Bayesian fractional polynomial approach to quantile regression and variable selection with application in the analysis of blood pressure among US adults

Although the fractional polynomials (FPs) can act as a concise and accurate formula for examining smooth relationships between response and predictors, modelling conditional mean functions observes the partial view of a distribution of response variable, as distributions of many response variables such as blood pressure (BP) measures are typically skew. Conditional quantile functions with FPs provide a comprehensive relationship between the response variable and its predictors, such as median and extremely high-BP measures that may be often required in practical data analysis generally. To the best of our knowledge, this is new in the literature. Therefore, in this article, we develop and employ Bayesian variable selection with quantile-dependent prior for the FP model to propose a Bayesian variable selection with parametric non-linear quantile regression model. The objective is to examine a non-linear relationship between BP measures and their risk factors across median and upper quantile levels using data extracted from the 2007 to 2008 National Health and Nutrition Examination Survey (NHANES). The variable selection in the model analysis identified that the non-linear terms of continuous variables (body mass index, age), and categorical variables (ethnicity, gender, and marital status) were selected as important predictors in the model across all quantile levels.