  Targeted therapies on the basis of genomic aberrations analysis of the tumor
have shown promising results in cancer prognosis and treatment. Regardless of
tumor type, trials that match patients to targeted therapies for their
particular genomic aberrations have become a mainstream direction of
therapeutic management of patients with cancer. Therefore, finding the
subpopulation of patients who can most benefit from an aberration-specific
targeted therapy across multiple cancer types is important. We propose an
adaptive Bayesian clinical trial design for patient allocation and
subpopulation identification. We start with a decision theoretic approach,
including a utility function and a probability model across all possible
subpopulation models. The main features of the proposed design and population
finding methods are that we allow for variable sets of covariates to be
recorded by different patients, adjust for missing data, allow high order
interactions of covariates, and the adaptive allocation of each patient to
treatment arms using the posterior predictive probability of which arm is best
for each patient. The new method is demonstrated via extensive simulation
studies.
