For nonnegative count responses in health services research, a large proportion of zero counts are frequently encountered. For such data, the frequency of zero counts is typically larger than its expected counterpart under the classical parametric models, such as Poisson or negative binomial model. In this thesis, a semiparametric zero-inflated regression model is proposed for count data that directly relates covariates to the marginal mean response representing the desired target of inference. The model specifically assumes two semiparametric forms: the log-linear form for the marginal mean and the logistic-linear form for the susceptible probability, in which the fully linear models are replaced with partially linear link functions. A spline-based estimation is proposed for the nonparametric components of the model. Asymptotic properties are discussed for the estimators of the parametric and nonparametric components of the models. Specifically, the estimators are shown to be strong consistent and asymptotically efficient under mild regularity conditions. A bootstrap hypothesis test is performed to evaluate difference involving the nonparametric component. Simulation studies are conducted to evaluate the finite sample performance of the model. Finally, the model is applied to dental caries indices in low income African-American children to evaluate the nonlinear effects of sugar intake on caries development. The conclusion shows that the effect of sugar intake on caries indices is nonlinear, especially among young children under the age of 2. And children whose caregivers are unemployed and have poor oral healthy exhibit higher dental caries rates.
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