A continuous-time Markov model for estimating readmission risk for hospital inpatients

Research concerning hospital readmissions has mostly focused on statistical and machine learning models that attempt to predict this unfortunate outcome for individual patients. These models are useful in certain settings, but their performance in many cases is insufficient for implementation in practice, and the dynamics of how readmission risk changes over time is often ignored. Our objective is to develop a model for aggregated readmission risk over time - using a continuous-time Markov chain - beginning at the point of discharge. We derive point and interval estimators for readmission risk, and find the asymptotic distributions for these probabilities. Finally, we validate our derived estimators using simulation, and apply our methods to estimate readmission risk over time using discharge and readmission data for surgical patients.