{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T04:13:26Z","timestamp":1772165606722,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Med Res Methodol"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>A variety of methods exist for the analysis of longitudinal data, many of which are characterized with the assumption of fixed visit time points for study individuals. This, however is not always a tenable assumption. Phenomenon that alter subject visit patterns such as adverse events due to investigative treatment administered, travel or any other emergencies may result in unbalanced data and varying individual visit time points. Visit times can be considered informative, because subsequent or current subject outcomes can change or be adapted due to previous subject outcomes.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>In this paper, a Bayesian Bernoulli-Exponential model for analyzing joint binary outcomes and exponentially distributed informative visit times is developed. Via statistical simulations, the influence of controlled variations in visit patterns, prior and sample size schemes on model performance is assessed. As an application example, the proposed model is applied to a Bladder Cancer Recurrence data.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results and conclusions<\/jats:title>\n                    <jats:p>Results from the simulation analysis indicated that the Bayesian Bernoulli-Exponential joint model converged in stationarity, and performed relatively better for small to medium sample size scenarios with less varying time sequences regardless of the choice of prior. In larger samples, the model performed better for less varying time sequences. This model\u2019s application to the bladder cancer data showed a statistically significant effect of prior tumor recurrence on the probability of subsequent recurrences.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12874-024-02160-2","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T01:03:07Z","timestamp":1709254987000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bayesian Bernoulli-Exponential joint model for binary longitudinal outcomes and informative time with applications to bladder cancer recurrence data"],"prefix":"10.1186","volume":"24","author":[{"given":"Michael\u00a0Safo","family":"Oduro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"2160_CR1","doi-asserted-by":"crossref","unstructured":"Fitzmaurice GM, Laird NM, Ware JH. Applied longitudinal analysis. Wiley;\u00a02012.","DOI":"10.1002\/9781119513469"},{"key":"2160_CR2","unstructured":"Molenberghs G, Verbeke G. Models for discrete longitudinal data.\u00a02005."},{"key":"2160_CR3","doi-asserted-by":"crossref","unstructured":"Rizopoulos D. Joint models for longitudinal and time-to-event data: With applications in R. CRC Press; 2012.","DOI":"10.1201\/b12208"},{"key":"2160_CR4","doi-asserted-by":"crossref","unstructured":"Twisk JW. Applied longitudinal data analysis for epidemiology: a practical guide. Cambridge University Press; 2013.","DOI":"10.1017\/CBO9781139342834"},{"key":"2160_CR5","doi-asserted-by":"crossref","unstructured":"Verbeke G. Linear mixed models for longitudinal data. In: Linear mixed models in practice. Springer; 1997. p. 63\u2013153.","DOI":"10.1007\/978-1-4612-2294-1_3"},{"key":"2160_CR6","unstructured":"Bronsert MR. A joint model of a longitudinal process and informative time schedule data. University of Northern Colorado; 2009."},{"key":"2160_CR7","unstructured":"Alomair MA. A Joint Model of Longitudinal Data and Informative Time with Time-Dependent Covariate. University of Northern Colorado; 2017."},{"key":"2160_CR8","unstructured":"Seo J. Joint Models of Longitudinal Outcomes and Informative Time. 2015."},{"key":"2160_CR9","unstructured":"Zaagan AAA. Bayesian Approach of Joint Models of Longitudinal Outcomes and Informative Time. University of Northern Colorado; 2020."