title: Zero-inflated and hurdle models of count data with extra zeros: examples from an HIV-risk reduction intervention trial.
abstract: BACKGROUND
  In clinical trials of behavioral health interventions, outcome variables often take the form of counts, such as days using substances or episodes of unprotected sex. Classically, count data follow a Poisson distribution; however, in practice such data often display greater heterogeneity in the form of excess zeros (zero-inflation) or greater spread in the values (overdispersion) or both. Greater sample heterogeneity may be especially common in community-based effectiveness trials, where broad eligibility criteria are implemented to achieve a generalizable sample.
  
  
  OBJECTIVE
  This article reviews the characteristics of Poisson model and the related models that have been developed to handle overdispersion (negative binomial (NB) model) or zero-inflation (zero-inflated Poisson (ZIP) and Poisson hurdle (PH) models) or both (zero-inflated negative binomial (ZINB) and negative binomial hurdle (NBH) models).
  
  
  METHODS
  All six models were used to model the effect of an HIV-risk reduction intervention on the count of unprotected sexual occasions (USOs), using data from a previously completed clinical trial among female patients (N = 515) participating in community-based substance abuse treatment (Tross et al. Effectiveness of HIV/AIDS sexual risk reduction groups for women in substance abuse treatment programs: Results of NIDA Clinical Trials Network Trial. J Acquir Immune Defic Syndr 2008; 48(5):581-589). Goodness of fit and the estimates of treatment effect derived from each model were compared.
  
  
  RESULTS
  The ZINB model provided the best fit, yielding a medium-sized effect of intervention.
  
  
  CONCLUSIONS
  This article illustrates the consequences of applying models with different distribution assumptions on the data. If a model used does not closely fit the shape of the data distribution, the estimate of the effect of the intervention may be biased, either over- or underestimating the intervention effect.
authors.affiliation: Department of Psychiatry, Columbia University, New York, NY, USA.
authors.forename: Mei-Chen
authors.initials: MC
authors.lastname: Hu
authors.forename: Martina
authors.initials: M
authors.lastname: Pavlicova
authors.forename: Edward V
authors.initials: EV
authors.lastname: Nunes
mesh_terms: D000328:Adult; D015982:Bias; D003153:Community Health Services; D005260:Female; D005500:Follow-Up Studies; D015658:HIV Infections / Q000517:prevention & control*; D006801:Humans; D015233:Models, Statistical; D016012:Poisson Distribution; D040242:Risk Reduction Behavior; D012309:Risk-Taking; D019966:Substance-Related Disorders / Q000534:rehabilitation*; D047568:Unsafe Sex / Q000706:statistics & numerical data*