Data analysis and modeling of patient flow in emergency services in hospitals

Abstract

[eng] We have at our disposal the emergency department’s data from the public hospitals of Balearic Islands thanks to an agreement with the ’Conselleria de Salut’ and ’Universitat de les Illes Balears’. Our work is divided in two different parts. The first part consists of an analysis of the patterns found in the arrival and disclosure times of patients attending the emergency departments. Special emphasis is given to the different periodicities and trends found using a Fourier analysis. In the second part, we use well-known statistical tools in order to perform predictions about the number of arrivals at specific days and times. We now summarize our main findings. In the first part we have performed a detailed analysis of the time series corresponding to the period 2014-2019. The first characteristic is a steady increase over the years in the number of arrivals of patients to the emergency departments. After subtracting this annual trend, the Fourier analysis of the data allows us to unveil three different structures: daily, weekly and annual. We have found remarkable differences between those patients that end up hospitalized and those that were dispatched. While at night the number of patients that comes to the emergency department is much lower than in the morning, a large fraction of them represent severe cases that require hospitalization. Monday is the day of the week with the largest number of arrivals, in contrast to the weekend days. The daily data exhibits two maxima of arrivals (around 11 am and 3 pm). The annual structure displays very different behavior for patients that end up hospitalized and those that are dispatched. In summer the number of arrivals reaches its maximum, most probably due to tourism, but the number of hospitalized patients remains almost constant over time. We have additionally performed an analysis of the waiting times since the patient’s arrival and disclosure. The hospitalized patients tend to spend more time in the emergency department and their mean waiting time increases significantly in January when the hospitals tend to be saturated. In the second part, we have used mathematical models in order to predict the number of arrivals. In particular we have applied to the data the set of statistical tools SARIMA in order to predict the number of arrival at a specific day and time. Our model is consistent with the fact that patients visit the emergency department independently of each other but with a rate that depends on external factors. We obtain the best results if we first pre-process the data. Using the Fourier transform we identify the most important frequencies of the data. We then use the principal modes in order to subtract the seasonal effects, and apply the SARIMA predictor to the resulting data. The lack of structure of the correlation function of the residuals indicates the impossibility of a better prediction.