{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T18:47:34Z","timestamp":1772736454083,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s11222-023-10295-3","type":"journal-article","created":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T03:34:55Z","timestamp":1695872095000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bayesian hierarchical models incorporating measurement error for interrupted time series design"],"prefix":"10.1007","volume":"33","author":[{"given":"Masud","family":"Rana","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Justin","family":"Kosar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaqil","family":"Peermohamed","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"issue":"3","key":"10295_CR1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0017419","volume":"6","author":"F Barone-Adesi","year":"2011","unstructured":"Barone-Adesi, F., Gasparrini, A., Vizzini, L., Merletti, F., Richiardi, L.: Effects of Italian smoking regulation on rates of hospital admission for acute coronary events: a country-wide study. PLoS ONE 6(3), e17419 (2011). https:\/\/doi.org\/10.1371\/journal.pone.0017419","journal-title":"PLoS ONE"},{"issue":"7","key":"10295_CR2","doi-asserted-by":"publisher","first-page":"2047","DOI":"10.1093\/jac\/dkw055","volume":"71","author":"J Boel","year":"2016","unstructured":"Boel, J., et al.: Impact of antibiotic restriction on resistance levels of Escherichia coli: a controlled interrupted time series study of a hospital-wide antibiotic stewardship programme. J. Antimicrob. Chemother. 71(7), 2047\u20132051 (2016). https:\/\/doi.org\/10.1093\/jac\/dkw055","journal-title":"J. Antimicrob. Chemother."},{"key":"10295_CR3","volume-title":"Time Series Analysis: Forecasting and Control","author":"G Box","year":"2015","unstructured":"Box, G., Jenkins, G., Reinsel, G., Ljung, G.: Time Series Analysis: Forecasting and Control, 5th edn. Wiley, New Jersey (2015)","edition":"5"},{"key":"10295_CR4","doi-asserted-by":"publisher","unstructured":"B\u00fcrkner, P.-C.: Advanced Bayesian Multilevel Modeling with the R Package brms. R J. 10(1), 395 (2018). https:\/\/doi.org\/10.32614\/RJ-2018-017. arXiv:1705.11123","DOI":"10.32614\/RJ-2018-017"},{"key":"10295_CR5","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v080.i01","author":"P-C B\u00fcrkner","year":"2017","unstructured":"B\u00fcrkner, P.-C.: brms\u202f: an R package for bayesian multilevel models using stan. J. Stat. Softw. (2017). https:\/\/doi.org\/10.18637\/jss.v080.i01","journal-title":"J. Stat. Softw."},{"key":"10295_CR6","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v076.i01","author":"B Carpenter","year":"2017","unstructured":"Carpenter, B., et al.: Stan: a probabilistic programming language. J. Stat. Softw. (2017). https:\/\/doi.org\/10.18637\/jss.v076.i01","journal-title":"J. Stat. Softw."},{"key":"10295_CR7","doi-asserted-by":"publisher","unstructured":"Clark, J.S.: Uncertainty and variability in demography and population growth: a hierarchical approach. Spec. Feature Ecol. 84(6), 1370\u20131381 (2003). https:\/\/doi.org\/10.1890\/0012-9658","DOI":"10.1890\/0012-9658"},{"issue":"3","key":"10295_CR8","doi-asserted-by":"publisher","first-page":"671","DOI":"10.2307\/2532003","volume":"43","author":"D Clayton","year":"1987","unstructured":"Clayton, D., Kaldor, J.: Empirical bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43(3), 671 (1987). https:\/\/doi.org\/10.2307\/2532003","journal-title":"Biometrics"},{"key":"10295_CR9","doi-asserted-by":"publisher","unstructured":"Cruz, M., Bender, M., Ombao, H.: A robust interrupted time series model for analyzing complex health care intervention data. Stat. Med. 36(29), 4660\u20134676 (2017). https:\/\/doi.org\/10.1002\/sim.7443. (arXiv:1707.01861)","DOI":"10.1002\/sim.7443"},{"issue":"9974","key":"10295_CR10","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1016\/S0140-6736(14)62007-9","volume":"385","author":"MJ Dayer","year":"2015","unstructured":"Dayer, M.J., et al.: Incidence of infective endocarditis in England, 2000\u201313: a secular trend, interrupted time-series analysis. Lancet 385(9974), 1219\u20131228 (2015). https:\/\/doi.org\/10.1016\/S0140-6736(14)62007-9","journal-title":"Lancet"},{"issue":"2","key":"10295_CR11","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1111\/jels.12219","volume":"16","author":"JJ Donohue","year":"2019","unstructured":"Donohue, J.J., Aneja, A., Weber, K.D.: Right-to-carry laws and violent crime: a comprehensive assessment using panel data and a state-level synthetic control analysis. J. Empiri. Legal Stud. 16(2), 198\u2013247 (2019). https:\/\/doi.org\/10.1111\/jels.12219","journal-title":"J. Empiri. Legal Stud."