Robustness of Proactive Intensive Care Unit Transfer Policies

Patients whose transfer to the intensive care unit (ICU) is unplanned are prone to higher mortality rates and longer length of stay. Recent advances in machine learning to predict patient deterioration have introduced the possibility of proactive transfer from the ward to the ICU. In this work, we study the problem of finding robust patient transfer policies that account for the important problem of uncertainty in statistical estimates because of 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. This is an important issue, which can lead to choosing significantly suboptimal policies. 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 are able to show that the robust policy also has a threshold structure under fairly general assumptions and that 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 data set of hospitalizations at 21 Kaiser Permanente Northern California hospitals and present empirical evidence of the sensitivity of various hospital metrics (mortality, length of stay, and average ICU occupancy) to small changes in the parameters. Although threshold policies are a simplification of the actual complex sequence of decisions leading (or not) to a transfer to the ICU, 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.