Implementation of maximin efficient designs in dose-finding studies

An equivalence theorem for design optimality with respect to a multi-objective criterion

Maxi-min efficiency criteria are a kind of multi-objective criteria, since they enable us to take into consideration several tasks expressed by different component-wise criteria. However, they are difficult to manage because of their lack of differentiability. As a consequence, maxi-min efficiency designs are frequently built through heuristic and ad hoc algorithms, without the possibility of checking for their optimality. The main contribution of this study is to prove that the maxi-min efficiency optimality is equivalent to a Bayesian criterion, which is differentiable. In addition, we provide an analytic method to find the prior probability associated with a maxi-min efficient design, making feasible the application of the equivalence theorem. Two illustrative examples show how the proposed theory works.

Optimal dose-finding for efficacy-safety models

Dose-finding is an important part of the clinical development of a new drug. The purpose of dose-finding studies is to determine a suitable dose for future development based on both efficacy and safety. Optimal experimental designs have already been used to determine the design of this kind of studies, however, often that design is focused on efficacy only. We consider an efficacy-safety model, which is a simplified version of the bivariate Emax model. We use here the clinical utility index concept, which provides the desirable balance between efficacy and safety. By maximizing the utility of the patients, we get the estimated dose. This desire leads us to locally c -optimal designs. An algebraic solution for c -optimal designs is determined for arbitrary c vectors using a multivariate version of Elfving's method. The solution shows that the expected therapeutic index of the drug is a key quantity determining both the number of doses, the doses itself, and their weights in the optimal design. A sequential design is proposed to solve the complication of parameter dependency, and it is illustrated in a simulation study.