  We propose a novel adaptive design for clinical trials with time-to-event
outcomes and covariates (which may consist of or include biomarkers). Our
method is based on the expected entropy of the posterior distribution of a
proportional hazards model. The expected entropy is evaluated as a function of
a patient's covariates, and the information gained due to a patient is defined
as the decrease in the corresponding entropy. Candidate patients are only
recruited onto the trial if they are likely to provide sufficient information.
Patients with covariates that are deemed uninformative are filtered out. A
special case is where all patients are recruited, and we determine the optimal
treatment arm allocation. This adaptive design has the advantage of potentially
elucidating the relationship between covariates, treatments, and survival
probabilities using fewer patients, albeit at the cost of rejecting some
candidates. We assess the performance of our adaptive design using data from
the German Breast Cancer Study group and numerical simulations of a biomarker
validation trial.
