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Since its introduction in 1978 by Koenker and Basset, quantile regression has grown to be a significant tool and is being accepted more widely in a variety of applications it is a technique for measuring the relationship between a predictor and a response variable.It also provides information more than linear regression. Recently, it was recommended to use the Bayesian quantile regression method to handle model uncertainty and unknown parameters. Quantile regression thereafter saw the emergence of numerous Bayesian techniques. The current work focuses on studying the methods (Bayesian lasso quantile regression, and Bayesian adaptive lasso quantile regression) in addition to quantile regression and Bayesian quantile regression, and offering a comparison between the aforementioned methods based on the value of MSE, after calculating the parameters and interpreting them in terms of medical logic. A simulation study was provided, and we also conducted a practical study of thalassemia patients' data in Iraq - Babylon city for the year 2021 applying the methods indicated above. The simulation and practical study indicate that the Bayesian Adaptive lasso quantile regression method outperforms the other methods studied.