},{"issue":"1","key":"10295_CR12","doi-asserted-by":"publisher","first-page":"148","DOI":"10.2105\/AJPH.2011.300283","volume":"102","author":"D Dowell","year":"2012","unstructured":"Dowell, D., et al.: Changes in fluoroquinolone use for gonorrhea following publication of revised treatment guidelines. Am. J. Public Health 102(1), 148\u2013155 (2012). https:\/\/doi.org\/10.2105\/AJPH.2011.300283","journal-title":"Am. J. Public Health"},{"issue":"8","key":"10295_CR13","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1002\/gps.4536","volume":"32","author":"F Etchepare","year":"2017","unstructured":"Etchepare, F., Pambrun, E., Verdoux, H., Tournier, M.: Trends in patterns of antidepressant use in older general population between 2006 and 2012 following publication of practice guidelines. Int. J. Geriatr. Psychiatry 32(8), 849\u2013859 (2017). https:\/\/doi.org\/10.1002\/gps.4536","journal-title":"Int. J. Geriatr. Psychiatry"},{"key":"10295_CR14","doi-asserted-by":"publisher","first-page":"411","DOI":"10.2147\/JMDH.S241085","volume":"13","author":"JE Ewusie","year":"2020","unstructured":"Ewusie, J.E., et al.: Methods, applications and challenges in the analysis of interrupted time series data: a scoping review. J. Multidiscip. Healthc. 13, 411\u2013423 (2020). https:\/\/doi.org\/10.2147\/JMDH.S241085","journal-title":"J. Multidiscip. Healthc."},{"key":"10295_CR15","doi-asserted-by":"publisher","unstructured":"Gabry, J., Simpson, D., Vehtari, A., Betancourt, M., Gelman, A.: Visualization in Bayesian workflow. J. R. Stat. Soc. Ser. A (Stat. Soc.) 182(2), 389\u2013402 (2019). https:\/\/doi.org\/10.1111\/rssa.12378. (arXiv:1709.01449)","DOI":"10.1111\/rssa.12378"},{"issue":"1","key":"10295_CR16","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0165-1765(03)00149-6","volume":"81","author":"TA Garrett","year":"2003","unstructured":"Garrett, T.A.: Aggregated versus disaggregated data in regression analysis: implications for inference. Econ. Lett. 81(1), 61\u201365 (2003). https:\/\/doi.org\/10.1016\/S0165-1765(03)00149-6","journal-title":"Econ. Lett."},{"issue":"12","key":"10295_CR17","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.1017\/S0950268812000179","volume":"140","author":"V Gebski","year":"2012","unstructured":"Gebski, V., Ellingson, K., Edwards, J., Jernigan, J., Kleinbaum, D.: Modelling interrupted time series to evaluate prevention and control of infection in healthcare. Epidemiol. Infect. 140(12), 2131\u20132141 (2012). https:\/\/doi.org\/10.1017\/S0950268812000179","journal-title":"Epidemiol. Infect."},{"issue":"2","key":"10295_CR18","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1177\/0149206314525208","volume":"41","author":"A Gelman","year":"2015","unstructured":"Gelman, A.: The connection between varying treatment effects and the crisis of unreplicable research. J. Manage. 41(2), 632\u2013643 (2015). https:\/\/doi.org\/10.1177\/0149206314525208","journal-title":"J. Manage."},{"key":"10295_CR19","unstructured":"Hox, J.J.: Multilevel analysis: techniques and applications, 2nd edn. Lawrence Erlbaum, Mahwah (2010)"},{"issue":"8","key":"10295_CR20","doi-asserted-by":"publisher","first-page":"950","DOI":"10.1016\/j.jclinepi.2014.12.018","volume":"68","author":"R Jandoc","year":"2015","unstructured":"Jandoc, R., Burden, A.M., Mamdani, M., L\u00e9vesque, L.E., Cadarette, S.M.: Interrupted time series analysis in drug utilization research is increasing: systematic review and recommendations. J. Clin. Epidemiol. 68(8), 950\u2013956 (2015). https:\/\/doi.org\/10.1016\/j.jclinepi.2014.12.018","journal-title":"J. Clin. Epidemiol."},{"key":"10295_CR21","doi-asserted-by":"publisher","unstructured":"Jiao, Y., Hayes, C., Cort\u00e9s, E.: Hierarchical Bayesian approach for population dynamics modelling of fish complexes without species-specific data. ICES J. Mar. Sci. 66(2), 367\u2013377 (2009). https:\/\/doi.org\/10.1093\/icesjms\/fsn162","DOI":"10.1093\/icesjms\/fsn162"},{"issue":"1","key":"10295_CR22","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1186\/s13012-014-0109-9","volume":"9","author":"M Kastner","year":"2014","unstructured":"Kastner, M., et al.: A knowledge translation tool improved osteoporosis disease management in primary care: an interrupted time series analysis. Implement. Sci. 9(1), 109 (2014). https:\/\/doi.org\/10.1186\/s13012-014-0109-9","journal-title":"Implement. Sci."