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The issue of left before treatment complete (LBTC) patients is common in emergency departments (EDs). This issue represents a medico-legal risk and may cause a revenue loss. Thus, understanding the factors that cause patients to leave before treatment is complete is vital to mitigate and potentially eliminate these adverse effects. This paper proposes a framework for studying the factors that affect LBTC outcomes in EDs. The framework integrates machine learning, metaheuristic optimization, and model interpretation techniques. Metaheuristic optimization is used for hyperparameter optimization--one of the main challenges of machine learning model development. Three metaheuristic optimization algorithms are employed for optimizing the parameters of extreme gradient boosting (XGB), which are simulated annealing (SA), adaptive simulated annealing (ASA), and adaptive tabu simulated annealing (ATSA). The optimized XGB models are used to predict the LBTC outcomes for the patients under treatment in ED. The designed algorithms are trained and tested using four data groups resulting from the feature selection phase. The model with the best predictive performance is interpreted using SHaply Additive exPlanations (SHAP) method. The findings show that ATSA-XGB outperformed other mode configurations with an accuracy, area under the curve (AUC), sensitivity, specificity, and F1-score of 86.61%, 87.50%, 85.71%, 87.51%, and 86.60%, respectively. The degree and the direction of effects of each feature were determined and explained using the SHAP method.