Joint penalized spline modeling of multivariate longitudinal data, with application to HIV-1 RNA load levels and CD4 cell counts

Lihui Zhao, Tom Chen, Vladimir Novitsky, Rui Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Motivated by the need to jointly model the longitudinal trajectories of HIV viral load levels and CD4 counts during the primary infection stage, we propose a joint penalized spline modeling approach that can be used to model the repeated measurements from multiple biomarkers of various types (eg, continuous, binary) simultaneously. This approach allows for flexible trajectories for each marker, accounts for potentially time-varying correlation between markers, and is robust to misspecification of knots. Despite its advantages, the application of multivariate penalized spline models, especially when biomarkers may be of different data types, has been limited in part due to its seemingly complexity in implementation. To overcome this, we describe a procedure that transforms the multivariate setting to the univariate one, and then makes use of the generalized linear mixed effect model representation of a penalized spline model to facilitate its implementation with standard statistical software. We performed simulation studies to evaluate the validity and efficiency through joint modeling of correlated biomarkers measured longitudinally compared to the univariate modeling approach. We applied this modeling approach to longitudinal HIV-1 RNA load and CD4 count data from Southern African cohorts to estimate features of the joint distributions such as the correlation and the proportion of subjects with high viral load levels and high CD4 cell counts over time.

Original languageEnglish (US)
Pages (from-to)1061-1074
Number of pages14
Issue number3
StatePublished - Sep 2021


  • bivariate
  • joint modeling
  • longitudinal
  • penalized spline
  • random effects

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Statistics and Probability


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