Joint modelling for organ transplantation outcomes for patients with diabetes and the end-stage renal disease

Abstract

This article is motivated by jointly modelling longitudinal and time-to-event clinical data of patients with diabetes and end-stage renal disease. All patients are on the waiting list for the pancreas transplant after kidney transplant, and some of them have a pancreas transplant before kidney transplant failure or death. Scant literature has studied the dynamical joint relationship of the estimated glomerular filtration rates trajectory, the effect of pancreas transplant, and time-to-event outcomes, although it remains an important clinical question. In an attempt to describe the association in the multiple outcomes, we propose a new joint model with a longitudinal submodel and an accelerated failure time submodel, which are linked by some latent variables. The accelerated failure time submodel is used to determine the relationship of the time-to-event outcome with all predictors. In addition, the piecewise linear function in the survival submodel is used to calculate the dynamic hazard ratio curve of a time-dependent side event, because the effect of the side event on the time-to-event outcome is non-proportional. The model parameters are estimated with a Monte Carlo EM algorithm. The finite sample performance of the proposed method is investigated in simulation studies. Our method is demonstrated by fitting the joint model for the clinical data of 13,635 patients with diabetes and the end-stage renal disease.

Keywords: Jointly modelling; glomerular filtration rates; longitudinal data; organ transplantation; survival analysis.