International Journal of Statistics in Medical Research, 2013, 2, 55-66 55 E-ISSN: 1929-6029/13 © 2013 Lifescience Global Development and Validation of Models to Predict Hospital Admission for Emergency Department Patients Bin Xie 1,2,* 1 Department of Obstetrics & Gyneocology; 2 Department of Epidemiology & Biostatistics, University of Western Ontario, Ontario, Canada Abstract: Background: Boarding, or patients waiting to be admitted to hospital, has been shown as a significant contributing factor at overcrowding in emergency departments (ED). Predicting hospital admission at triage has been proposed as having the potential to help alleviate ED overcrowding. The objective of this paper is to develop and validate a model to predict hospital admission at triage to help alleviate ED overcrowding. Methods: Administrative records between April 1, 2010 and November 31, 2010 in an adult ED were used to derive and validate two prediction models, one based on Coxian phase type distribution (the PH model), the other based on logistic regression. Separate data sets were used for model development (data between April 1, 2010 and July 31, 2010) and validation (data between August 1, 2010 and November 31, 2010). Results: There were a total of 14,542 ED visits and 2,602 (17.89%) hospital admissions in the derivation cohort. In both models, acuity levels, model of arrival, and main reason of the visit are strong predictors of hospital admission; number of patients at the ED, as well as gender, are also predictors, albeit with ORs closer to 1. Patient age and timing of visits are not strong predictors. The PH model has an AUC of 0.89 compared with AUC of 0.83 for logistic regression model; with a cut- off value of 0.50, the PH model correctly predicted 86.3% of visits, compared to 84.4% for the logistic regression model. Results of the validation cohort were similar: the PH model has an AUC of 0.88, compared to AUC of 0.83 for the logistic model. Conclusions: PH and logistic models can be used to provide reasonably accurate prediction of hospital admission for ED patients, with the PH model offering more accurate predictions. Keywords: Hospital admission, Emergency department, Wait times, Overcrowding, Coxian phase type distribution. 1. BACKGROUND Lengthy wait times and overcrowding at emergency departments (ED) have been a serious problem in many communities [1-4]. Consequences for such lengthy wait times and overcrowding include decreased patient satisfaction [4, 5], increased patient morbidity and mortality [6-9], and increased costs [9, 10]. Many measures have been proposed or attempted to address this issue, with various degrees of success [1, 3, 9]. It has been shown that boarding, or the holding up of ED resources by patients waiting for hospital beds to be admitted, is a major contributor of ED overcrowding [11], as boarding reduces the overall throughput of the ED and negatively impact patient outcomes [12-14]. To minimize the negative impacts of boarding, it has been suggested that predicting hospital admission at the time of triage to enable advanced planning could help manage ED resources more effectively [15, 16]. A variety of approaches have been reported in the literature to predict hospital admission for ED patients, *Address correspondence to this author at the Room E2-620B, LHSC-VH, 800 Commissioners Road East, London, Ontario, N6A 5W9, Canada; Tel: +1 519- 685-8500-55174; Fax: +1 519-685-8176; E-mail: bxie5@uwo.ca including statistical models based on logistic regression [15, 17, 18], artificial intelligence models such as bayesian network or artificial neural network models [12, 16, 19], or human prediction by staff [20-24]. The literature reported mixed performances of these approaches, [15, 17, 20-25], with some studies reported impressive performance using statistics such as area under curve (AUC) statistics for receiver operating characteristic (ROC) curve [15, 17], and other studies reported less impressive results [20-25]. Statistical models that increase the accuracy of admission prediction can therefore enhance the practical values of models currently in the literature. One potential way to increase accuracy is to utilize information on the process under which patients went through the EDs by using models based on Coxian phase-type distributions (hereafter referred to as PH distributions). PH distributions are a special type of Markov chain model that describes duration until an event occurs in terms of a process consisting of a sequence of latent phases [9, 26]. These distributions have the ability to model probabilities of transition from one phase to another as well as probabilities of absorption from various phases, and have been used in various healthcare settings and have been shown to offer