Covariate-adjusted ROC regressions and the extensions in trend tests.

In 2008 the faculty and doctoral graduate students within the Department of Statistical Sciences at Baylor University met with statisticians from Eli Lilly and Company to discuss ongoing long-term problems with the possibility that the department would begin collaborative work with the Lilly statisticians. One such problem led to several doctoral dissertations over the subsequent 8-10 years. The initial approach made use of the area under (AUC) the receiver operating characteristic (ROC) curve's diagnostic ability as a binary classifier for continuous outcomes. A generalized linear model (GLM) framework enabled one to investigate covariate effects to model the ROC using parametric and semi-parametric regression methods. The latest addition to this ongoing investigation into problems of this type made use of the beta regression for placement values and the property that their CDF is the ROC curve. The underlying motivation for the dissertation is to revisit the previous work using various models with the AUC and ROC regression with beta regression using covariate-adjusted placement values. The parametric and beta regression ROC models are introduced in Chapter Two. Both methods were applied to clinical data with different combinations of covariate effects. An extension of the ROC regression methods to the Jonckheere trend test is presented in Chapter Three. A further extension of the ROC regression models to determining the minimum effective dose is presented in Chapter Four, where the parametric and beta regression approaches were compared through a simulation study. Chapter Five applied ROC regression in three real clinical studies: incontinence data, pancreatic data, and breast cancer data. The beta ROC regression and parametric methodology were compared using the real data examples.