Quantile Regression for Mixed Models

Cardiometabolic diseases have substantially increased in China in the past 20 years and blood pressure is a primary modifiable risk factor. Using data from the China Health and Nutrition Survey we examine blood pressure trends in China from 1991 to 2009, with a concentration on age cohorts and urbanicity. Very large values of blood pressure are of interest, so we model the conditional quantile functions of systolic and diastolic blood pressure. This allows the covariate effects in the middle of the distribution to vary from those in the upper tail, the focal point of our analysis. We join the distributions of systolic and diastolic blood pressure using a copula, which permits the relationships between the covariates and the two responses to share information and enables probabilistic statements about systolic and diastolic blood pressure jointly. Our copula maintains the marginal distributions of the group quantile effects while accounting for within-subject dependence, enabling inference at the population and subject levels. We present ∗To whom correspondence should be addressed.