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Quantile Regression for Mixed Models with an Application to Examine Blood Pressure Trends in China


Smith, Luke B.; Fuentes, Montserrat; Gordon-Larsen, Penny; & Reich, Brian J. (2015). Quantile Regression for Mixed Models with an Application to Examine Blood Pressure Trends in China. Annals of Applied Statistics, 9(3), 1226-1246. PMCID: PMC5217786


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. Our population-level regression effects change across quantile level, year and blood pressure type, providing a rich environment for inference. To our knowledge, this is the first quantile function model to explicitly model within-subject autocorrelation and is the first quantile function approach that simultaneously models multivariate conditional response. We find that the association between high blood pressure and living in an urban area has evolved from positive to negative, with the strongest changes occurring in the upper tail. The increase in urbanization over the last twenty years coupled with the transition from the positive association between urbanization and blood pressure in earlier years to a more uniform association with urbanization suggests increasing blood pressure over time throughout China, even in less urbanized areas. Our methods are available in the R package BSquare.


Reference Type

Journal Article

Year Published


Journal Title

Annals of Applied Statistics


Smith, Luke B.
Fuentes, Montserrat
Gordon-Larsen, Penny
Reich, Brian J.