| 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.{09}The objective of this dissertation is to estimate adverse risks encountered in settings when the statistical model is formally defined and developed. From this, simultaneous statistical inferences on the risk are conducted.; The first model for risk is a two-parameter Abbott-adjusted model. The simplicity of this model allows for the construction of a variety of simultaneous confidence bands, based on a Wald approach, a likelihood ratio approach, and three bootstrap approaches. Each method appeals to an asymptotic approximation, hence there is interest in assessing the small-sample coverage properties of the various methods. These are addressed via Monte Carlo computer simulations. We find that all our methods operate reasonably well at large sample sizes. In practice, small sample sizes are more common, and in this case the likelihood ratio method appears to exhibit the greatest level of stability.; While the simplicity of the two-parameter model offers a wide variety of inferences, the model itself may not provide sufficient flexibility to fit some datasets properly. Thus, we studied a more complicated, Abbott-adjusted Weibull model. Inferences on the extra risk and the benchmark dose were performed using a Scheffe-style confidence band on the extra risk, which again appeals to an asymptotic approximation. After undertaking a Monte Carlo simulation study, it was found that the Scheffe-style confidence band produces conservative results.; A final Abbot-adjusted model was introduced based on the Logistic growth curve. We proceeded with inferences on the extra risk and benchmark dose by again appealing to a Scheffe-style simultaneous confidence band on the extra risk. In order to understand the operating characteristics of the method, another Monte Carlo simulation study was undertaken. This study produced similar results to those found using the Abbott-adjusted Weibull model. |
