Designing a Forecasting Model for Inpatient Occupancy in Middlemore Hospital, Auckland
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Background Occupancy is a primary factor of resource use in hospitals. Fluctuations in occupancy complicate decisions related to staffing and bed management; they also have a direct impact on both quality of patient care and staffing cost (Littig & Isken, 2007). The demand for health services has increased in Middlemore Hospital (Auckland, New Zealand) in recent years. It is observed that an accurate forecast for future demand helps with proper decision making and assists with the efficient management of staff and resources to meet workload and improve patient care and staffing job satisfaction. There is no denying the uncertainties in future demand but some key variables that drive demand for health‐care services in Middlemore Hospital can be identified, and the relationships among these variables can be quantified and projected. An accurate future occupancy forecasting tool is a critical element in the planning process; it can also help Middlemore Hospital management to understand the key variables that underlie inpatient occupancy within a particular service area and how and why these variables might change over time. Purpose The purpose of this research is to apply state‐of‐the‐art techniques to an existing issue at Middlemore Hospital. It is not envisaged that new methodological knowledge will be created; rather, it is expected that a model will be produced, that may eventually be used at Middlemore and elsewhere to forecast occupancy. The predictive model is to be adapted to each service of the hospital and to be based on historical occupancy data. Method The approach that we have taken is a Bayesian Multivariate Dynamic Autoregressive Model implemented by Markov chain Monte Carlo (MCMC) sampling. The software platforms used are the R environment for pre‐processing of the data and post‐processing of the MCMC results, and Stan, via the rstan package, for encoding the model and carrying out the MCMC sampling. The Bayesian model uses daily historical data from the previous 3 years and involves variables of several types to forecast daily occupancy alongside daily numbers of admissions and the Average length of stay, collectively called Patient‐flow variables. Variable selection for model building was based on the relationships among different factors that drive Patient‐flow variable demand for a particular specialty using visual assessment and frequentist autoregressive models. Aside from historical Patient‐flow variable data, the models potentially account for annual and weekday patterns and other cyclical trends, weather fluctuations, annual growth rate, public holidays, school holidays and any special event such as Christmas or Easter period to extrapolate future demand for hospital inpatient beds for the forecast periods of one‐month, three‐month and six‐month durations. Results Our work shows that Bayesian forecasting is feasible for predicting occupancy for both short‐term and long‐term periods. The generic model we developed in this project can be used to forecast occupancy for each specialty or service in Middlemore Hospital or elsewhere. The model is flexible in that the addition of new variables involves simple modifications to the code, and removing variables from the model can be done using control data without recoding. Amongst future variables to be investigated are the numbers of staff scheduled for the shift or the day in the wards concerned. The model also provides an account of the forecast uncertainty by constructing credibility intervals for the predicted Patient‐flow variables. The current forecasting system, CapPlan, does not provide any measure of uncertainty in the prediction. In addition to these, the model can predict the annual growth rate based on historical data, which is a more reliable approach than the informal guesses that were provided as input to the current forecasting system. Conclusion By the model presented in this paper, we can forecast quite satisfactory daily occupancy of Middlemore Hospital by the composition of various variables that identified are effective. The credible intervals produced by the model are useful to define minimum and maximum resource requirement for the future in a risk management setting. Full implementation of a specialty‐level occupancy forecasting system would require reasonably powerful parallel computing resources and an investigation into the determinants of Patient‐flow variables in the specialties not covered by the present work.