  An individualized treatment regime (ITR) is a decision rule that assigns
treatments based on patients' characteristics. The value function of an ITR is
the expected outcome in a counterfactual world had this ITR been implemented.
Recently, there has been increasing interest in combining heterogeneous data
sources, such as leveraging the complementary features of randomized controlled
trial (RCT) data and a large observational study (OS). Usually, a covariate
shift exists between the source and target population, rendering the
source-optimal ITR unnecessarily optimal for the target population. We present
an efficient and robust transfer learning framework for estimating the optimal
ITR with right-censored survival data that generalizes well to the target
population. The value function accommodates a broad class of functionals of
survival distributions, including survival probabilities and restrictive mean
survival times (RMSTs). We propose a doubly robust estimator of the value
function, and the optimal ITR is learned by maximizing the value function
within a pre-specified class of ITRs. We establish the $N^{-1/3}$ rate of
convergence for the estimated parameter indexing the optimal ITR, and show that
the proposed optimal value estimator is consistent and asymptotically normal
even with flexible machine learning methods for nuisance parameter estimation.
We evaluate the empirical performance of the proposed method by simulation
studies and a real data application of sodium bicarbonate therapy for patients
with severe metabolic acidaemia in the intensive care unit (ICU), combining a
RCT and an observational study with heterogeneity.
