Beyond the 3+3 method: expanded algorithms for dose- escalation in Phase I oncology trials of two agents

The number of published Phase I trials for determining a maximum tolerated combination of two agents is increasing, with a majority of those trials suffering from poor study design. A recent editorial proposed a 3+3+3 design, which takes the traditional 3+3 design used for one-agent dose-finding and adds an additional possible cohort of three patients.

To investigate the utility and performance of the 3+3+3, and more generally, A+B+C algorithmic designs, in Phase I trials of two-agent combinations and to discuss the issues related to such designs.

Operating characteristics for an A+B+C design can be computed exactly in the statistical software package R using publicly available functions created by the authors. Using those functions, six different A+B+C designs are compared in six different settings with respect to the dose-limiting toxicity rate of combinations that each design selects as the maximum tolerated combination, as well as the average total number of patients required by each design and the average number of patients assigned to each combination.

Allowing for simultaneous escalation of doses of both agents does not increase patients' exposure to overly toxic combinations, yet increases the probability of identifying the maximum tolerated combination when it occurs at higher doses of either agent, than a design that forbids simultaneous escalation. Designs in which A ≤ 3 tend to target combinations with dose-limiting toxicity rates higher than designs in which A ≥ 4.

The implicitly targeted dose-limiting toxicity rate of any given algorithmic design is not transparent, requiring computation of results under a variety of settings to help understand the operating characteristics of that design. Thus, the appropriate A+B+C design will vary from trial to trial. A+B+C designs also have 'short memory', as escalation decisions are based primarily on the most recent cohort of patients.

Algorithmic A+B+C designs are potentially useful in the design of Phase I trials of combinations of two agents. However, a head-to-head comparison to model-based designs is needed to warrant their general use.