  It is increasingly common for therapies in oncology to be given in
combination. In some cases, patients can benefit from the interaction between
two drugs, although often at the risk of higher toxicity. A large number of
designs to conduct phase I trials in this setting are available, where the
objective is to select the maximum tolerated dose combination (MTC). Recently,
a number of model-free (also called model-assisted) designs have provoked
interest, providing several practical advantages over the more conventional
approaches of rule-based or model-based designs. In this paper, we demonstrate
a novel calibration procedure for model-free designs to determine their most
desirable parameters. Under the calibration procedure, we compare the behaviour
of model-free designs to a model-based approach in a comprehensive simulation
study, covering a number of clinically plausible scenarios. It is found that
model-free designs are competitive with the model-based design in terms of the
proportion of correct selections of the MTC. However, there are a number of
scenarios in which model-free designs offer a safer alternative. This is also
illustrated in the application of the designs to a case study using data from a
phase I oncology trial.
