A family of modified Huber loss functions for continual reassessment methods in clinical trials

In most Phase I dose-finding trials, the primary goal is to establish the safety of a proposed therapeutic regimen and determine its optimal dose for the subsequent phases of the trial. Methods for determining the optimal dose require improvements in terms of efficiency and cost. We propose and investigate a new family of loss functions used in the dose-finding paradigm. Our loss functions can penalize overdosing and underdosing symmetrically or asymmetrically, depending on the clinical setting under investigation. Compared with well-known dose-selection methods, our approach with symmetric penalties, selects correct doses and performs well across the spectrum of dose-escalation schemes seen in clinical settings, while requiring fewer subjects.

When our approach penalizes overdosing and underdosing differently, the simulation study shows that in certain scenarios, it is more likely to select the correct dose as the optimal dose. This advantage comes with the cost of requiring a slightly larger sample size compared to the approach penalizing overdosing and underdosing equally. The approach with asymmetric penalties performs as well as, if not better than well-known dose-selection methods while requiring fewer subjects than some of them. However, it is important to note that setting the parameter for this approach with asymmetric penalties can be intricate.

We have developed an R package (bayescrm), including a vignette, user manual, and illustrative examples, to be made available to practitioners with the hopes of disseminating these findings to a grander audience.