Comparative efficacy of three Bayesian variable selection methods in the context of weight loss in obese women

The use of high-dimensional data has expanded in many fields, including in clinical research, thus making variable selection methods increasingly important compared to traditional statistical approaches. The work aims to compare the performance of three supervised Bayesian variable selection methods to detect the most important predictors among a high-dimensional set of variables and to provide useful and practical guidelines of their use. We assessed the variable selection ability of: (1) Bayesian Kernel Machine Regression (BKMR), (2) Bayesian Semiparametric Regression (BSR), and (3) Bayesian Least Absolute Shrinkage and Selection Operator (BLASSO) regression on simulated data of different dimensions and under three scenarios with disparate predictor-response relationships and correlations among predictors. This is the first study describing when one model should be preferred over the others and when methods achieve comparable results. BKMR outperformed all other models with small synthetic datasets. BSR was strongly dependent on the choice of its own intrinsic parameter, but its performance was comparable to BKMR with large datasets. BLASSO should be preferred only when it is reasonable to hypothesise the absence of synergies between predictors and the presence of monotonous predictor-outcome relationships. Finally, we applied the models to a real case study and assessed the relationships among anthropometric, biochemical, metabolic, cardiovascular, and inflammatory variables with weight loss in 755 hospitalised obese women from the Follow Up OBese patients at AUXOlogico institute (FUOBAUXO) cohort.