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Hypertension is a highly prevalent chronic medical condition and a strongrisk factor for cardiovascular disease (CVD), as it accounts for more than$45\%$ of CVD. The relation between blood pressure (BP) and its risk factorscannot be explored clearly by standard linear models. Although the fractionalpolynomials (FPs) can act as a concise and accurate formula for examiningsmooth relationships between response and predictors, modelling conditionalmean functions observes the partial view of a distribution of responsevariable, as the distributions of many response variables such as BP measuresare typically skew. Then modelling 'average' BP may link to CVD but extremelyhigh BP could explore CVD insight deeply and precisely. So, existing mean-basedFP approaches for modelling the relationship between factors and BP cannotanswer key questions in need. Conditional quantile functions with FPs provide acomprehensive relationship between the response variable and its predictors,such as median and extremely high BP measures that may be often required inpractical data analysis generally. To the best of our knowledge, this is new inthe literature. Therefore, in this paper, we employ Bayesian variable selectionwith quantile-dependent prior for the FP model to propose a Bayesian variableselection with parametric nonlinear quantile regression model. The objective isto examine a nonlinear relationship between BP measures and their risk factorsacross median and upper quantile levels using data extracted from the 2007-2008National Health and Nutrition Examination Survey (NHANES). The variableselection in the model analysis identified that the nonlinear terms ofcontinuous variables (body mass index, age), and categorical variables(ethnicity, gender and marital status) were selected as important predictors inthe model across all quantile levels.

Bayesian Fractional Polynomial Approach to Quantile Regression and  Variable Selection with Application in the Analysis of Blood Pressure among  US Adults