Prediction of 30-day unplanned hospital readmission through survival analysis

Background and Objective: Unplanned hospital readmissions are a severe and recurrent problem that affects all health systems. Estimating the risk of being readmitted the following days after discharge is difficult since many heterogeneous factors can influence this. The extensive work concerning this problem proposes solutions mostly based on classification machine-learning models. Survival analysis methods could make a better match with the assessment of readmission risk and are yet to become well-established in this field. Methods: We compare different statistical and machine learning survival analysis models trained with right-censored all-cause hospital admission data with covariates available at the moment of discharge. The main focus is on tree-ensemble regression methods based on the assumption of proportional hazards. These models are more thoroughly evaluated at a 30-day time period after discharge, although the actual prediction could be set to any time up to 90 days.Results: The mean performance obtained by each of the proposed survival models ranges from 0.707 to 0.716 C-Index and 0.709 to 0.72 ROC-AUC at a 30-day time period after discharge. The model with the lower performance on both metrics was Cox Proportional Hazards, while the model marking the upper end on both ranges is an XGBoost Regression model with a Cox objective function. Conclusions: Our findings indicate that survival models perform well addressing the hospital readmission problem, machine-learning models getting the edge over statistical methods. There seems to be an improvement over classification models when attempting to predict at a 30-day period since discharge, perhaps due to a better handling of cases nearing the 30-day boundary. Some preprocessing steps, such as limiting the observation period to 90 days after discharge, are also highlighted since they resulted in a performance boost.