Clustering inter-arrival time of health care encounters for high utilizers

Patients with a large number of health care encounters receive great attention in health care research because their expensive and problematic health care utilization has important implications for the US health care system. The large volume of emergency department (ED) visits and inpatient hospital stays through time provides a unique opportunity to apply data-driven methods for identifying temporal signals associated with these patients. The micro variations in the inter-arrival time of these encounters within this population are not well-studied. Computational approaches for distinguishing various temporal visiting patterns leads to the problem of efficiently clustering asynchronous time series. Thus, we propose a Wasserstein distance based spectral clustering for this problem. Asynchronous time series are first represented as histograms of inter-arrival time and their pairwise similarities are computed under Wasserstein distance. Spectral clustering operates on the similarity matrix as input thereby avoiding the computational bottleneck of Wasserstein barycenters. The effectiveness of this method is demonstrated by synthetic data and application to a large real world health insurance encounters dataset, identifying potential associations between temporal visiting patterns and health factors from a population of frequent ED and inpatient hospital users.