A major component of quantitative risk assessment involves dose-response modeling. Therein, an appropriate statistical model that approximately quantifies the relationship between exposure level (dose) and response (adverse endpoint) is fit to experimental data. The objective of this dissertation is to estimate adverse risks encountered in settings when the statistical model is formally defined and developed. From this, statistical inferences on the risk are conducted.;First introduced are eight parametric models. The advantage of parametric models is they can produce consistent result when the selected model fits the dose-response curve very well. The simplicity of knowing the expression of these models allows for the construction of a variety of lower confidence limits, based on the Wald approach.;However, if the true dose-response curve deviates significantly from a posited parametric model, the result may perform poorly. Non-parametric methods are then needed. The percentile bootstrap method from linear splines with Pool Adjacent Violator is first introduced. The method appeals to an asymptotic approximation, hence there is interest in assessing the small-sample coverage properties of this method. These are addressed via Monte Carlo computer simulations. We find that this method with four doses operates reasonably well at large sample sizes except for the concave increasing dose-response curve. In practice, small sample sizes are more common, therefore we turn to increasing the number of doses. We do see that, in general, the coverage becomes better as the doses number increases.;To study the most common four dose design, the biased-corrected and accelerated bootstrap method from linear spline with Pool Adjacent Violator and discrete delta approach are also introduced. Simulation results show that the coverage are similar from these methods and have no improvement over the concave increasing dose-response curve.;A final quadratic spline is then considered. For four doses design, this is repeated at four different points, to find an averaged extra risk function. In order to understand the operating characteristics of the method, another Monte Carlo simulation study is undertaken. This study produces similar results to those found using the percentile bootstrap method from linear splines.
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