Efficacy/toxicity dose-finding using hierarchical modeling for multiple populations

Traditionally, Phase I oncology trials evaluate the safety profile of a novel agent and identify a maximum tolerable dose based on toxicity alone. With the development of biologically targeted agents, investigators believe the efficacy of a novel agent may plateau or diminish before reaching the maximum tolerable dose while toxicity continues to increase. This motivates dose-finding based on the simultaneous evaluation of toxicity and efficacy. Previously, we investigated hierarchical modeling in the context of Phase I dose-escalation studies for multiple populations and found borrowing strength across populations improved operating characteristics. In this article, we discuss three hierarchical extensions to commonly used probability models for efficacy and toxicity in Phase I-II trials and adapt our previously proposed dose-finding algorithm for multiple populations to this setting. First, we consider both parametric and non-parametric bivariate models for binary outcomes and, in addition, we consider an under-parameterized model that combines toxicity and efficacy into a single trinary outcome. Our simulation results indicate hierarchical modeling increases the probability of correctly identifying the optimal dose and increases the average number of patients treated at the optimal dose, with the under-parameterized hierarchical model displaying desirable and robust operating characteristics.