Optimal design of clinical trials with biologics using dose-time-response models

Biologics, in particular monoclonal antibodies, are important therapies in serious diseases such as cancer, psoriasis, multiple sclerosis, or rheumatoid arthritis. While most conventional drugs are given daily, the effect of monoclonal antibodies often lasts for months, and hence, these biologics require less frequent dosing. A good understanding of the time-changing effect of the biologic for different doses is needed to determine both an adequate dose and an appropriate time-interval between doses. Clinical trials provide data to estimate the dose-time-response relationship with semi-mechanistic nonlinear regression models. We investigate how to best choose the doses and corresponding sample size allocations in such clinical trials, so that the nonlinear dose-time-response model can be precisely estimated. We consider both local and conservative Bayesian D-optimality criteria for the design of clinical trials with biologics. For determining the optimal designs, computer-intensive numerical methods are needed, and we focus here on the particle swarm optimization algorithm. This metaheuristic optimizer has been successfully used in various areas but has only recently been applied in the optimal design context. The equivalence theorem is used to verify the optimality of the designs. The methodology is illustrated based on results from a clinical study in patients with gout, treated by a monoclonal antibody.