Trends, structural changes, and assessment of time series models for forecasting hospital discharge due to death at a Mexican tertiary care hospital

Background: Data on hospital discharges can be used as a valuable instrument for hospital planning and management. The quantification of deaths can be considered a measure of the effectiveness of hospital intervention, and a high percentage of hospital discharges due to death can be associated with deficiencies in the quality of hospital care. Objective: To determine the overall percentage of hospital discharges due to death in a Mexican tertiary care hospital from its opening, to describe the characteristics of the time series generated from the monthly percentage of hospital discharges due to death and to make and evaluate predictions. Methods: This was a retrospective study involving the medical records of 81,083 patients who were discharged from a tertiary care hospital from April 2007 to December 2019 (first 153 months of operation). The records of the first 129 months (April 2007 to December 2017) were used for the analysis and construction of the models (training dataset). In addition, the records of the last 24 months (January 2018 to December 2019) were used to evaluate the predictions made (test dataset). Structural change was identified (Chow test), ARIMA models were adjusted, predictions were estimated with and without considering the structural change, and predictions were evaluated using error indices (MAE, RMSE, MAPE, and MASE). Results: The total percentage of discharges due to death was 3.41%. A structural change was observed in the time series (March 2009, p>0.001), and ARIMA(0,0,0)(1,1,2)12 with drift models were adjusted with and without consideration of the structural change. The error metrics favored the model that did not consider the structural change (MAE = 0.63, RMSE = 0.81, MAPE = 25.89%, and MASE = 0.65). Conclusion: Our study suggests that the ARIMA models are an adequate tool for future monitoring of the monthly percentage of hospital discharges due to death, allowing us to detect observations that depart from the described trend and identify future structural changes.