},{"key":"10295_CR23","doi-asserted-by":"crossref","unstructured":"Kleiber, C., Zeileis, A.: Applied econometrics with R, Springer New York, New York (2008). http:\/\/link.springer.com\/10.1007\/978-0-387-77318-6","DOI":"10.1007\/978-0-387-77318-6"},{"issue":"1","key":"10295_CR24","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1093\/ageing\/afx128","volume":"47","author":"B Liu","year":"2018","unstructured":"Liu, B., et al.: Outcomes of mobilisation of vulnerable elders in Ontario (MOVE ON): a multisite interrupted time series evaluation of an implementation intervention to increase patient mobilisation. Age Ageing 47(1), 112\u2013119 (2018). https:\/\/doi.org\/10.1093\/ageing\/afx128","journal-title":"Age Ageing"},{"key":"10295_CR25","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyw098","author":"J Lopez Bernal","year":"2016","unstructured":"Lopez Bernal, J., Cummins, S., Gasparrini, A.: Interrupted time series regression for the evaluation of public health interventions: a tutorial. Int. J. Epidemiol. (2016). https:\/\/doi.org\/10.1093\/ije\/dyw098","journal-title":"Int. J. Epidemiol."},{"key":"10295_CR26","doi-asserted-by":"crossref","unstructured":"Lott, J.R., Mustard, D.: in Crime, deterrence, and right-to-carry concealed handguns, pp. 129\u2013200 (2008). http:\/\/www.crcnetbase.com\/doi\/abs\/10.4324\/9780203930885.ch8","DOI":"10.4324\/9780203930885.ch8"},{"issue":"1","key":"10295_CR27","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1186\/1471-2288-5-14","volume":"5","author":"GH Lyman","year":"2005","unstructured":"Lyman, G.H., Kuderer, N.M.: The strengths and limitations of meta-analyses based on aggregate data. BMC Med. Res. Methodol. 5(1), 14 (2005). https:\/\/doi.org\/10.1186\/1471-2288-5-14","journal-title":"BMC Med. Res. Methodol."},{"issue":"2","key":"10295_CR28","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1177\/0962280212447152","volume":"23","author":"YC MacNab","year":"2014","unstructured":"MacNab, Y.C.: On identification in Bayesian disease mapping and ecological-spatial regression models. Stat. Methods Med. Res. 23(2), 134\u2013155 (2014). https:\/\/doi.org\/10.1177\/0962280212447152","journal-title":"Stat. Methods Med. Res."},{"issue":"40","key":"10295_CR29","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.21105\/joss.01541","volume":"4","author":"D Makowski","year":"2019","unstructured":"Makowski, D., Ben-Shachar, M., L\u00fcdecke, D.: bayestestR: describing effects and their uncertainty, existence and significance within the Bayesian framework. J. Open Sour. Softw. 4(40), 1541 (2019). https:\/\/doi.org\/10.21105\/joss.01541","journal-title":"J. Open Sour. Softw."},{"key":"10295_CR30","unstructured":"McElreath, R.: Statistical Rethinking. Chapman and Hall\/CRC, Boca Raton (2018) https:\/\/www.taylorfrancis.com\/books\/9781315362618"},{"key":"10295_CR31","doi-asserted-by":"publisher","first-page":"2074","DOI":"10.1002\/sim.8086","volume":"38","author":"TP Morris","year":"2019","unstructured":"Morris, T.P., White, I.R., Crowther, M.J.: Using simulation studies to evaluate statistical methods. Stat. Med. 38, 2074\u20132102 (2019). https:\/\/doi.org\/10.1002\/sim.8086","journal-title":"Stat. Med."},{"issue":"6","key":"10295_CR32","doi-asserted-by":"publisher","first-page":"S38","DOI":"10.1016\/j.acap.2013.08.002","volume":"13","author":"RB Penfold","year":"2013","unstructured":"Penfold, R.B., Zhang, F.: Use of interrupted time series analysis in evaluating health care quality improvements. Acad. Pediatr. 13(6), S38\u2013S44 (2013). https:\/\/doi.org\/10.1016\/j.acap.2013.08.002","journal-title":"Acad. Pediatr."},{"issue":"6","key":"10295_CR33","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007043","volume":"15","author":"P Piray","year":"2019","unstructured":"Piray, P., Dezfouli, A., Heskes, T., Frank, M.J., Daw, N.D.: Hierarchical Bayesian inference for concurrent model fitting and comparison for group studies. PLOS Comput. Biol. 15(6), e1007043 (2019). https:\/\/doi.org\/10.1371\/journal.pcbi.1007043","journal-title":"PLOS Comput. Biol."