  Phase I clinical trials are designed to test the safety (non-toxicity) of
drugs and find the maximum tolerated dose (MTD). This task becomes
significantly more challenging when multiple-drug dose-combinations (DC) are
involved, due to the inherent conflict between the exponentially increasing DC
candidates and the limited patient budget. This paper proposes a novel Bayesian
design, SDF-Bayes, for finding the MTD for drug combinations in the presence of
safety constraints. Rather than the conventional principle of escalating or
de-escalating the current dose of one drug (perhaps alternating between drugs),
SDF-Bayes proceeds by cautious optimism: it chooses the next DC that, on the
basis of current information, is most likely to be the MTD (optimism), subject
to the constraint that it only chooses DCs that have a high probability of
being safe (caution). We also propose an extension, SDF-Bayes-AR, that accounts
for patient heterogeneity and enables heterogeneous patient recruitment.
Extensive experiments based on both synthetic and real-world datasets
demonstrate the advantages of SDF-Bayes over state of the art DC trial designs
in terms of accuracy and safety.
