Mortality prediction after major surgery in a mixed population through machine learning: a multi-objective symbolic regression approach

Abstract

Introduction: Understanding 1-year mortality following major surgery offers valuable insights into patient outcomes and the quality of peri-operative care. Few models exist that predict 1-year mortality accurately. This study aimed to develop a predictive model for 1-year mortality in patients undergoing complex non-cardiac surgery using a novel machine-learning technique called multi-objective symbolic regression.

Methods: A single-institution database of patients undergoing major elective surgery with previous cardiopulmonary exercise testing was divided into three datasets: pre-operative clinical data; cardiorespiratory and physiological data; and combined. A multi-objective symbolic regression model was developed and compared against existing models. Model performance was evaluated using the F1 score. Shapley additive explanations analysis was used to identify the major contributors to model performance.

Results: From 2145 patients in the database, 1190 were included, with 952 in the training dataset and 238 in the test dataset. Median (IQR [range]) age was 71 (61-79 [45-89]) years and 825 (69%) were male. The multi-objective symbolic regression model demonstrated robust consistency with an F1 score of 0.712. Shapley additive explanations analysis indicated that ventilatory equivalents for carbon dioxide, oxygen at peak exercise and BMI influenced model performance most significantly, surpassing surgery type and named comorbidities.

Discussion: This study confirms the feasibility of developing a multi-objective symbolic regression-based model for predicting 1-year postoperative mortality in a mixed non-cardiac surgical population. The model's strong performance underscores the critical role of physiological data, particularly cardiorespiratory fitness, in surgical risk assessment and emphasises the importance of pre-operative optimisation to identify and manage high-risk patients. The multi-objective symbolic regression model demonstrated high sensitivity and a good F1 score, highlighting its potential as an effective tool for peri-operative risk prediction.

Keywords: cardiopulmonary exercise testing; machine learning; mortality; multi‐objective symbolic regression.

Figure 1

Patient flow diagram.

Figure 2

(a) Shapley additive explanations (SHAP) analysis for a multi‐objective symbolic regression model. (b) Graphs analysing the influence of specific respiratory and physiological variables on a predictive model. VE.V̇CO₂ ^‐1, ventilatory efficiency/carbon dioxide output; VE.V̇O₂ ^‐1, ventilatory efficiency/oxygen consumption; RER, respiratory equivalent ratio; AT, anaerobic threshold; PetCO₂, partial pressure of end‐tidal carbon dioxide; HR, heart rate; V̇O₂, oxygen consumption; Hb, haemoglobin; BP, blood pressure; V̇CO₂, carbon dioxide output.