The Annals of Applied Statistics

A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development

Hai Liu and Wanzhu Tu

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This research examines the simultaneous influences of height and weight on longitudinally measured systolic and diastolic blood pressure in children. Previous studies have shown that both height and weight are positively associated with blood pressure. In children, however, the concurrent increases of height and weight have made it all but impossible to discern the effect of height from that of weight. To better understand these influences, we propose to examine the joint effect of height and weight on blood pressure. Bivariate thin plate spline surfaces are used to accommodate the potentially nonlinear effects as well as the interaction between height and weight. Moreover, we consider a joint model for paired blood pressure measures, that is, systolic and diastolic blood pressure, to account for the underlying correlation between the two measures within the same individual. The bivariate spline surfaces are allowed to vary across different groups of interest. We have developed related model fitting and inference procedures. The proposed method is used to analyze data from a real clinical investigation.

Article information

Ann. Appl. Stat., Volume 6, Number 4 (2012), 1861-1882.

First available in Project Euclid: 27 December 2012

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Zentralblatt MATH identifier

Bootstrap factor-by-surface interaction mixed effects model paired outcomes penalized estimation thin plate spline


Liu, Hai; Tu, Wanzhu. A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development. Ann. Appl. Stat. 6 (2012), no. 4, 1861--1882. doi:10.1214/12-AOAS567.

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Supplemental materials

  • Supplementary material: Detailed model-fitting algorithm and model diagnostics. We provide the computational details of the model-fitting algorithm with sample R code and an R function to visualize the predicted bivariate surfaces. Some model diagnostics plots are also provided.