Generalized Likelihood Ratios for Understanding, Comparing and Constructing Interval Designs of Dose-Finding Studies
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Dose-finding studies 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. In this article, I propose to use generalized likelihood ratios (GLRs) to measure statistical evidence and support dose transition decisions. This 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. The GLR-based 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 four popular interval designs reveals that the BOIN and TEQR designs require similar amounts of evidence for escalation and de-escalation, while the mTPI and i3+3 designs require more evidence for de-escalation than for escalation. Simulation results demonstrate that the last two designs tend to produce higher proportions of over-treated patients than the first two. These observations motivate the consideration of GLR-based designs that require more evidence for escalation than for de-escalation. Such designs are shown to reduce the proportion of over-treated patients while maintaining the same accuracy of dose selection, as compared to the four popular interval designs.
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