{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T02:53:13Z","timestamp":1770519193901,"version":"3.49.0"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T00:00:00Z","timestamp":1766275200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T00:00:00Z","timestamp":1766275200000},"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":[[2026,2]]},"DOI":"10.1007\/s11222-025-10802-8","type":"journal-article","created":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T11:34:41Z","timestamp":1766316881000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian inference of longitudinal count data with informative dropouts using a zero-inflated negative binomial mixed model"],"prefix":"10.1007","volume":"36","author":[{"given":"Miaojie","family":"Xia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Guan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiang","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,21]]},"reference":[{"issue":"1","key":"10802_CR1","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1177\/0962280217715051","volume":"28","author":"J Ahn","year":"2019","unstructured":"Ahn, J., Morita, S., Wang, W., et al.: Bayesian analysis of longitudinal dyadic data with informative missing data using a dyadic shared-parameter model. Stat. Methods Med. Res. 28(1), 70\u201383 (2019). https:\/\/doi.org\/10.1177\/0962280217715051","journal-title":"Stat. Methods Med. Res."},{"issue":"3","key":"10802_CR2","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1191\/1471082X03st058oa","volume":"3","author":"JG Booth","year":"2003","unstructured":"Booth, J.G., Casella, G., Friedl, H., et al.: Negative binomial loglinear mixed models. Statistical Modeling 3(3), 179\u2013191 (2003). https:\/\/doi.org\/10.1191\/1471082X03st058oa","journal-title":"Statistical Modeling"},{"issue":"421","key":"10802_CR3","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1080\/01621459.1993.10594284","volume":"88","author":"NE Breslow","year":"1993","unstructured":"Breslow, N.E., Clayton, D.G.: Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc. 88(421), 9\u201325 (1993). https:\/\/doi.org\/10.1080\/01621459.1993.10594284","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10802_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v076.i01","volume":"76","author":"B Carpenter","year":"2017","unstructured":"Carpenter, B., Gelman, A., Hoffman, M.D., et al.: Stan: A probabilistic programming language. Journal of Statistical Software 76(1), 1\u201329 (2017). https:\/\/doi.org\/10.18637\/jss.v076.i01","journal-title":"Journal of Statistical Software"},{"issue":"12","key":"10802_CR5","doi-asserted-by":"publisher","first-page":"4530","DOI":"10.1016\/j.csda.2009.07.020","volume":"53","author":"JS Chan","year":"2009","unstructured":"Chan, J.S., Leung, D.Y., Boris Choy, S., et al.: Nonignorable dropout models for longitudinal binary data with random effects: An application of monte carlo approximation through the gibbs output. Computational Statistics & Data Analysis 53(12), 4530\u20134545 (2009). https:\/\/doi.org\/10.1016\/j.csda.2009.07.020. (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0167947309002552)","journal-title":"Computational Statistics & Data Analysis"},{"issue":"1","key":"10802_CR6","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00180-010-0213-5","volume":"26","author":"JSK Chan","year":"2011","unstructured":"Chan, J.S.K., Wan, W.Y.: Bayesian approach to analysing longitudinal bivariate binary data with informative dropout. Comput. Statistics 26(1), 121\u2013144 (2011)","journal-title":"Comput. Statistics"},{"issue":"16","key":"10802_CR7","doi-asserted-by":"publisher","first-page":"2770","DOI":"10.1002\/sim.6892","volume":"35","author":"T Chen","year":"2016","unstructured":"Chen, T., Wu, P., Tang, W., et al.: Variable selection for distribution-free models for longitudinal zero-inflated count responses. Stat. Med. 35(16), 2770\u20132785 (2016)","journal-title":"Stat. Med."},{"issue":"1","key":"10802_CR8","first-page":"49","volume":"43","author":"P Diggle","year":"1994","unstructured":"Diggle, P., Kenward, M.G.: Informative drop-out in longitudinal data analysis. J. R. Stat. Soc.: Ser. C: Appl. Stat. 43(1), 49\u201373 (1994)","journal-title":"J. R. Stat. Soc.: Ser. C: Appl. Stat."},{"issue":"1","key":"10802_CR9","doi-asserted-by":"publisher","first-page":"117","DOI":"10.6339\/JDS.2006.04(1).257","volume":"4","author":"F Famoye","year":"2006","unstructured":"Famoye, F., Singh, K.P.: Zero-inflated generalized poisson regression model with an application to domestic violence data. Journal of Data Science 4(1), 117\u2013130 (2006)","journal-title":"Journal of Data Science"},{"issue":"4","key":"10802_CR10","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1111\/j.2517-6161.1995.tb02056.x","volume":"57","author":"GM Fitzmaurice","year":"1995","unstructured":"Fitzmaurice, G.M., Molenberghs, G., Lipsitz, S.R.: Regression models for longitudinal binary responses with informative drop-outs. J. Roy. Stat. Soc.: Ser. B (Methodol.) 57(4), 691\u2013704 (1995)","journal-title":"J. Roy. Stat. Soc.: Ser. B (Methodol.)"},{"key":"10802_CR11","doi-asserted-by":"publisher","DOI":"10.1002\/sim.10347","volume":"44","author":"A Gasparini","year":"2025","unstructured":"Gasparini, A., Crowther, M.J., Hoogendijk, E.O., et al.: Analysis of cohort stepped wedge cluster-randomized trials with nonignorable dropout via joint modeling. Stat. Med. 44, e10347 (2025). https:\/\/doi.org\/10.1002\/sim.10347","journal-title":"Stat. Med."},{"issue":"4","key":"10802_CR12","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1214\/ss\/1177011136","volume":"7","author":"A Gelman","year":"1992","unstructured":"Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Stat. Sci. 7(4), 457\u2013472 (1992)","journal-title":"Stat. Sci."},{"key":"10802_CR13","doi-asserted-by":"publisher","unstructured":"Geweke, J.: Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments. In: Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting, Dedicated to the memory of Morris H. DeGroot, 1931\u20131989. Oxford University Press, (1992) https:\/\/doi.org\/10.1093\/oso\/9780198522669.003.0010","DOI":"10.1093\/oso\/9780198522669.003.0010"},{"issue":"4","key":"10802_CR14","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1111\/j.0006-341X.2000.01030.x","volume":"56","author":"DB Hall","year":"2000","unstructured":"Hall, D.B.: Zero-inflated poisson and binomial regression with random effects: A case study. Biometrics 56(4), 1030\u20131039 (2000)","journal-title":"Biometrics"},{"issue":"4","key":"10802_CR15","doi-asserted-by":"publisher","first-page":"1487","DOI":"10.5705\/ss.2013.063","volume":"24","author":"M Han","year":"2014","unstructured":"Han, M., Song, X., Sun, L., et al.: Joint modeling of longitudinal data with informative observation times and dropouts. Stat. Sin. 24(4), 1487\u20131504 (2014). https:\/\/doi.org\/10.5705\/ss.2013.063","journal-title":"Stat. Sin."},{"key":"10802_CR16","volume-title":"Longitudinal data analysis","author":"D Hedeker","year":"2006","unstructured":"Hedeker, D., Gibbons, R.D.: Longitudinal data analysis. Wiley Series in Probability and Statistics, Wiley-Interscience, Hoboken, NJ, US (2006)"},{"issue":"4","key":"10802_CR17","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1111\/j.0006-341X.2004.00240.x","volume":"60","author":"JW Hogan","year":"2004","unstructured":"Hogan, J.W., Lin, X., Herman, B.: Mixtures of varying coefficient models for longitudinal data with discrete or continuous nonignorable dropout. Biometrics 60(4), 