Adaptive dose-finding in two-dimensions: A phase 1 oncology example
AstraZeneca, Cheshire, UK
Cytotoxins are widely used in combination, despite similar toxicities, for example in the bone marrow or gastronintestinal tract. Finding an optimal dose in terms of toxicity with a single drug (one dimension) has proven to be far from simple, due to the ethical limitations on the trial design and complexities of dealing with noisy data concerning multiple-organ systems. The traditional Markov-style scheme used in one dimension has limitations, however uptake of continual reassessment methodologies has been slow. Further challenges arise in finding the optimal combination of doses for two or more agents. The typical approach of "collapsing" the two-dimensional problem into a one-dimensional series of ordered dose may not find the optimal balance of toxicity and efficacy. The application of adaptive designs in two dimensions requires explicit consideration of the toxicity and efficacy surfaces that are a function of dose of each drug and requires that we unmask several critical assumptions, particularly concerning synergy. A simple mathematical framework applicable to the incidence of DLTs is described and its limitations highlighted. This relatively simple model allows the application of a CRM-style dose finding scheme in more than one dimension, and some illustrative simulations help to assess performance. Practical aspects of adaptive designs are also considered, including elicitation of sensible priors and description within a protocol. Finally, an example of the successful application of this methodology at the University of Newcastle is presented, along with lessons learned. Approaches to extending the model, for example with biomarkers of toxicity or efficacy, are also discussed.