Journal of Biostatistics and Epidemiology 2017. 3(2):41-48.

Comparing zero-inflated Poisson, Poisson gamma, and Poisson lognormal regression models in dental health data
Farzaneh Neysari, Abbas Bahrampour, Yunes Jahani Jahani


Background & Aim: Statistical modeling is one of the most suitable methods for analyzing the relationship between health and medical issues. In the situation of analysis of zero-inflated data, there are different methods. In this study, the models Poisson, Poisson gamma, and Poisson lognormal regression were compared.
Methods & Materials: This cross-sectional study was conducted to determine the influential factors on decay-missing-filled (DMF) index by the three mentioned models using the data of 808 first-grade children of the primary school in Kerman, Iran. The command PROC NLMIXED in SAS software was applied for fitting the models on data. For comparing the models, we applied the Akaike’s criterion (AIC), mean square error (MSE) criterion and confidence interval (CI).
Results: The AIC and CI showed that the Poisson lognormal model was better than the others due to a level of significance. The variables of the students’ place of living, mothers’ jobs, fathers’ jobs, the region, sex, optic problems, and behavioral problems had a significant effect on DMF index.
Conclusion: Poisson lognormal was better than the other models in dental health data.


Poisson distribution; Regression; Decayed, missing and filled teeth; Decay-missing-filled index

Full Text:



Saied-Moallemi Z, Virtanen JI, Ghofranipour F, Murtomaa H. Influence of mothers' oral health knowledge and attitudes on their children's dental health. Eur Arch Paediatr Dent 2008; 9(2): 79-83.

Lord D, Washington SP, Ivan JN. Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: Balancing statistical fit and theory. Accid Anal Prev

; 37(1): 35-46.

Nodtvedt A, Sanchez J, Dohoo I. Applying a zero-inflated negative binomial model to hierarchical count data. Proceedings of the 10th Symposium of the International Society for Veterinary Epidemiology and Economics; 2003 Nov. 17-21; Vina del Mar, Chile; 2003. p. 307 [Online]. [cited Nov. 2003]; Available from: URL:

Renner HM, Reynolds JH, Sims M, Renner M. Evaluating the power of surface attendance counts to detect long-term trends in populations of crevice-nesting auklets. Environ Monit Assess 2011; 177(1-4): 665-79.

Bonate PL, Sung C, Welch K, Richards S. Conditional modeling of antibody titers using a zero-inflated poisson random effects model: Aapplication to Fabrazyme. J Pharmacokinet Pharmacodyn 2009; 36(5): 443-59.

Fang R. Zero-inflated negative binomial (ZINB) regression model for over-dispersed count data with excess zeros and repeated measures, an application to human micro biota sequence data [MSc Thesis]. Tangshan, China: North China Coal Medical University; 2008.

Lambert D. Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics 1992; 34(1): 1-14.

Pahel BT, Preisser JS, Stearns SC, Rozier RG. Multiple imputation of dental caries data using a zero-inflated Poisson regression model. J Public Health Dent 2011; 71(1): 71-8.

Erdman D, Jackson L, Sinko A. Zero-inflated Poisson and zero-inflated negative binomial models using the countreg procedure. Cary, NC: SAS Institute Inc; 2009.

Hall DB. Zero-inflated Poisson and binomial regression with random effects: A case study. Biometrics 2000; 56(4): 1030-9.

Millar RB. Comparison of hierarchical Bayesian models for overdispersed count data using DIC and Bayes' factors. Biometrics 2009; 65(3): 962-9.

Flynn M. More flexible GLMs zero-inflated models and hybrid models [Online]. [cited 2009]; Available from: URL:

Chow NT, Steenhard D. A flexible count data regression model using SAS- PROC NLMIXED. Denver, CO: SAS Global Forum: Statistics and Data Analysis; 2009.

Aguero-Valverde J. Full Bayes Poisson gamma, Poisson lognormal, and zero-inflated random effects models: Comparing the precision of crash frequency estimates. Accid Anal Prev 2013; 50: 289-97.

Staub KE, Winkelmann R. Consistent estimation of zero-inflated count models. Health Econ 2013; 22(6): 673-86.

Izsak R. Maximum likelihood fitting of the Poisson lognormal distribution. Environ Ecol Stat 2008; 15(2): 143-56.

Williams MS, Ebel ED. Methods for fitting the Poisson-lognormal distribution to microbial testing data. Food Control 2012; 27(1): 73-80.

Ridout M, Dem´etrio CG, Hinde J. Models for count data with many zeros. Proceedings of the International Biometrics Conference; 1998 Dec. 13-18; Cape Town, South Africa.

Schmidt AM, Pereira BM, Vieira PP. Do we always need a zero-inflated model to capture an apparent excess of zeros? [Online]. [cited 2008]; Available from: URL:

Ngatchou-Wandji J, Paris C. On the Zero-Inated Count Models with Application to Modeling Annual Trends in Incidences of Some Occupational Allergic Diseases in France. J Data Sci 2011; 9: 639-59.

Cheng J, Cheng NF, Guo Z, Gregorich S, Ismail AI, Gansky SA. Mediation analysis for count and zero-inflated count data. Stat Methods Med Res 2016; 962280216686131.


  • There are currently no refbacks.

Creative Commons Attribution-NonCommercial 3.0

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License which allows users to read, copy, distribute and make derivative works for non-commercial purposes from the material, as long as the author of the original work is cited properly.