The Impact of Estimation: A New Method for Clustering and Trajectory Estimation in Patient Flow Modeling

Abstract: The ability to accurately forecast and control inpatient census, and thereby workloads, is a critical and longstanding problem in hospital management. Majority of current literature focuses on optimal scheduling of inpatients, but largely ignores the process of accurate estimation of the trajectory of patients throughout the treatment and recovery process. The result is that current scheduling models are optimizing based on inaccurate input data. We developed a Clustering and Scheduling Integrated (CSI) approach to capture patient flows through a network of hospital services. CSI functions by clustering patients into groups based on similarity of trajectory using a novel Semi-Markov model (SMM)-based clustering scheme proposed in this paper, as opposed to clustering by admit type or condition as in previous literature. The methodology is validated by simulation and then applied to real patient data from a partner hospital where we see it outperforms current methods. Further, we demonstrate that extant optimization methods achieve significantly better results on key hospital performance measures under CSI, compared with traditional estimation approaches, increasing elective admissions by 97% and utilization by 22% compared to 30% and 8% using traditional estimation techniques. From a theoretical standpoint, the SMM-clustering is a novel approach applicable to any temporal-spatial stochastic data that is prevalent in many industries and application areas.