854\u2013864 (2004). https:\/\/doi.org\/10.1111\/j.0006-341X.2004.00240.x","journal-title":"Biometrics"},{"key":"10802_CR18","doi-asserted-by":"publisher","unstructured":"Hsieh, P.I., Chen, Y.C., Chen, T.F., et\u00a0al.: Multimorbid patterns and cognitive performance in the presence of informative dropout among community-dwelling taiwanese older adults. Innovation in Aging 7(2). (2023) https:\/\/doi.org\/10.1093\/geroni\/igad012","DOI":"10.1093\/geroni\/igad012"},{"issue":"1","key":"10802_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11749-009-0138-x","volume":"18","author":"JG Ibrahim","year":"2009","unstructured":"Ibrahim, J.G., Molenberghs, G.: Missing data methods in longitudinal studies: a review. TEST 18(1), 1\u201343 (2009). https:\/\/doi.org\/10.1007\/s11749-009-0138-x","journal-title":"TEST"},{"key":"10802_CR20","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.jmva.2014.06.016","volume":"131","author":"S Jolani","year":"2014","unstructured":"Jolani, S.: An analysis of longitudinal data with nonignorable dropout using the truncated multivariate normal distribution. J. Multivar. Anal. 131, 163\u2013173 (2014). https:\/\/doi.org\/10.1016\/j.jmva.2014.06.016. (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0047259X14001468)","journal-title":"J. Multivar. Anal."},{"issue":"1","key":"10802_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/1269547","volume":"34","author":"D Lambert","year":"1992","unstructured":"Lambert, D.: Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics 34(1), 1\u201314 (1992)","journal-title":"Technometrics"},{"issue":"1","key":"10802_CR22","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1191\/0962280206sm429oa","volume":"15","author":"A Lee","year":"2006","unstructured":"Lee, A., Wang, K., Scott, J., et al.: Multi-level zero-inflated poisson regression modelling of correlated count data with excess zeros. Stat. Methods Med. Res. 15(1), 47\u201361 (2006). https:\/\/doi.org\/10.1191\/0962280206sm429oa","journal-title":"Stat. Methods Med. Res."},{"issue":"4","key":"10802_CR23","doi-asserted-by":"publisher","first-page":"2765","DOI":"10.3758\/s13428-024-02359-7","volume":"56","author":"H Li","year":"2024","unstructured":"Li, H., Luo, W., Baek, E.: Multilevel modeling in single-case studies with zero-inflated and overdispersed count data. Behav. Res. Methods 56(4), 2765\u20132781 (2024)","journal-title":"Behav. Res. Methods"},{"issue":"1","key":"10802_CR24","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s11676-018-0854-8","volume":"31","author":"Y Li","year":"2020","unstructured":"Li, Y., Kang, X., Zhang, Q., et al.: Modelling tree mortality across diameter classes using mixed-effects zero-inflated models. Journal of Forestry Research 31(1), 131\u2013140 (2020)","journal-title":"Journal of Forestry Research"},{"key":"10802_CR25","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.csda.2013.06.021","volume":"71","author":"HK Lim","year":"2014","unstructured":"Lim, H.K., Li, W.K., Yu, P.L.: Zero-inflated poisson regression mixture model. Computational Statistics & Data Analysis 71, 151\u2013158 (2014). https:\/\/doi.org\/10.1016\/j.csda.2013.06.021. (https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0167947313002338)","journal-title":"Computational Statistics & Data Analysis"},{"issue":"431","key":"10802_CR26","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1080\/01621459.1995.10476615","volume":"90","author":"RJA Little","year":"1995","unstructured":"Little, R.J.A.: Modeling the drop-out mechanism in repeated-measures studies. J. Am. Stat. Assoc. 90(431), 1112\u20131121 (1995)","journal-title":"J. Am. Stat. Assoc."},{"key":"10802_CR27","unstructured":"Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data, 1st edn. Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York (1987)"},{"issue":"4","key":"10802_CR28","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1023\/A:1008929526011","volume":"10","author":"D Lunn","year":"2000","unstructured":"Lunn, D., Thomas, A., Best, N., et al.: Winbugs - a bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput. 10(4), 325\u2013337 (2000)","journal-title":"Stat. Comput."},{"issue":"1","key":"10802_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1191\/1471082X05st084oa","volume":"5","author":"Y Min","year":"2005","unstructured":"Min, Y., Agresti, A.: Random effect models for repeated measures of zero-inflated count data. Stat. Model. 5(1), 1\u201319 (2005). https:\/\/doi.org\/10.1191\/1471082X05st084oa","journal-title":"Stat. Model."},{"key":"10802_CR30","doi-asserted-by":"publisher","unstructured":"Neal, R.M.: Mcmc using hamiltonian dynamics. In: Brooks S, Gelman A, Jones G, et\u00a0al (eds) Handbook of Markov Chain Monte Carlo. Chapman and Hall\/CRC, Boca Raton, FL, p 113\u2013162, (2011) https:\/\/doi.org\/10.1201\/b10905","DOI":"10.1201\/b10905"},{"issue":"3","key":"10802_CR31","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1214\/18-BA1132","volume":"14","author":"B Neelon","year":"2019","unstructured":"Neelon, B.: Bayesian zero-inflated negative binomial regression based on p\u00f3lya-gamma mixtures. Bayesian Anal. 14(3), 829\u2013855 (2019). https:\/\/doi.org\/10.1214\/18-BA1132","journal-title":"Bayesian Anal."},{"key":"10802_CR32","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1146\/annurev-statistics-030718-105048","volume":"6","author":"G Papageorgiou","year":"2019","unstructured":"Papageorgiou, G., Mauff, K., Tomer, A., et al.: An overview of joint modeling of time-to-event and longitudinal outcomes. Annual Review of Statistics and Its Application 6, 223\u2013240 (2019). https:\/\/doi.org\/10.1146\/annurev-statistics-030718-105048","journal-title":"Annual Review of Statistics and Its Application"},{"key":"10802_CR33","unstructured":"Plummer, M.: JAGS: A program for analysis of bayesian hierarchical models using gibbs sampling. In: Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), Vienna, Austria (2003)"},{"issue":"504","key":"10802_CR34","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1080\/01621459.2013.829001","volume":"108","author":"NG Polson","year":"2013","unstructured":"Polson, N.G., Scott, J.G., Windle, J.: Bayesian inference for logistic models using p\u00f3lya\u2013gamma latent variables. J. Am. Stat. Assoc. 108(504), 1339\u20131349 (2013). https:\/\/doi.org\/10.1080\/01621459.2013.829001","journal-title":"J. Am. Stat. Assoc."},{"issue":"429","key":"10802_CR35","doi-asserted-by":"publisher","first-page":"106","DOI":"10.2307\/2291134","volume":"90","author":"JM Robins","year":"1995","unstructured":"Robins, J.M., Rotnitzky, A., Zhao, L.P.: Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. J. Am. Stat. Assoc. 90(429), 106\u2013121 (1995). https:\/\/doi.org\/10.2307\/2291134","journal-title":"J. Am. Stat. Assoc."},{"key":"10802_CR36","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.csda.2016.01.007","volume":"99","author":"KF Sellers","year":"2016","unstructured":"Sellers, K.F., Raim, A.: A flexible zero-inflated model to address data dispersion. Computational Statistics & Data Analysis 99, 68\u201380 (2016). https:\/\/doi.org\/10.1016\/j.csda.2016.01.007","journal-title":"Computational Statistics & Data Analysis"},{"issue":"5","key":"10802_CR37","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1080\/02331888.2022.2110250","volume":"56","author":"Y Shao","year":"2022","unstructured":"Shao, Y., Ma, W., Wang, L.: Robust statistical inference for longitudinal data with nonignorable dropouts. Statistics 56(5), 1072\u20131094 (2022). https:\/\/doi.org\/10.1080\/02331888.2022.2110250","journal-title":"Statistics"},{"issue":"14","key":"10802_CR38","doi-asserted-by":"publisher","first-page":"2686","DOI":"10.1080\/02664763.2025.2481458","volume":"52","author":"SK Sinha","year":"2025","unstructured":"Sinha, S.K.: Zero-inflated poisson mixed model for longitudinal count data with informative dropouts. J. Appl. Stat. 52(14), 2686\u20132706 (2025). https:\/\/doi.org\/10.1080\/02664763.2025.2481458","journal-title":"J. Appl. Stat."