Optimal designs for dose-escalation trials and individual allocations in cohorts

Dose escalation trials are crucial in the development of new pharmaceutical products to optimize the amount of drug administered while avoiding undesirable side effects. We adopt the framework established by Bailey (2009) where the individuals are grouped into cohorts, to the subjects in which the placebo or previously defined doses are administered and responses measured. Successive cohorts allow testing higher doses of drug if negative responses have not been observed in earlier cohorts.We propose Mixed Integer Nonlinear Programming formulations for systematically computing optimal experimental designs for dose escalation.We demonstrate its application with i. different optimality criteria; ii. standard and extended designs; and iii. non-constrained (or traditional), strict halving and uniform halving designs. Additionally, we address the allocation of the individuals in a cohort considering previously known prognostic factors. To handle the problem we propose i. an enumerative algorithm; and ii. a Mixed Integer Nonlinear Programming formulation.We demonstrate the application of the enumeration scheme for allocating individuals on an individual arrival basis, and of the latter formulation for allocation on a within cohort basis.