Early phase clinical trials during drug development are vital to the success of an investigational compound. In these phases, an important goal of a dose-finding study is the determination of a dose that is safe and/or effective. Dose-finding trials based on safety outcomes are typically among the first studies conducted for any novel compound. Subsequently, another trial may be conducted to determine which dose among the range of safe doses is the most effective thereby generating a dose-effectiveness profile. When both safety and efficacy are simultaneously considered in a single trial, this is called a phase I/II trial. These trials are advantageous in that they are likely to save both time and resources. This dissertation reviews current phase I/II methods, explores key limitations of these methods, and presents an innovative approach that addresses some of these limitations. The new approaches are compared to one of the most widely known methods of this type.
A common phase I/II method is the bivariate Continual Reassessment Method (bCRM; Braun, 2002). The bCRM models dichotomous safety and effectiveness outcomes for use in dose escalation and dose selection decisions. Its overall statistical model is based upon both safety and efficacy models that assume the probabilities of these outcomes increase linearly with dose. The effects of violating the linear monotonicity assumption are explored. It is shown that there are a number of scenarios in which the bCRM performs poorly, including those where effectiveness does not increase beyond a certain dose and when the most efficacious dose is not the highest dose. This indicates that an approach where linearity is not assumed could have great value.
The generalized bivariate Continual Reassessment Method (gbCRM) framework is developed as an alternative to dose-finding methods with fixed models. With this approach, the model could be modified to fit a variety of trends that typically arise during dose-finding. It is shown that there are scenarios where the gbCRM provides major advantages when the proper models are used. However, there also exist a number of scenarios where there is an increased risk of choosing an unsafe dose when improper models are used. This study indicates that the use of statistical model selection procedures is likely to improve the performance of the gbCRM by gaining the benefits of proper model selection while avoiding some of the consequences of improper model selection. To address these concerns, an extension of the gbCRM, called the flexible bivariate Continual Reassessment Method (fbCRM), is developed. The fbCRM incorporates model selection and averaging to help make statistical decisions within the gbCRM framework. A simulation study shows that, under many scenarios, the fbCRM is vastly superior to methods with fixed models.
Finally, the bCRM, gbCRM and fbCRM are applied to data from a small clinical trial whose goal was to describe the dose-response relationship of the colonization of the Haemophilus influenzae bacterium. These methods are used to define the dose-colonization of this bacterium when applied to human subjects, and to explore how the dose escalation scheme of this trial might have differed if the fbCRM had been used.