},{"issue":"4","key":"10802_CR39","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1111\/1467-9868.00353","volume":"64","author":"DJ Spiegelhalter","year":"2002","unstructured":"Spiegelhalter, D.J., Best, N.G., Carlin, B.P., et al.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64(4), 583\u2013616 (2002). https:\/\/doi.org\/10.1111\/1467-9868.00353","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"10802_CR40","doi-asserted-by":"publisher","unstructured":"Sun, Z.: Regression analysis of asynchronous longitudinal data with informative dropout and dependent observation. Communications in Statistics - Simulation and Computation https:\/\/doi.org\/10.1080\/03610918.2024.2363952, early access: June 2024 (2024)","DOI":"10.1080\/03610918.2024.2363952"},{"issue":"12","key":"10802_CR41","doi-asserted-by":"publisher","first-page":"4348","DOI":"10.1016\/j.csda.2012.03.018","volume":"56","author":"NS Tang","year":"2012","unstructured":"Tang, N.S., Duan, X.D.: A semiparametric bayesian approach to generalized partial linear mixed models for longitudinal data. Computational Statistics & Data Analysis 56(12), 4348\u20134365 (2012). https:\/\/doi.org\/10.1016\/j.csda.2012.03.018","journal-title":"Computational Statistics & Data Analysis"},{"issue":"1","key":"10802_CR42","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1186\/s12874-023-01846-3","volume":"23","author":"C Touraine","year":"2023","unstructured":"Touraine, C., Cuer, B., Conroy, T., et al.: When a joint model should be preferred over a linear mixed model for analysis of longitudinal health-related quality of life data in cancer clinical trials. BMC Med. Res. Methodol. 23(1), 36 (2023). https:\/\/doi.org\/10.1186\/s12874-023-01846-3","journal-title":"BMC Med. Res. Methodol."},{"issue":"5","key":"10802_CR43","doi-asserted-by":"publisher","first-page":"1338","DOI":"10.1177\/0962280219859915","volume":"29","author":"EL Turner","year":"2020","unstructured":"Turner, E.L., Yao, L., Li, F., et al.: Properties and pitfalls of weighting as an alternative to multilevel multiple imputation in cluster randomized trials with missing binary outcomes under covariate-dependent missingness. Stat. Methods Med. Res. 29(5), 1338\u20131353 (2020). https:\/\/doi.org\/10.1177\/0962280219859915","journal-title":"Stat. Methods Med. Res."},{"key":"10802_CR44","doi-asserted-by":"publisher","unstructured":"Vehtari, A., Gelman, A., Gabry, J.: Practical bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat. Comput. 27(5), 1413\u20131432 (2017). https:\/\/doi.org\/10.1007\/s11222-016-9696-4","DOI":"10.1007\/s11222-016-9696-4"},{"key":"10802_CR45","doi-asserted-by":"publisher","first-page":"S121","DOI":"10.1111\/insr.12288","volume":"87","author":"L Wang","year":"2019","unstructured":"Wang, L., Qi, C., Shao, J.: Model-assisted regression estimators for longitudinal data with nonignorable dropout. Int. Stat. Rev. 87, S121\u2013S138 (2019)","journal-title":"Int. Stat. Rev."