Abstract
Analysis of multivariate longitudinal data becomes complicated when the outcomes are of high dimension and informative right censoring is prevailing. Here, we propose a likelihood based approach for high dimensional outcomes wherein we jointly model the censoring process along with the slopes of the multivariate outcomes in the same likelihood function. We utilized pseudo likelihood function to generate parameter estimates for the population slopes and Empirical Bayes estimates for the individual slopes. The proposed approach was applied to jointly model longitudinal measures of blood urea nitrogen, plasma creatinine, and estimated glomerular filtration rate which are key markers of kidney function in a cohort of renal transplant patients followed from kidney transplant to kidney failure. Feasibility of the proposed joint model for high dimensional multivariate outcomes was successfully demonstrated and its performance was compared to that of a pairwise bivariate model. Our simulation study results suggested that there was a significant reduction in bias and mean squared errors associated with the joint model compared to the pairwise bivariate model.
Highlights
Kidney function is assessed using the markers serum creatinine, blood urea nitrogen (BUN), and estimated glomerular filtration rate
For the cohort of renal transplantation we considered in this study, longitudinal measures of creatinine and BUN are recorded and estimated glomerular filtration rate (eGFR) levels are computed post transplant repeatedly over time till patient experiences renal graft failure
The baseline measures for BUN, creatinine, and eGFR recorded prior to the transplantation do not have any impact on kidney function after the transplantation since a new organ is transplanted and post operative measures of these markers determine the progression of disease
Summary
Kidney function is assessed using the markers serum creatinine, blood urea nitrogen (BUN), and estimated glomerular filtration rate (eGFR). What is more important is monitoring the rate of change in serum creatinine, BUN and eGFR over time to determine disease progression or to ascertain if state of disease is stable or changing [6]. This is done by taking repeated measures of these markers on the same patient and by calculating the rate of change or slopes for each of these markers to provide an evaluation of disease progression over time. Patients who experience graft failure will have an incomplete set of repeated measures on their creatinine, BUN and eGFR, a situation referred to as informative right censoring
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