A Likelihood Perspective on Dose‐Finding Study Designs in Oncology

Dose-finding studies in oncology often include an up-and-down dose transition rule that assigns a dose to each cohort of patients based on accumulating data on dose-limiting toxicity (DLT) events. In making a dose transition decision, a key scientific question is whether the true DLT rate of the current dose exceeds the target DLT rate, and the statistical question is how to evaluate the statistical evidence in the available DLT data with respect to that scientific question. This article introduces generalized likelihood ratios (GLRs) that can be used to measure statistical evidence and support dose transition decisions. Applying this approach to a single-dose likelihood leads to a GLR-based interval design with three parameters: the target DLT rate and two GLR cut-points representing the levels of evidence required for dose escalation and de-escalation. This design gives a likelihood interpretation to each existing interval design and provides a unified framework for comparing different interval designs in terms of how much evidence is required for escalation and de-escalation. A GLR-based comparison of commonly used interval designs reveals important differences and motivates alternative designs that reduce over-treatment while maintaining MTD estimation accuracy. The GLR-based approach can also be applied to a joint likelihood based on a nonparametric (e.g., isotonic regression) model or a parametric model. Simulation results indicate that the isotonic GLR performs similarly to the single-dose GLR but the GLR based on a parsimonious model can improve MTD estimation when the underlying model is correct.