  In parametric Bayesian designs of early phase cancer clinical trials with
drug combinations exploring a discrete set of partially ordered doses, several
authors claimed that there is no added value in including an interaction term
to model synergism between the two drugs. In this paper, we investigate these
claims in the setting of continuous dose levels of the two agents. Parametric
models will be used to describe the relationship between the doses of the two
agents and the probability of dose limiting toxicity and efficacy. Trial design
proceeds by treating cohorts of two patients simultaneously receiving different
dose combinations and response adaptive randomization. We compare trial safety
and efficiency of the estimated maximum tolerated dose (MTD) curve between
models that include an interaction term with models without the synergism
parameter with extensive simulations. Under a selected class of dose-toxicity
models and dose escalation algorithm, we found that not including an
interaction term in the model can compromise the safety of the trial and reduce
the pointwise reliability of the estimated MTD curve.
