Longitudinal zero-inflated count data frequently arise in various fields such as medicine and social sciences. Standard hurdle models separate zero and positive counts, but fail to directly infer marginal means, limiting their ability to assess overall covariate effects. This paper introduces overall marginalized hurdle random effects models (OMHREMs) for zero-inflated count data, which extends the traditional hurdle model by directly modeling the marginal mean while considering random effects to account for heterogeneity. OMHREMs enable population-average effects of covariates like odds ratio, providing how covariates influence the overall mean in zero-inflated count data. Through simulation studies, we evaluate the performance of OMHREMs. Furthermore, we apply our approach to systemic lupus erythematosus data to compare its effectiveness against existing models.
LambertD. Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics1992; 34: 1–14.
2.
MinYAgrestiA. Random effect models for repeated measures of zero-inflated count data. Stat Modelling2005; 5: 1–19.
3.
FengC. A comparison of zero-inflated and hurdle models for modeling zero-inflated count data. J Stat Distrib Appl2021; 8: 8. doi:10.1186/s40488-021-00121-4
4.
MullahyJ. Specification and testing of some modified count data models. J Econom1986; 33: 341–365.
5.
GilthorpeMFrydenbergMChengY, et al.Modelling count data with excessive zeros: the need for class prediction in zero-inflated models and the issue of data generation in choosing between zero-inflated and generic mixture models for dental caries data. Stat Med2009; 28: 3539–3553.
6.
NeelonBHO’MalleyAJNormandSLT. A Bayesian model for repeated measures zero-infalted count data with application to outpatient psychiatrix service use. Stat Modelling2010; 10: 421–439.
7.
BuuALiRTanX, et al.Statistical models for longitudinal zero-inflated count data with applications to the substance abuse field. Stat Med2012; 31: 257–278.
8.
ZhuHLuoDDeSantisSM. Zero-inflated count models for longitudinal measurements with heterogeneous random effects. Stat Methods Med Res2015; 26: 1774–1786.
9.
KangTGaskinsJLevyS, et al.A longitudinal Bayesian mixed effects model with hurdle conway-Maxwell-poisson distribution. Stat Med2020; 40: 1336–1356.
10.
HallDBZhangZ. Marginal models for zero inflated clustered data. Stat Modelling2004; 4: 161–180.
11.
LeeKJooYSongJJ, et al.Analysis of zero-inflated clustered count data: a marginalized model approach. Comput Stat Data Anal2011; 55: 824–837.
12.
MwaliliSLesaffreEDeclerckD. The zero-inflated negative binomial regression model with correlation for misclassification: an example in caries research. Stat Methods Med Res2008; 17: 123–139.
13.
LongDLPreisserJSHerringAH, et al.A marginalized zero-inflated poisson regression model with overall exposure effects. Stat Med2014; 33: 5151–5165.
14.
LongDLPreisserJSHerringAH, et al.A marginalized zero-inflated poisson regression model with random effects. Journal of the Royal Statistical Society: Series C2015; 64: 815–830.
KimHJangEJChoSK, et al.Cost-of-illness changes before and after the diagnosis of systemic lupus erythematosus: a nationwide, population-based observational study in Korea. Rheumatology2025; 64: 180–187.
18.
ChenLZhangMXiangS, et al.Post-traumatic stress disorder and risk of systemic lupus erythematosus: Meta-analysis and Mendelian randomization study. J Psychosom Res2025; 190: 112049.
19.
HanJChoSKangG, et al.Cardiovascular disease risk in Korean patients with systemic lupus erythematosus compared to diabetes mellitus and the general poplulation. Sci Rep2025; 15: 3208.
20.
JangEJRheeAChoS, et al.Analysis of longitudinal lupus data using multivariate t-linear models. Stat Med2025; 44: e10248.
21.
CharlsonMEPompeiPAlesKL, et al.A new method of classifying prognostic comorbidity in longitudinal studies: development and validation. J. Chronic Dis1987; 40: 373–383.
22.
TierneyLKadaneJB. Accurate approximations for posterior moments and marginal densities. J Am Stat Assoc1986; 81: 82–86.
23.
PinheiroJCBatesDM. Approximations to the log-likelihood function in the nonlinear mixed-effects model. J Comput Graph Stat1995; 4: 12–35.
24.
MolasMLesaffreE. Hurdle models for multilevel zero-inflated data via h-likelihood. Stat Med2010; 29: 3294–3310.
25.
ParkJSimKYangD, et al.Nonparametric Bayesian poisson hurdle random effects model: an application to temperature-suicide association study. Environ Ecol Stat2025; 32: 579–601.
26.
ZhangXKanoMTaniM, et al.Hurdle modeling for defet data with excess zeros in steel manufacturing process. IFAC-PapersOnLine2018; 51: 375–380.
