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Optimal dose‐finding for efficacy–safety models
Author(s) -
Tsirpitzi Renata Eirini,
Miller Frank
Publication year - 2021
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.202000181
Subject(s) - optimal design , bivariate analysis , mathematical optimization , maximum tolerated dose , multivariate statistics , computer science , key (lock) , mathematics , medicine , statistics , clinical trial , computer security , pathology
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.