Marginally-specified Mean Models for Counts with Mixture Distributions Public Deposited

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  • March 20, 2019
Creator
  • Benecha, Habtamu
    • Affiliation: Gillings School of Global Public Health, Department of Biostatistics
Abstract
  • Counts from heterogeneous populations are often modeled using mixture distributions. These models assume that observations are generated from multiple unobserved subpopulations and estimate parameters having latent class interpretations. When interest is to make inferences about marginal means and incidence density ratios for the effects of risk factors in the overall population, regression coefficients obtained from common mixture models do not provide direct interpretations for these population-level parameters. While indirect techniques such as the use of post-modeling transformations may be employed to estimate the marginal effects of explanatory variables of interest, there are many instances where latent class model formulations fail to fully explain relationships between covariates and population-wide parameters (Preisser et al., 2012; Long et al., 2014). First, we employ two-component mixtures of non-degenerate count data distributions to estimate the overall effects of exposure variables on marginal means of zero-inflated and other heterogeneous counts. The models are examined using simulations and further applied to a double-blind dental caries incidence trial. Next, we develop a marginalized model for bivariate zero-inflated counts that allows the estimation of parameters for the overall effects of exposure variables on the marginal means of the two correlated outcomes. The model employs four-component mixture distributions and estimates marginally interpretable regression coefficients. We demonstrate the application of the method by using simulations and dental caries indices of primary and permanent teeth among children from a school-based fluoride mouthrinse study. Finally, extending earlier approaches, we propose an estimation method for marginalized zero-inflated count models when covariates are missing at random. The method, which can also be applied to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data.
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Rights statement
  • In Copyright
Advisor
  • Herring, Amy
  • Divaris, Kimon
  • Preisser, John
  • Zeng, Donglin
  • Neelon, Brian
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2016
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