PKL-Optimality Criterion in Copula Models for Efficacy-Toxicity Response

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