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Comparative Study
. 2012 Nov 20;31(26):3147-64.
doi: 10.1002/sim.5385. Epub 2012 Jun 26.

Multivariate multilevel spline models for parallel growth processes: application to weight and mean arterial pressure in pregnancy

Corrie Macdonald-Wallis  1 , Debbie A Lawlor, Tom Palmer, Kate Tilling
Affiliations
Free PMC article
Comparative Study

Multivariate multilevel spline models for parallel growth processes: application to weight and mean arterial pressure in pregnancy

Corrie Macdonald-Wallis et al. Stat Med. .
Free PMC article

Abstract

Growth models are commonly used in life course epidemiology to describe growth trajectories and their determinants or to relate particular patterns of change to later health outcomes. However, methods to analyse relationships between two or more change processes occurring in parallel, in particular to assess evidence for causal influences of change in one variable on subsequent changes in another, are less developed. We discuss linear spline multilevel models with a multivariate response and show how these can be used to relate rates of change in a particular time period in one variable to later rates of change in another variable by using the variances and covariances of individual-level random effects for each of the splines. We describe how regression coefficients can be calculated for these associations and how these can be adjusted for other parameters such as random effect variables relating to baseline values or rates of change in earlier time periods, and compare different methods for calculating the standard errors of these regression coefficients. We also show that these models can equivalently be fitted in the structural equation modelling framework and apply each method to weight and mean arterial pressure changes during pregnancy, obtaining similar results for multilevel and structural equation models. This method improves on the multivariate linear growth models, which have been used previously to model parallel processes because it enables nonlinear patterns of change to be modelled and the temporal sequence of multivariate changes to be determined, with adjustment for change in earlier time periods.

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Figures

Figure 1
Figure 1
Path diagram for bivariate response spline model in structural equation format. Path diagram assumes that measurements formula image occur at equally spaced time points.
Figure 2
Figure 2
Average trajectories of (a) weight and (b) mean arterial pressure across pregnancy predicted by univariate multilevel linear spline models (N = 11,650).
See this image and copyright information in PMC

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