Dose‐finding methods for Phase I clinical trials using pharmacokinetics in small populations

The aim of phase I clinical trials is to obtain reliable information on safety, tolerability, pharmacokinetics (PK), and mechanism of action of drugs with the objective of determining the maximum tolerated dose (MTD). In most phase I studies, dose‐finding and PK analysis are done separately and no attempt is made to combine them during dose allocation. In cases such as rare diseases, paediatrics, and studies in a biomarker‐defined subgroup of a defined population, the available population size will limit the number of possible clinical trials that can be conducted. Combining dose‐finding and PK analyses to allow better estimation of the dose‐toxicity curve should then be considered. In this work, we propose, study, and compare methods to incorporate PK measures in the dose allocation process during a phase I clinical trial. These methods do this in different ways, including using PK observations as a covariate, as the dependent variable or in a hierarchical model. We conducted a large simulation study that showed that adding PK measurements as a covariate only does not improve the efficiency of dose‐finding trials either in terms of the number of observed dose limiting toxicities or the probability of correct dose selection. However, incorporating PK measures does allow better estimation of the dose‐toxicity curve while maintaining the performance in terms of MTD selection compared to dose‐finding designs that do not incorporate PK information. In conclusion, using PK information in the dose allocation process enriches the knowledge of the dose‐toxicity relationship, facilitating better dose recommendation for subsequent trials.