Modeling Throughput of Emergency Departments via Time Series: An Expectation Maximization Algorithm

In this article, the expectation maximization (EM) algorithm is applied for modeling the throughput of emergency departments via available time-series data. The dynamics of emergency department throughput is developed and evaluated, for the first time, as a stochastic dynamic model that consists of the noisy measurement and first-order autoregressive (AR) stochastic dynamic process. By using the EM algorithm, the model parameters, the actual throughput, as well as the noise intensity, can be identified simultaneously. Four real-world time series collected from an emergency department in West London are employed to demonstrate the effectiveness of the introduced algorithm. Several quantitative indices are proposed to evaluate the inferred models. The simulation shows that the identified model fits the data very well.

[1]  John Kelly,et al.  A System for Patient Management Based Discrete-Event Simulation and Hierarchical Clustering , 2006, 19th IEEE Symposium on Computer-Based Medical Systems (CBMS'06).

[2]  R. Spicer.  Targets harm patients and are destroying the English NHS , 2009, International journal of clinical practice.

[3]  W. Knottenbelt,et al.  Predicting patient arrivals to an accident and emergency department , 2009, Emergency Medicine Journal.

[4]  Geoffrey E. Hinton,et al.  Parameter estimation for linear dynamical systems , 1996 .

[5]  Armann Ingolfsson,et al.  The application of forecasting techniques to modeling emergency medical system calls in Calgary, Alberta , 2007, Health care management science.

[6]  Simon Cooper,et al.  The “4-hour target”: emergency nurses’ views , 2007, Emergency Medicine Journal.

[7]  Gwyn Bevan.  Have targets done more harm than good in the English NHS? No , 2009 .

[8]  Sara A Kreindler,et al.  Policy strategies to reduce waits for elective care: a synthesis of international evidence. , 2010, British medical bulletin.

[9]  John Bowers,et al.  Success and failure in the simulation of an Accident and Emergency department , 2009 .

[10]  F. P. Wieland,et al.  UNDERSTANDING ACCIDENT AND EMERGENCY DEPARTMENT PERFORMANCE USING SIMULATION , 2006 .

[11]  James R. Wilson,et al.  Modeling and simulating Poisson processes having trends or nontrigonometric cyclic effects , 2001, Eur. J. Oper. Res..

[12]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[13]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[14]  S. Mason,et al.  Are these emergency department performance data real? , 2006, Emergency Medicine Journal.

[15]  Jane Coughlan,et al.  Simulating the use of re-prioritisation as a wait-reduction strategy in an emergency department , 2010, Emergency Medicine Journal.

[16]  Fuwen Yang,et al.  Stochastic Dynamic Modeling of Short Gene Expression Time-Series Data , 2008, IEEE Transactions on NanoBioscience.

[17]  Zosia Kmietowicz.  Four hour targets for accident and emergency are to be scrapped , 2010, BMJ : British Medical Journal.

[18]  Ruth Davies.  “See and Treat” or “See” and “Treat” in an emergency department , 2007, 2007 Winter Simulation Conference.

[19]  Ehud Weinstein,et al.  Iterative and sequential algorithms for multisensor signal enhancement , 1994, IEEE Trans. Signal Process..

[20]  Douglas McKelvie,et al.  Coping but not coping in health and social care: masking the reality of running organisations beyond safe design capacity† , 2007 .

[21]  N. Rathlev,et al.  Time series analysis of variables associated with daily mean emergency department length of stay. , 2007, Annals of emergency medicine.

[22]  Ilan Ziskind,et al.  Maximum-likelihood localization of narrow-band autoregressive sources via the EM algorithm , 1993, IEEE Trans. Signal Process..

[23]  M Pidd,et al.  Understanding target-driven action in emergency department performance using simulation , 2009, Emergency Medicine Journal.

[24]  Roger Maull,et al.  An evaluation of ‘fast track’ in A&E: a discrete event simulation approach , 2009 .

[25]  L Mayhew,et al.  Using queuing theory to analyse the Government’s 4-h completion time target in Accident and Emergency departments , 2008, Health care management science.

[26]  Gwyn Bevan,et al.  Have targets done more harm than good in the English NHS? No , 2009, BMJ : British Medical Journal.

[27]  Zidong Wang,et al.  Inference of Nonlinear State-Space Models for Sandwich-Type Lateral Flow Immunoassay Using Extended Kalman Filtering , 2011, IEEE Transactions on Biomedical Engineering.

[28]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[29]  McCleanSally,et al.  Modeling Throughput of Emergency Departments via Time Series , 2013 .

[30]  Sarah E. Taranto,et al.  An update on a successful simulation project: the UNOS Liver Allocation Model , 2000, Winter simulation conference : proceedings.

[31]  James R. Wilson,et al.  Modeling patient arrivals in community clinics , 2008 .

[32]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.