Modeling the Length of Stay of Respiratory Patients in Emergency Department Using Coxian Phase-Type Distributions With Covariates

Variability and unpredictability are typical features of emergency departments (EDs) where patients randomly arrive with diverse conditions. Patient length of stay (LOS) represents the consumption level of hospital resources, and it is positively skewed and heterogeneous. Both accurate modeling of patient ED LOS and analysis of potential blocking causes are especially useful for patient scheduling and resource management. To tackle the uncertainty of ED LOS, this paper introduces two methods: statistical modeling and distribution fitting. The models are applied to 894 respiratory diseases patients data in the year 2014 from ED of a Chinese public tertiary hospital. Covariates recorded include patient region, gender, age, arrival time, arrival mode, triage category, and treatment area. A Coxian phase-type (PH) distribution model with covariates is proposed as an alternative method for modeling ED LOS. The expectation-maximization (EM) algorithm is used to implement parameter estimation. The results show that ED LOS data can be modeled well by the proposed models. Distributions of ED LOS differ significantly with respect to patients’ gender, arrival mode, and treatment area. Using the fitted Coxian PH model will assist ED managers in identifying patients who are most likely to have an extreme ED LOS and in predicting the forthcoming workload for resources.

[1]  Li Luo,et al.  Characteristics of patients who leave the emergency department without being seen: The first report in China , 2014, Emergency medicine Australasia : EMA.

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

[3]  S. Mahapatra,et al.  Pairing emergency severity index5-level triage data with computer aided system design to improve emergency department access and throughput , 2003, Proceedings of the 2003 Winter Simulation Conference, 2003..

[4]  D. Aronsky,et al.  Systematic review of emergency department crowding: causes, effects, and solutions. , 2008, Annals of emergency medicine.

[5]  Yingkang Shi,et al.  Sequence-Dependent Anesthesia-Controlled Times: A Retrospective Study in an Ophthalmology Department of a Single-Site Hospital , 2014, Anesthesia and analgesia.

[6]  M. Cooke,et al.  The effect of a separate stream for minor injuries on accident and emergency department waiting times , 2002, Emergency medicine journal : EMJ.

[7]  R. Beveridge,et al.  CAEP issues. The Canadian Triage and Acuity Scale: a new and critical element in health care reform. Canadian Association of Emergency Physicians. , 1998, The Journal of emergency medicine.

[8]  Christos Vasilakis,et al.  Modelling nationwide hospital length of stay: opening the black box , 2005, J. Oper. Res. Soc..

[9]  Sally McClean,et al.  Analysing data on lengths of stay of hospital patients using phase‐type distributions , 1999 .

[10]  P R Harper,et al.  Mathematical modelling and simulation for planning critical care capacity * , 2003, Anaesthesia.

[11]  Kwai-Sang Chin,et al.  A medical procedure-based patient grouping method for an emergency department , 2014, Appl. Soft Comput..

[12]  A. Andersson,et al.  Triage in the emergency department--a qualitative study of the factors which nurses consider when making decisions. , 2006, Nursing in critical care.

[13]  Paula Tanabe,et al.  Emergency Severity Index version 4: clarifying common questions. , 2007, Journal of emergency nursing: JEN : official publication of the Emergency Department Nurses Association.

[14]  Mark Fackrell,et al.  Modelling healthcare systems with phase-type distributions , 2009, Health care management science.

[15]  Houcai Shen,et al.  Inventory rationing in a make-to-stock system with batch production and lost sales , 2014 .

[16]  A. H. Marshalla,et al.  Conditional phase-type distributions for modelling patient length of stay in hospital , 2003 .

[17]  Ken Hillman,et al.  Access block and emergency department overcrowding , 2011, Critical care.

[18]  Adele H. Marshall,et al.  Using the hidden Markov model to capture quality of care in Lombardy geriatric wards , 2015 .

[19]  L. Lind,et al.  A systematic review of triage-related interventions to improve patient flow in emergency departments , 2011, Scandinavian journal of trauma, resuscitation and emergency medicine.

[20]  Adele H Marshall,et al.  Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital , 2004, Health care management science.

[21]  Joseph C. Gardiner,et al.  Modeling heavy-tailed distributions in healthcare utilization by parametric and Bayesian methods , 2012 .

[22]  Paul Robert Harper,et al.  Modelling for the planning and management of bed capacities in hospitals , 2002, J. Oper. Res. Soc..

[23]  Anthony N. Pettitt,et al.  A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean , 2009, Comput. Stat. Data Anal..

[24]  J. Wiler,et al.  Optimizing emergency department front-end operations. , 2010, Annals of emergency medicine.

[25]  Zhehui Luo,et al.  Modeling hospital length of stay by Coxian phase‐type regression with heterogeneity , 2012, Statistics in medicine.

[26]  Adele H. Marshall,et al.  Modelling the Length of Stay of Geriatric Patients in Emilia Romagna Hospitals Using Coxian Phase-Type Distributions with Covariates , 2014 .

[27]  Karin V Rhodes,et al.  A conceptual model of emergency department crowding. , 2003, Annals of emergency medicine.

[28]  D. Cox.  A use of complex probabilities in the theory of stochastic processes , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[29]  Elizabeth A Henneman,et al.  Emergency department patients who stay more than 6 hours contribute to crowding. , 2010, The Journal of emergency medicine.

[30]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .