\u201cContributions to Statistics\u201d mODa11 \u2013 Advances in Model-Oriented Design and Analysis, a cura di: J. Kunert, C.H. Muller, A.C. Atkinson, Springer (ISBN: 978-3-319-31264-4)

In recent years, there has been an increasing interest in developing dose finding methods incorporating both efficacy and toxicity outcomes. It is reasonable to assume that efficacy and toxicity are associated; therefore, we need to model their stochastic dependence. Copula functions are very useful tools to model different kinds of dependence with arbitrary marginal distributions. We consider a binary efficacy-toxicity response with logit marginal distributions. Since the dose which maximizes the probability of efficacy without toxicity (P-optimal dose) changes depending on different copula functions, we propose a criterion which is useful for choosing between the rival copula models but also protects patients against doses that are far away from the P-optimal dose. The performance of this compromise criterion (called PKL) is illustrated for different choices of the parameter values