Bayesian ordered lattice design for Phase I clinical trials

We develop a new framework specifically for early Phase I clinical trials called Bayesian Ordered Lattice Design (BOLD). This study is motivated by two key factors. First, Phase I clinical trials typically involve relatively small sample sizes, making prior information regarding dose-limiting toxicity (DLT) highly significant. To address this challenge, the proposed Bayesian methodology incorporates prior information and posterior updating based on experimental results to guide dose selection, toxicity monitoring, early stopping, and identification of the maximum tolerable dose (MTD). Second, a natural ordering among toxicity probabilities across different dose levels can be utilized, with the idea being that analysis of dose-level posterior probabilities can and should acquire insights from data obtained at other dose levels, by leveraging their order relationship. Our proposed approach employs straightforward and intuitive dose-level Bayesian specifications and relies on intuitive and clinically interpretable toxicity-related posterior probabilities for decision making. Importantly, we show that it is either comparable to or outperforms popular methods, in terms of accuracy in determining the MTD and efficiency in number of patients needed in testing. This Bayesian approach is also computationally simple and avoids simulation.