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

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.

Figure 1

Temporal trends of bilirubin and GFR for a “typical patient” (b_i = (0,0)^⊤). GFR: glomerular filtration rate.

Figure 2

Goodness of fit: Observed versus predicted profiles for each response under three different scenario. r_c depicts the concordance statistic—value closer to 1, better the model fit.

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

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

Shapes of phases and temporal trends used in simulating a bivariate normal response.

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.