Optimized adaptive enrichment designs

Based on a Bayesian decision theoretic approach, we optimize frequentist single- and adaptive two-stage trial designs forthe development of targeted therapies, where in addition to an overall population, a pre-defined subgroup is investigated.In such settings, the losses and gains of decisions can be quantified by utility functions that account for the preferences ofdifferent stakeholders. In particular, we optimize expected utilities from the perspectives both of a commercial sponsor,maximizing the net present value, and also of the society, maximizing cost-adjusted expected health benefits of a newtreatment for a specific population. We consider single-stage and adaptive two-stage designs with partial enrichment,where the proportion of patients recruited from the subgroup is a design parameter. For the adaptive designs, we use adynamic programming approach to derive optimal adaptation rules. The proposed designs are compared to trials whichare non-enriched (i.e. the proportion of patients in the subgroup corresponds to the prevalence in the underlyingpopulation). We show that partial enrichment designs can substantially improve the expected utilities. Furthermore,adaptive partial enrichment designs are more robust than single-stage designs and retain high expected utilities even if theexpected utilities are evaluated under a different prior than the one used in the optimization. In addition, we find thattrials optimized for the sponsor utility function have smaller sample sizes compared to trials optimized under the societalview and may include the overall population (with patients from the complement of the subgroup) even if there issubstantial evidence that the therapy is only effective in the subgroup