  In this article, we propose a phase I-II design in two stages for the
combination of molecularly targeted therapies. The design is motivated by a
published case study that combines a MEK and a PIK3CA inhibitors; a setting in
which higher dose levels do not necessarily translate into higher efficacy
responses. The goal is therefore to identify dose combination(s) with a
prespecified desirable risk-benefit trade-off. We propose a flexible cubic
spline to model the marginal distribution of the efficacy response. In stage I,
patients are allocated following the escalation with overdose control (EWOC)
principle whereas, in stage II, we adaptively randomize patients to the
available experimental dose combinations based on the continuously updated
model parameters. A simulation study is presented to assess the design's
performance under different scenarios, as well as to evaluate its sensitivity
to the sample size and to model misspecification. Compared to a recently
published dose finding algorithm for biologic drugs, our design is safer and
more efficient at identifying optimal dose combinations.
