Machine learning-based prediction of hospital prolonged length of stay admission at emergency department: a Gradient Boosting algorithm analysis

Objective: This study aims to develop and compare different models to predict the Length of Stay (LoS) and the Prolonged Length of Stay (PLoS) of inpatients admitted through the emergency department (ED) in general patient settings. This aim is not only to promote any specific model but rather to suggest a decision-supporting tool (i.e., a prediction framework). MethodsWe analyzed a dataset of patients admitted through the ED to the "Sant"Orsola Malpighi University Hospital of Bologna, Italy, between January 1 and October 26, 2022. PLoS was defined as any hospitalization with LoS longer than 6 days. We deployed six classification algorithms for predicting PLoS: Random Forest (RF), Support Vector Machines (SVM), Gradient Boosting (GB), AdaBoost, K-Nearest Neighbors (KNN), and logistic regression (LoR). We evaluated the performance of these models with the Brier score, the area under the ROC curve (AUC), accuracy, sensitivity (recall), specificity, precision, and F1-score. We further developed eight regression models for LoS prediction: Linear Regression (LR), including the penalized linear models Least Absolute Shrinkage and Selection Operator (LASSO), Ridge and Elastic-net regression, Support vector regression, RF regression, KNN, and eXtreme Gradient Boosting (XGBoost) regression. The model performances were measured by their mean square error, mean absolute error, and mean relative error. The dataset was randomly split into a training set (70%) and a validation set (30%). ResultsA total of 12,858 eligible patients were included in our study, of whom 60.88% had a PloS. The GB classifier best predicted PloS (accuracy 75%, AUC 75.4%, Brier score 0.181), followed by LoR classifier (accuracy 75%, AUC 75.2%, Brier score 0.182). These models also showed to be adequately calibrated. Ridge and XGBoost regressions best predicted LoS, with the smallest total prediction error. The overall prediction error is between 6 and 7 days, meaning there is a 6-7 day mean difference between actual and predicted LoS. ConclusionOur results demonstrate the potential of machine learning-based methods to predict LoS and provide valuable insights into the risks behind prolonged hospitalizations. In addition to physicians' clinical expertise, the results of these models can be utilized as input to make informed decisions, such as predicting hospitalizations and enhancing the overall performance of a public healthcare system.