},{"key":"10802_CR46","doi-asserted-by":"publisher","unstructured":"Wang, X., Chinchilli, V.M.: Analysis of crossover designs for longitudinal binary data with ignorable and nonignorable dropout. Stat. Methods Med. Res. 31(1), 119\u2013138 (2022). https:\/\/doi.org\/10.1177\/09622802211047177","DOI":"10.1177\/09622802211047177"},{"issue":"2","key":"10802_CR47","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1214\/19-BA1165","volume":"15","author":"ZQ Wang","year":"2020","unstructured":"Wang, Z.Q., Tang, N.S.: Bayesian Quantile Regression with Mixed Discrete and Nonignorable Missing Covariates. Bayesian Anal. 15(2), 579\u2013604 (2020). https:\/\/doi.org\/10.1214\/19-BA1165","journal-title":"Bayesian Anal."},{"key":"10802_CR48","doi-asserted-by":"publisher","first-page":"3571","DOI":"10.5555\/1756006.1953045","volume":"11","author":"S Watanabe","year":"2010","unstructured":"Watanabe, S.: Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res. 11, 3571\u20133594 (2010). https:\/\/doi.org\/10.5555\/1756006.1953045","journal-title":"J. Mach. Learn. Res."},{"key":"10802_CR49","doi-asserted-by":"publisher","unstructured":"Wu, J., Ibrahim, J.G., Chen, M.H., et\u00a0al.: Bayesian modeling and inference for nonignorably missing longitudinal binary response data with applications to hiv prevention trials. Statistica Sinica 28(4, SI):1929\u20131963. (2018) https:\/\/doi.org\/10.5705\/ss.202016.0319","DOI":"10.5705\/ss.202016.0319"},{"key":"10802_CR50","doi-asserted-by":"crossref","unstructured":"Yip, K.C., Yau, K.K.: On modeling claim frequency data in general insurance with extra zeros. Insurance: Mathematics and Economics 36(2):153\u2013163 (2005)","DOI":"10.1016\/j.insmatheco.2004.11.002"},{"issue":"8","key":"10802_CR51","doi-asserted-by":"publisher","first-page":"2345","DOI":"10.1093\/bioinformatics\/btz973","volume":"36","author":"X Zhang","year":"2020","unstructured":"Zhang, X., Yi, N.: Fast zero-inflated negative binomial mixed modeling approach for analyzing longitudinal metagenomics data. Bioinformatics 36(8), 2345\u20132351 (2020)","journal-title":"Bioinformatics"},{"issue":"1","key":"10802_CR52","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1186\/s12859-020-03803-z","volume":"21","author":"X Zhang","year":"2020","unstructured":"Zhang, X., Yi, N.: Nbzimm: negative binomial and zero-inflated mixed models, with application to microbiome\/metagenomics data analysis. BMC Bioinformatics 21(1), 488 (2020)","journal-title":"BMC Bioinformatics"},{"issue":"2","key":"10802_CR53","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1109\/TPAMI.2013.211","volume":"37","author":"M Zhou","year":"2015","unstructured":"Zhou, M., Carin, L.: Negative binomial process count and mixture modeling. IEEE Trans. Pattern Anal. Mach. Intell. 37(2), 307\u2013320 (2015). https:\/\/doi.org\/10.1109\/TPAMI.2013.211","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"10802_CR54","doi-asserted-by":"publisher","first-page":"1774","DOI":"10.1177\/0962280215588224","volume":"26","author":"H Zhu","year":"2017","unstructured":"Zhu, H., Sheng, L., DeSantis, S.M.: Zero-inflated count models for longitudinal measurements with heterogeneous random effects. Stat. Methods Med. Res. 26(4), 1774\u20131786 (2017). https:\/\/doi.org\/10.1177\/0962280215588224","journal-title":"Stat. Methods Med. Res."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10802-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-025-10802-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10802-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T03:54:04Z","timestamp":1770436444000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-025-10802-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,21]]},"references-count":54,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10802"],"URL":"https:\/\/doi.org\/10.1007\/s11222-025-10802-8","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,21]]},"assertion":[{"value":"5 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2025","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 declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"44"}}