},{"key":"2160_CR10","doi-asserted-by":"crossref","unstructured":"Byar D. The veterans administration study of chemoprophylaxis for recurrent stage i bladder tumours: comparisons of placebo, pyridoxine and topical thiotepa. In: Bladder tumors and other topics in urological oncology. Springer; 1980. p. 363\u2013370.","DOI":"10.1007\/978-1-4613-3030-1_74"},{"key":"2160_CR11","doi-asserted-by":"crossref","unstructured":"Byar D, Blackard C, Veterans\u00a0Administration\u00a0Cooperative\u00a0Urological\u00a0Research\u00a0Group, et\u00a0al. Comparisons of placebo, pyridoxine, and topical thiotepa in preventing recurrence of stage I bladder cancer. Urology. 1977;10(6):556\u2013561.","DOI":"10.1016\/0090-4295(77)90101-7"},{"issue":"3","key":"2160_CR12","first-page":"370","volume":"135","author":"JA Nelder","year":"1972","unstructured":"Nelder JA, Wedderburn RW. Generalized linear models. J R Stat Soc: Ser A (General). 1972;135(3):370\u201384.","journal-title":"J R Stat Soc: Ser A (General)."},{"key":"2160_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3242-6","volume-title":"Generalized linear models","author":"P McCullagh","year":"1989","unstructured":"McCullagh P, Nelder J. Generalized linear models. 2nd ed. London: Chapman & Hall\/CRC; 1989.","edition":"2"},{"key":"2160_CR14","doi-asserted-by":"crossref","unstructured":"Lin, Ying Z. Semiparametric and nonparametric regression analysis of longitudinal data. J Am Stat Assoc. 2001;96(453):103\u2013126.","DOI":"10.1198\/016214501750333018"},{"key":"2160_CR15","doi-asserted-by":"crossref","unstructured":"Lin, Scharfstein DO, Rosenheck RA. Analysis of longitudinal data with irregular, outcome-dependent follow-up. J R Stat Soc Ser B (Stat Methodol). 2004;66(3):791\u2013813.","DOI":"10.1111\/j.1467-9868.2004.b5543.x"},{"key":"2160_CR16","doi-asserted-by":"crossref","unstructured":"Liang, Lu W, Ying Z. Joint modeling and analysis of longitudinal data with informative observation times. Biometrics. 2009;65(2):377\u2013384.","DOI":"10.1111\/j.1541-0420.2008.01104.x"},{"issue":"471","key":"2160_CR17","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1198\/016214505000000060","volume":"100","author":"J Sun","year":"2005","unstructured":"Sun J, Park DH, Sun L, Zhao X. Semiparametric regression analysis of longitudinal data with informative observation times. J Am Stat Assoc. 2005;100(471):882\u20139.","journal-title":"J Am Stat Assoc."},{"key":"2160_CR18","doi-asserted-by":"crossref","unstructured":"Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis Chapman & Hall. CRC Texts in Statistical Science; 2004.","DOI":"10.1201\/9780429258480"},{"key":"2160_CR19","doi-asserted-by":"crossref","unstructured":"Lesaffre E, Lawson AB. Bayesian biostatistics. Wiley; 2012.","DOI":"10.1002\/9781119942412"},{"issue":"4","key":"2160_CR20","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1111\/j.1365-2664.2009.01671.x","volume":"46","author":"JV Murray","year":"2009","unstructured":"Murray JV, Goldizen AW, O\u2019Leary RA, McAlpine CA, Possingham HP, Choy SL. How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabies Petrogale penicillata. J Appl Ecol. 2009;46(4):842\u201351.","journal-title":"J Appl Ecol."},{"issue":"1","key":"2160_CR21","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1111\/j.1523-1739.2011.01806.x","volume":"26","author":"TG Martin","year":"2012","unstructured":"Martin TG, Burgman MA, Fidler F, Kuhnert PM, Low-Choy S, McBride M, et al. Eliciting expert knowledge in conservation science. Conserv Biol. 2012;26(1):29\u201338.","journal-title":"Conserv Biol."},{"key":"2160_CR22","doi-asserted-by":"crossref","unstructured":"Congdon P. Bayesian models for categorical data. Wiley; 2005.","DOI":"10.1002\/0470092394"},{"key":"2160_CR23","doi-asserted-by":"crossref","unstructured":"Wu L. Mixed effects models for complex data. CRC Press; 2009.","DOI":"10.1201\/9781420074086"},{"key":"2160_CR24","unstructured":"Ntzoufras I. Bayesian modeling using WinBUGS. vol. 698. Wiley; 2011."},{"issue":"1007","key":"2160_CR25","first-page":"453","volume":"186","author":"H Jeffreys","year":"1946","unstructured":"Jeffreys H. An invariant form for the prior probability in estimation problems. Proc R Soc Lond Ser A Math Phys Sci. 1946;186(1007):453\u201361.","journal-title":"Proc R Soc Lond Ser A Math Phys Sci."