The importance of loss functions: A note on the evolution of the Toxicity Probability Interval design

The Toxicity Probability Interval Design by Ji et al. (2007), which was subsequently modified by the mTPI (Ji et al., 2010), proposed a more efficient approach to early-phase dose-finding than conventional designs like 3 + 3. Subsequent authors reported issues with the method, finding that it tends to stay at a dose level when clinical intuition would suggest the toxicity level warrants decrease. Several iterations of refinement proceeded in an effort to address these issues, including the mTPI-2 and the keyboard method, as well as alternative approaches such as the BOIN. This author suggests the reason for these safety issues involves the underlying loss function. The TPI and mTPI used the identify function defined over wide intervals. As explained in this paper, this function and its domain can be problematic as a model of patients' loss experience. Later refinements moved the loss function closer to one more consistent with clinical intuition, and this explains their improved safety performance. Greater attention to quality as defined by fitness for use, including early evaluation of patient-experience and clinical-intuition implications of proposed loss functions, may improve future design efforts.