Distribution-free inference of zero-inflated binomial data for longitudinal studies

Abstract

Count responses with structural zeros are very common in medical and psychosocial research, especially in alcohol and HIV research, and the zero-inflated Poisson (ZIP) and zero-inflated negative binomial models are widely used for modeling such outcomes. However, as alcohol drinking outcomes such as days of drinkings are counts within a given period, their distributions are bounded above by an upper limit (total days in the period) and thus inherently follow a binomial or zero-inflated binomial (ZIB) distribution, rather than a Poisson or ZIP distribution, in the presence of structural zeros. In this paper, we develop a new semiparametric approach for modeling ZIB-like count responses for cross-sectional as well as longitudinal data. We illustrate this approach with both simulated and real study data.

Keywords:

• bounded count response
• COMBINE Study
• distribution-free models
• generalizedestimating equations
• structural zero
• zero-inflated binomial

AMS Subject Classification:

• 62G08
• 62G20

Acknowledgements

The authors thank professors Xin Tu and Wan Tang for their constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data and research materials

Supplemental data for this article can be accessed at 10.1080/02664763.2015.1023270.

Additional information

Funding

The study was supported in part by National Institute on Drug Abuse grant [R33DA027521], National Institute of General Medical Sciences grant [R01GM108337], UR CTSI grants [8UL1TR000042-07] and [8UL1TR000042-09].