Derivative estimation for longitudinal data analysis: Examining features of blood pressure measured repeatedly during pregnancy

Andrew J. Simpkin*, Maria Durban, Debbie A. Lawlor, Corrie MacDonald-Wallis, Margaret T. May, Chris Metcalfe, Kate Tilling

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
269 Downloads (Pure)


Estimating velocity and acceleration trajectories allows novel inferences in the field of longitudinal data analysis, such as estimating change regions rather than change points, and testing group effects on nonlinear change in an outcome (ie, a nonlinear interaction). In this article, we develop derivative estimation for 2 standard approaches—polynomial mixed models and spline mixed models. We compare their performance with an established method—principal component analysis through conditional expectation through a simulation study. We then apply the methods to repeated blood pressure (BP) measurements in a UK cohort of pregnant women, where the goals of analysis are to (i) identify and estimate regions of BP change for each individual and (ii) investigate the association between parity and BP change at the population level. The penalized spline mixed model had the lowest bias in our simulation study, and we identified evidence for BP change regions in over 75% of pregnant women. Using mean velocity difference revealed differences in BP change between women in their first pregnancy compared with those who had at least 1 previous pregnancy. We recommend the use of penalized spline mixed models for derivative estimation in longitudinal data analysis.

Original languageEnglish
Pages (from-to)2836-2854
Number of pages19
JournalStatistics in Medicine
Issue number19
Early online date20 May 2018
Publication statusPublished - 30 Aug 2018

Structured keywords

  • Centre for Surgical Research


  • derivative estimation
  • functional data analysis
  • longitudinal data analysis
  • penalized splines

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  • Projects

    MRC UoB UNITE Unit - Programme 5

    Lawlor, D. A. & Lawlor, D. A.


    Project: Research

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