  Recent exploration of optimal individualized decision rules (IDRs) for
patients in precision medicine has attracted a lot of attention due to the
heterogeneous responses of patients to different treatments. In the existing
literature of precision medicine, an optimal IDR is defined as a decision
function mapping from the patients' covariate space into the treatment space
that maximizes the expected outcome of each individual. Motivated by the
concept of Optimized Certainty Equivalent (OCE) introduced originally in
\cite{ben1986expected} that includes the popular conditional-value-of risk
(CVaR) \cite{rockafellar2000optimization}, we propose a decision-rule based
optimized covariates dependent equivalent (CDE) for individualized decision
making problems. Our proposed IDR-CDE broadens the existing expected-mean
outcome framework in precision medicine and enriches the previous concept of
the OCE. Numerical experiments demonstrate that our overall approach
outperforms existing methods in estimating optimal IDRs under heavy-tail
distributions of the data.
