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GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries

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  • Kong, Maiying
  • Xu, Sheng
  • Levy, Steven M.
  • Datta, Somnath

Abstract

Use of zero-inflated count data models is common in applications where the number of zero counts exceeds that predicted from a traditional count data model such as Poisson or negative binomial. When count data exhibiting inflated zero counts are correlated among subjects, a natural approach will be to fit a marginal model with the help of generalized estimating equations (GEE) that can incorporate subject-to-subject correlations. A GEE based zero-inflated negative binomial (ZINB) model is proposed to fit clustered counts with excessive zeros. However, the corresponding sandwich variance estimator appears to underestimate the true variance. The theoretical reasons for its failure are explained and a correction under additional modeling assumptions is offered. In addition, a clustered resampling (bootstrap) procedure is proposed to estimate the variance and it is shown that the bootstrap procedure captures the correct variance under no additional model assumptions. Utility of this marginal GEE based ZINB model over two other competing models has been assessed using a thorough simulation study. The resulting inference procedure is applied to study the association between the dental caries and fluoride exposures using a dataset extracted from the Iowa Fluoride Study. A number of risk factors of clinical significance are reliably identified using the proposed model.

Suggested Citation

  • Kong, Maiying & Xu, Sheng & Levy, Steven M. & Datta, Somnath, 2015. "GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 54-66.
    • Handle: RePEc:eee:csdana:v:85:y:2015:i:c:p:54-66
    DOI: 10.1016/j.csda.2014.11.014
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    References listed on IDEAS

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    1. Feng-Chang Xie & Jin-Guan Lin & Bo-Cheng Wei, 2014. "Bayesian zero-inflated generalized Poisson regression model: estimation and case influence diagnostics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1383-1392, June.
    2. Zeileis, Achim & Kleiber, Christian & Jackman, Simon, 2008. "Regression Models for Count Data in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i08).
    3. Abbas Moghimbeigi & Mohammed Reza Eshraghian & Kazem Mohammad & Brian Mcardle, 2008. "Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1193-1202.
    4. Garay, Aldo M. & Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Lachos, Víctor H., 2011. "On estimation and influence diagnostics for zero-inflated negative binomial regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1304-1318, March.
    5. Lim, Hwa Kyung & Song, Juwon & Jung, Byoung Cheol, 2013. "Score tests for zero-inflation and overdispersion in two-level count data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 67-82.
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    Cited by:

    1. Nasim Vahabi & Anoshirvan Kazemnejad & Somnath Datta, 2018. "A Marginalized Overdispersed Location Scale Model for Clustered Ordinal Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 103-134, December.
    2. Adrian Fianu & Hind Aissaoui & Nadège Naty & Victorine Lenclume & Anne-Françoise Casimir & Emmanuel Chirpaz & Olivier Maillard & Michel Spodenkiewicz & Nicolas Bouscaren & Michelle Kelly-Irving & Emma, 2022. "Health Impacts of the COVID-19 Lockdown Measure in a Low Socio-Economic Setting: A Cross-Sectional Study on Reunion Island," IJERPH, MDPI, vol. 19(21), pages 1-22, October.
    3. Soutik Ghosal & Timothy S. Lau & Jeremy Gaskins & Maiying Kong, 2020. "A hierarchical mixed effect hurdle model for spatiotemporal count data and its application to identifying factors impacting health professional shortages," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1121-1144, November.
    4. Chung‐Wei Shen & Chun‐Shu Chen, 2024. "Estimation and selection for spatial zero‐inflated count models," Environmetrics, John Wiley & Sons, Ltd., vol. 35(4), June.

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