},{"key":"10295_CR34","unstructured":"R Core Team. R: A Language and Environment for Statistical Computing (2021). https:\/\/www.r-project.org\/"},{"issue":"4","key":"10295_CR35","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1017\/S0266462303000576","volume":"19","author":"CR Ramsay","year":"2003","unstructured":"Ramsay, C.R., Matowe, L., Grilli, R., Grimshaw, J.M., Thomas, R.E.: Interrupted time series designs in health technology assessment: lessons from two systematic reviews of behavior change strategies. Int. J. Technol. Assess. Health Care 19(4), 613\u2013623 (2003). https:\/\/doi.org\/10.1017\/S0266462303000576","journal-title":"Int. J. Technol. Assess. Health Care"},{"key":"10295_CR36","doi-asserted-by":"publisher","unstructured":"Rana, M. et al.: In: Chaubey, Y.P., Lahmiri, S., Nebebe, F., Sen, A. (eds.) Modeling obesity rate with spatial auto-correlation: a case study. Applied Statistics and Data Science, vol. 375, Ch. 3, pp. 53\u201377. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-86133-9_3","DOI":"10.1007\/978-3-030-86133-9_3"},{"issue":"2","key":"10295_CR37","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1093\/ije\/dyn357","volume":"38","author":"W Robinson","year":"2009","unstructured":"Robinson, W.: Ecological correlations and the behavior of individuals. Int. J. Epidemiol. 38(2), 337\u2013341 (2009). https:\/\/doi.org\/10.1093\/ije\/dyn357","journal-title":"Int. J. Epidemiol."},{"key":"10295_CR38","unstructured":"Stan Development Team. RStan: the R interface to Stan (2020). http:\/\/mc-stan.org\/"},{"issue":"4","key":"10295_CR39","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1046\/j.1365-2710.2002.00430.x","volume":"27","author":"AK Wagner","year":"2002","unstructured":"Wagner, A.K., Soumerai, S.B., Zhang, F., Ross-Degnan, D.: Segmented regression analysis of interrupted time series studies in medication use research. J. Clin. Pharm. Ther. 27(4), 299\u2013309 (2002). https:\/\/doi.org\/10.1046\/j.1365-2710.2002.00430.x","journal-title":"J. Clin. Pharm. Ther."},{"key":"10295_CR40","unstructured":"Wang, J.J.J., Walter, S., Grzebieta, R., Olivier, J.: A comparison of statistical methods in interrupted time series analysis to estimate an intervention effect. Proceedings of the 2013 Australasian Road Safety Research, Policing & Education Conference (2013)"},{"key":"10295_CR41","unstructured":"Watanabe, S. Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res. (2010). arXiv:1004.2316"},{"key":"10295_CR42","unstructured":"Wickham, H. ggplot2: Elegant Graphics for Data Analysis Use R! (Springer International Publishing, Cham, 2016). http:\/\/link.springer.com\/10.1007\/978-3-319-24277-4"},{"issue":"43","key":"10295_CR43","doi-asserted-by":"publisher","first-page":"1686","DOI":"10.21105\/joss.01686","volume":"4","author":"H Wickham","year":"2019","unstructured":"Wickham, H., et al.: Welcome to the Tidyverse. J. Open Sour. Softw. 4(43), 1686 (2019). https:\/\/doi.org\/10.21105\/joss.01686","journal-title":"J. Open Sour. Softw."},{"issue":"2","key":"10295_CR44","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.jclinepi.2008.08.007","volume":"62","author":"F Zhang","year":"2009","unstructured":"Zhang, F., Wagner, A.K., Soumerai, S.B., Ross-Degnan, D.: Methods for estimating confidence intervals in interrupted time series analyses of health interventions. J. Clin. Epidemiol. 62(2), 143\u2013148 (2009). https:\/\/doi.org\/10.1016\/j.jclinepi.2008.08.007","journal-title":"J. Clin. Epidemiol."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10295-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-023-10295-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10295-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T10:09:13Z","timestamp":1697882953000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-023-10295-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,28]]},"references-count":44,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["10295"],"URL":"https:\/\/doi.org\/10.1007\/s11222-023-10295-3","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,28]]},"assertion":[{"value":"10 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have declared no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"The authors confirm that there are no similar articles published or submitted for publication elsewhere.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"127"}}