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In parametric Bayesian designs of early phase cancer clinical trials withdrug combinations exploring a discrete set of partially ordered doses, severalauthors claimed that there is no added value in including an interaction termto model synergism between the two drugs. In this paper, we investigate theseclaims in the setting of continuous dose levels of the two agents. Parametricmodels will be used to describe the relationship between the doses of the twoagents and the probability of dose limiting toxicity and efficacy. Trial designproceeds by treating cohorts of two patients simultaneously receiving differentdose combinations and response adaptive randomization. We compare trial safetyand efficiency of the estimated maximum tolerated dose (MTD) curve betweenmodels that include an interaction term with models without the synergismparameter with extensive simulations. Under a selected class of dose-toxicitymodels and dose escalation algorithm, we found that not including aninteraction term in the model can compromise the safety of the trial and reducethe pointwise reliability of the estimated MTD curve.

Modeling synergism in early phase cancer trials with drug combination with continuous dose levels: is there an added value?