One of the main challenges in multi-instance regression is the simultaneous selection of influential instances within each bag and predictors associated with the response. In this study, the Bayesian multi-instance regression framework based on Shotgun Stochastic Search (MIR-SSS) was applied to analyze data from burn patients, and its performance was compared with two benchmark methods, namely Aggregated Predictive Weighting (APW) regression and LASSO applied to bag-level representations. Within this framework, variable selection is performed using spike-and-slab priors, whereas instance selection is carried out through a logistic model. The methods were first evaluated under four simulation scenarios with different levels of sparsity and variability and were subsequently applied to real data from 2,024 patients admitted to Amir al-Momenin Burn Hospital in Shiraz, Iran. Simulation results showed that the MIR-SSS model achieved the lowest prediction error and high accuracy in selecting relevant variables under the baseline scenarios. However, under conditions of high variability and the presence of outliers, the APW method demonstrated superior predictive performance in terms of prediction error. The area under the ROC curve also confirmed the model's ability to identify influential instances. In the real-data analysis, MIR-SSS outperformed the two benchmark methods in predictive performance and identified several clinical factors associated with patient outcomes. The results indicate that this framework provides an interpretable tool for the simultaneous selection of instances and variables and enables uncertainty quantification in the analysis of complex medical data.