Precision medicine relies on the idea that only a subpopulation of patients are sensitive to a targeted agent and thus may benefit from it. In practice, based on pre-clinical data, it often is assumed that the sensitive subpopulation is known and the agent is substantively efficacious in that subpopulation. Subsequent patient data, however, often show that one or both of these assumptions are false. This paper provides a Bayesian randomized group sequential enrichment design to compare an experimental treatment to a control based on survival time. Early response is used as an ancillary outcome to assist with adaptive variable selection, enrichment, and futility stopping. A simulation study shows that the proposed design accurately identifies a sensitive subpopulation if it exists, yields much higher power than a conventional group sequential design, and is robust.