach for parameter estimation in multi-stage models,\nComm. Statist. Theory Methods 48 (2019), no. 10, 2459\u20132482.","DOI":"10.1080\/03610926.2018.1465090"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_010","doi-asserted-by":"crossref","unstructured":"H. Pham and H. T. T. Pham,\nA Bayesian approach for multi-stage models with linear time-dependent hazard rate,\nMonte Carlo Methods Appl. 25 (2019), no. 4, 307\u2013316.","DOI":"10.1515\/mcma-2019-2051"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_011","unstructured":"M. Qiu, T. Hu and H. Cui,\nParametric estimation for the incubation period distribution of COVID-19 under doubly interval censoring,\nActa Math. Appl. Sin. 43 (2020), no. 2, 200\u2013210."},{"key":"2024052809495401950_j_mcma-2024-2001_ref_012","doi-asserted-by":"crossref","unstructured":"B. Rai, A. Shukla and L. Dwivedi,\nIncubation period for covid-19: A systematic review and meta-analysis,\nJ. Public Health 30 (2021), 1\u20138.","DOI":"10.1007\/s10389-021-01478-1"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_013","doi-asserted-by":"crossref","unstructured":"K. L. Q. Read and J. R. Ashford,\nA system of models for the life cycle of a biological organism,\nBiometrika 55 (1968), no. 1, 211\u2013221.","DOI":"10.1093\/biomet\/55.1.211"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_014","doi-asserted-by":"crossref","unstructured":"C. P. Robert and G. Casella,\nIntroducing Monte Carlo Methods with R,\nSpringer, New York, 2010.","DOI":"10.1007\/978-1-4419-1576-4"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_015","doi-asserted-by":"crossref","unstructured":"H.-J. Schuh and R. L. Tweedie,\nParameter estimation using transform estimation in time-evolving models,\nMath. Biosci. 45 (1979), no. 1\u20132, 37\u201367.","DOI":"10.1016\/0025-5564(79)90095-6"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_016","doi-asserted-by":"crossref","unstructured":"Y. Wang, Zh. Wei and J. Cao,\nEpidemic dynamics of influenza-like diseases spreading in complex networks,\nNonlinear Dyn. 101 (2020), 1801\u20131820.","DOI":"10.1007\/s11071-020-05867-1"},{"key":"2024052809495401950_j_mcma-2024-2001_ref_017","doi-asserted-by":"crossref","unstructured":"M. Z. Yin, Q. W. Zhu and X. Lu,\nParameter estimation of the incubation period of covid-19 based on the doubly interval-censored data model,\nNonlinear Dyn. 106 (2021), no. 2, 1347\u20131358.","DOI":"10.1007\/s11071-021-06587-w"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2001\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2001\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T09:51:10Z","timestamp":1716889870000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2001\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,31]]},"references-count":17,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,10,24]]},"published-print":{"date-parts":[[2024,6,1]]}},"alternative-id":["10.1515\/mcma-2024-2001"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2001","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,31]]}}}