Highlighting uncertainty in clinical risk prediction using a model of emergency laparotomy mortality risk

Clinical prediction models typically make point estimates of risk. However, values of key variables are often missing during model development or at prediction time, meaning that the point estimates mask significant uncertainty and can lead to over-confident decision making. We present a model of mortality risk in emergency laparotomy which instead presents a distribution of predicted risks, highlighting the uncertainty over the risk of death with an intuitive visualisation. We developed and validated our model using data from 127134 emergency laparotomies from patients in England and Wales during 2013-2019. We captured the uncertainty arising from missing data using multiple imputation, allowing prospective, patient-specific imputation for variables that were frequently missing. Prospective imputation allows early prognostication in patients where these variables are not yet measured, accounting for the additional uncertainty this induces. Our model showed good discrimination and calibration (95% confidence intervals: Brier score 0.071-0.078, C statistic 0.859-0.873, calibration error 0.031-0.059) on unseen data from 37 hospitals, consistently improving upon the current gold-standard model. The dispersion of the predicted risks varied significantly between patients and increased where prospective imputation occurred. We present a case study that illustrates the potential impact of uncertainty quantification on clinical decision making. Our model improves mortality risk prediction in emergency laparotomy and has the potential to inform decision-makers and assist discussions with patients and their families. Our analysis code was robustly developed and is publicly available for easy replication of our study and adaptation to predicting other outcomes.