title: On performance of parametric and distribution-free models for zero-inflated and over-dispersed count responses.
abstract: Zero-inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero-inflated count responses. These models extend the Poisson and negative binomial (NB) to address excessive zeros in the count response. By adding a degenerate distribution centered at 0 and interpreting it as describing a non-risk group in the population, the ZIP (ZINB) models a two-component population mixture. As in applications of Poisson and NB, the key difference between ZIP and ZINB is the allowance for overdispersion by the ZINB in its NB component in modeling the count response for the at-risk group. Overdispersion arising in practice too often does not follow the NB, and applications of ZINB to such data yield invalid inference. If sources of overdispersion are known, other parametric models may be used to directly model the overdispersion. Such models too are subject to assumed distributions. Further, this approach may not be applicable if information about the sources of overdispersion is unavailable. In this paper, we propose a distribution-free alternative and compare its performance with these popular parametric models as well as a moment-based approach proposed by Yu et al. [Statistics in Medicine 2013; 32: 2390-2405]. Like the generalized estimating equations, the proposed approach requires no elaborate distribution assumptions. Compared with the approach of Yu et al., it is more robust to overdispersed zero-inflated responses. We illustrate our approach with both simulated and real study data.
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, U.S.A.
authors.forename: Wan
authors.initials: W
authors.lastname: Tang
authors.affiliation: Department of Management, Harbin Institute of Technology, Harbin, China.
authors.forename: Naiji
authors.initials: N
authors.lastname: Lu
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, U.S.A.
authors.forename: Tian
authors.initials: T
authors.lastname: Chen
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, U.S.A.
authors.forename: Wenjuan
authors.initials: W
authors.lastname: Wang
authors.affiliation: Center for Health Care Research & PolicyCase Western Reserve University, Cleveland, OH, U.S.A.
authors.forename: Douglas David
authors.initials: DD
authors.lastname: Gunzler
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, U.S.A.
authors.forename: Yu
authors.initials: Y
authors.lastname: Han
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY, U.S.A.|Department of PsychiatryUniversity of Rochester, Rochester, NY, U.S.A.|Center of Excellence for Suicide PreventionCanandaigua VA Medical Center, Canandaigua, NY, U.S.A.
authors.forename: Xin M
authors.initials: XM
authors.lastname: Tu
mesh_terms: D016010:Binomial Distribution; D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D015658:HIV Infections / Q000523:psychology; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D015233:Models, Statistical; D016012:Poisson Distribution; D016032:Randomized Controlled Trials as Topic
keywords: functional response models; generalized estimating equations; population mixtures; zero-inflated Poisson; zero-inflated Poisson with random effects; zero-inflated negative binomial