  For many years Phase I and Phase II clinical trials were conducted
separately, but there was a recent shift to combine these Phases. While a
variety of Phase~I/II model-based designs for cytotoxic agents were proposed in
the literature, methods for molecularly targeted agents (TA) are just starting
to develop. The main challenge of the TA setting is the unknown dose-efficacy
relation that can have either an increasing, plateau or umbrella shape. To
capture these, approaches with more parameters are needed to model the
dose-efficacy relationship or, alternatively, more orderings of the
dose-efficacy relationship are required to account for the uncertainty in the
curve shape. As a result, designs for more complex clinical trials, for
example, trials looking at schedules of a combination treatment involving TA,
have not been extensively studied yet. We propose a novel regimen-finding
design which is based on a derived efficacy-toxicity trade-off function. Due to
its special properties, an accurate regimen selection can be achieved without
any parametric or monotonicity assumptions. We illustrate how this design can
be applied in the context of a complex combination-schedule clinical trial. We
discuss practical and ethical issues such as coherence, delayed and missing
efficacy responses, safety and futility constraints.
