  Patients whose transfer to the Intensive Care Unit (ICU) is unplanned are
prone to higher mortality rates than those who were admitted directly to the
ICU. Recent advances in machine learning to predict patient deterioration have
introduced the possibility of \emph{proactive transfer} from the ward to the
ICU. In this work, we study the problem of finding \emph{robust} patient
transfer policies which account for uncertainty in statistical estimates due to
data limitations when optimizing to improve overall patient care. We propose a
Markov Decision Process model to capture the evolution of patient health, where
the states represent a measure of patient severity. Under fairly general
assumptions, we show that an optimal transfer policy has a threshold structure,
i.e., that it transfers all patients above a certain severity level to the ICU
(subject to available capacity). As model parameters are typically determined
based on statistical estimations from real-world data, they are inherently
subject to misspecification and estimation errors. We account for this
parameter uncertainty by deriving a robust policy that optimizes the worst-case
reward across all plausible values of the model parameters. We show that the
robust policy also has a threshold structure under fairly general assumptions.
Moreover, it is more aggressive in transferring patients than the optimal
nominal policy, which does not take into account parameter uncertainty. We
present computational experiments using a dataset of hospitalizations at 21
KNPC hospitals, and present empirical evidence of the sensitivity of various
hospital metrics (mortality, length-of-stay, average ICU occupancy) to small
changes in the parameters. Our work provides useful insights into the impact of
parameter uncertainty on deriving simple policies for proactive ICU transfer
that have strong empirical performance and theoretical guarantees.
