Although emergencies are difficult to foresee, this study demonstrated that daily patient attendances at ED can be predicted with good accuracy using the modeling techniques in time series analysis. During the study period, the daily variations noted were quite significant, with daily P1 attendances ranging from 10 to 72; P2 attendances ranging from 96 to 239; P3 attendances ranging from 138 to 307. The model developed has identified factors associated with these variations in a local setting; which in turn were used to forecast future workload. Although the P1 model showed the highest prediction error due to the very small number of daily P1 attendances, it still demonstrated good forecasting ability.
Unlike other studies [6
], this study showed that daily total ED attendances were not predicted by weather conditions. This could be because Singapore is a tropical city with little variation in its hot and humid weather conditions throughout the year. While there was no seasonal fluctuation, higher P1 attendances was predicted by moderate or poor ambient air quality (PSI > 50). This could be due to severe respiratory and heart diseases among the vulnerable elderly population, which make up the 70% of P1 cases, and as reported by other studies [16
]. On the other hand, PSI > 50 was significantly inversely correlated with P3 attendances; i.e. fewer P3 attendances on days with high PSI. Singapore's national advisory on days with moderate to poor PSI follow that of US EPA; to reduce outdoor activities especially among those with compromised heart and lung conditions. Reduced outdoor activities during days of bad PSI may possibly account for this as attendances for trauma associated with minor accidents also decreased.
There were predictable higher weekly attendances on Sundays and Mondays, contributed by P3 cases. This is attributed by the closure of primary care facilities, mainly of the public sector on Sundays and public holidays; and the build-up of demand on Mondays. Similarly public holidays were also strongly correlated with higher P3 attendances when the primary care facilities are closed. There were also higher monthly attendances from May to July, contributed by P3 cases. This is attributed to the perennial seasonal dengue outbreaks and mid-year influenza activity.
Similar modeling and predicting framework can be extended to time series analysis of different intervals, such as hourly, weekly, monthly or yearly, as well as for different disease groups. The model's performance is based on historical trends. It is imperative for the forecasts to be iterative and updated regularly as more data is available in order to improve the prediction performance. In this case, the model is updated 3-monthly and the framework has been put into practice, where the model is run weekly to forecast the workload the following week. The forecasts have been used by the ED management to plan its staff deployment on a weekly base.
In addition to the immediate weekly forecasts, the model has also been used to plan longer term ahead. The study has shown higher daily P3 attendances due to the seasonal dengue and influenza outbreaks mid-year. Moreover, there were also higher P1 and P3 attendances associated with high PSI readings caused by transboundary air pollution from the seasonal forest fires in neighboring countries. These secular annual forecasts help the department plan staff headcounts and budget allocation a year in advance.
The study has helped us understand the factors associated with variation of daily ED attendances in a local setting and develop a model to forecast the daily attendances. To our knowledge, it is the first such study in Singapore. This study suffers from a few limitations. One is that there may be other factors affecting the daily ED attendances, like the availability of other primary care facilities and their workload which may predict ED attendances. Another limitation is the use of average daily temperature. Although the temperature range throughout the day may not be wide, maximum and minimum temperature could be more useful as a predictor. Also, we did not evaluate alternate forms of the predictor variables (e.g., squared, cubed or other non-linear forms) in this study, which may give better prediction of ED attendances.