},{"key":"2160_CR26","doi-asserted-by":"crossref","unstructured":"Kass RE. The geometry of asymptotic inference. Stat Sci. 1989;188\u2013219.","DOI":"10.1214\/ss\/1177012480"},{"issue":"452","key":"2160_CR27","doi-asserted-by":"publisher","first-page":"1300","DOI":"10.1080\/01621459.2000.10474335","volume":"95","author":"AE Gelfand","year":"2000","unstructured":"Gelfand AE. Gibbs sampling. J Am Stat Assoc. 2000;95(452):1300\u20134.","journal-title":"J Am Stat Assoc."},{"key":"2160_CR28","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"S Geman","year":"1984","unstructured":"Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell. 1984;6:721\u201341.","journal-title":"IEEE Trans Pattern Anal Mach Intell."},{"issue":"6","key":"2160_CR29","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N Metropolis","year":"1953","unstructured":"Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machines. J Chem Phys. 1953;21(6):1087\u201392.","journal-title":"J Chem Phys."},{"issue":"4","key":"2160_CR30","first-page":"455","volume":"44","author":"WR Gilks","year":"1995","unstructured":"Gilks WR, Best NG, Tan KK. Adaptive rejection Metropolis sampling within Gibbs sampling. J R Stat Soc: Ser C (Appl Stat). 1995;44(4):455\u201372.","journal-title":"J R Stat Soc: Ser C (Appl Stat)."},{"issue":"6","key":"2160_CR31","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1287\/opre.31.6.1109","volume":"31","author":"P Heidelberger","year":"1983","unstructured":"Heidelberger P, Welch PD. Simulation run length control in the presence of an initial transient. Oper Res. 1983;31(6):1109\u201344.","journal-title":"Oper Res."},{"issue":"4","key":"2160_CR32","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1111\/1467-9868.00353","volume":"64","author":"DJ Spiegelhalter","year":"2002","unstructured":"Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc: Ser B (Stat Methodol). 2002;64(4):583\u2013639.","journal-title":"J R Stat Soc: Ser B (Stat Methodol)."},{"key":"2160_CR33","unstructured":"Lin YK. Hypothesis testing for the Gaussian-Exponential longitudinal model. 2011."},{"key":"2160_CR34","unstructured":"R\u00a0Core\u00a0Team. R: A Language and Environment for Statistical Computing. Vienna, Austria; 2017. https:\/\/www.R-project.org\/.\u00a0Accessed Feb 2021."},{"key":"2160_CR35","unstructured":"Sturtz S, Ligges U, Gelman A. R2OpenBUGS: a package for running OpenBUGS from R. J Stat Softw. 2019;31:1109\u201344."},{"key":"2160_CR36","unstructured":"Therneau T, Lumley T. R survival package. 2013."}],"container-title":["BMC Medical Research Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12874-024-02160-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12874-024-02160-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12874-024-02160-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T01:04:40Z","timestamp":1709255080000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcmedresmethodol.biomedcentral.com\/articles\/10.1186\/s12874-024-02160-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,1]]},"references-count":36,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["2160"],"URL":"https:\/\/doi.org\/10.1186\/s12874-024-02160-2","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3342540\/v1","asserted-by":"object"}]},"ISSN":["1471-2288"],"issn-type":[{"value":"1471-2288","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,1]]},"assertion":[{"value":"10 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Ethical approval was not required for this study since the data used for this study are secondary data and openly\/publicly available in R software.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The author declares no competing interests. Also, the author currently works for Pfizer Inc. Results, views or research findings expressed in this manuscript do not necessarily reflect those of Pfizer, Inc.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"54"}}