Jointly modelling multiple transplant outcomes by a competing risk model via functional principal component analysis

Jianghu Dong, Haolun Shi, Liangliang Wang, Ying Zhang, Jiguo Cao

Research output: Contribution to journalArticlepeer-review


In many clinical studies, longitudinal biomarkers are often used to monitor the progression of a disease. For example, in a kidney transplant study, the glomerular filtration rate (GFR) is used as a longitudinal biomarker to monitor the progression of the kidney function and the patient's state of survival that is characterized by multiple time-to-event outcomes, such as kidney transplant failure and death. It is known that the joint modelling of longitudinal and survival data leads to a more accurate and comprehensive estimation of the covariates' effect. While most joint models use the longitudinal outcome as a covariate for predicting survival, very few models consider the further decomposition of the variation within the longitudinal trajectories and its effect on survival. We develop a joint model that uses functional principal component analysis (FPCA) to extract useful features from the longitudinal trajectories and adopt the competing risk model to handle multiple time-to-event outcomes. The longitudinal trajectories and the multiple time-to-event outcomes are linked via the shared functional features. The application of our model on a real kidney transplant data set reveals the significance of these functional features, and a simulation study is carried out to validate the accurateness of the estimation method.

Original languageEnglish (US)
Pages (from-to)43-59
Number of pages17
JournalJournal of Applied Statistics
Issue number1
StatePublished - 2023


  • Competing risks
  • functional principal component analysis
  • joint model
  • kidney transplant
  • latent variables

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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