Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2018 Jul;27(7):2216-2230.
doi: 10.1177/0962280216678022. Epub 2016 Nov 16.

Evolution of association between renal and liver functions while awaiting heart transplant: An application using a bivariate multiphase nonlinear mixed effects model

Jeevanantham Rajeswaran  1 , Eugene H Blackstone  1 , John Barnard  1
Affiliations

Evolution of association between renal and liver functions while awaiting heart transplant: An application using a bivariate multiphase nonlinear mixed effects model

Jeevanantham Rajeswaran et al. Stat Methods Med Res. 2018 Jul.

Abstract

In many longitudinal follow-up studies, we observe more than one longitudinal outcome. Impaired renal and liver functions are indicators of poor clinical outcomes for patients who are on mechanical circulatory support and awaiting heart transplant. Hence, monitoring organ functions while waiting for heart transplant is an integral part of patient management. Longitudinal measurements of bilirubin can be used as a marker for liver function and glomerular filtration rate for renal function. We derive an approximation to evolution of association between these two organ functions using a bivariate nonlinear mixed effects model for continuous longitudinal measurements, where the two submodels are linked by a common distribution of time-dependent latent variables and a common distribution of measurement errors.

Keywords: Nonlinear model; additive regression; bivariate mixed effects model; evolution of correlation; mixed effects model; temporal decomposition.

PubMed Disclaimer

Conflict of interest statement

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1
Figure 1
Temporal trends of bilirubin and GFR for a “typical patient” (bi = (0,0)⊤). GFR: glomerular filtration rate.
Figure 2
Figure 2
Goodness of fit: Observed versus predicted profiles for each response under three different scenario. rc depicts the concordance statistic—value closer to 1, better the model fit.
Figure 3
Figure 3
Evolution of association between renal and liver function. Solid line is the approximate association estimated using the joint-full model. The symbols are crude “observed” correlation estimates based on the “moving window” approach.
Figure 4
Figure 4
Evolution of association between renal and liver function. Contour plot of the two responses at six different time points while on MCS. MCS: mechanical circulatory support.
Figure 5
Figure 5
Shapes of phases and temporal trends used in simulating a bivariate normal response.
Figure 6
Figure 6
Simulation results: large circle symbols depict the “true” marginal correlation and boxplots depict the distribution of estimated approximate marginal correlation based on simulated data.
See this image and copyright information in PMC

References

    1. Mason DP, Rajeswaran J, Murthy SC, et al. Spirometry after transplantation: how much better are two lungs than one? Ann Thorac Surg. 2008;85:1193–1201. - PubMed
    1. Beckett LA, Tancredi DJ, Wilson RS. Multivariate longitudinal models for complex change processes. Stat Med. 2004;23:231–239. - PubMed
    1. Fieuws S, Verbeke G. Joint modeling of multivariate longitudinal profiles: pitfalls of the random-effect approach. Stat Med. 2004;23:3093–3104. - PubMed
    1. Fieuws S, Verbeke G, Molenbergs G. Random-effects models for multivariate repeated measures. Stat Methods Med Res. 2007;16:387–397. - PubMed
    1. O’Brian PC. Procedures for comparing samples with multiple endpoints. Biometrics. 1984;40:1079–1087. - PubMed

Publication types