A general joint latent class model of longitudinal and survival data with a time-varying membership probability and covariance modelling

  • Ruoyu Miao

Student thesis: Phd


Joint latent class modelling (JLCM) has been developed considerably in the past two decades. Typically, the basic joint models for longitudinal measurements and survival outcomes are linked by shared parameters, random effects or by random effects sharing the same distribution. However, this kind of joint model is inappropriate when the potential subgroups exist in longitudinal measurements and time-to-event data. Joint latent class models which can handle underlying heterogeneous subtypes in the context of joint models, firstly were proposed by Lin et al. (2002) and further were developed by Proust-Lima et al. (2017). These models link the longitudinal and survival processes through latent classes but assume a static class membership probability for each subject. We relax this assumption by allowing subjects to change classes across time. We also consider modelling the variance of the heterogeneous random effects. In this thesis, we introduce two new extended joint latent class models. The first model, proposed in Chapter 4, is one with a time-varying membership probability. A Bayesian approach is used to do the estimation and a DIC criterion is used to decide the optimal number of classes. Simulation results indicate that the proposed model produces more accurate results and the time-varying JLCM outperforms the basic JLCM in terms of better classification and prediction. From the analysis of the aids data (Goldman et al., 1996), it is obvious that our proposed JLCM fits the data better than the basic JLCM according to DIC. In the dynamic prediction of survival probabilities, our model is generally more conservative than the basic JLCM and also more responsive to changes in the class membership over time. Based on the proposed time-varying JLCM in Chapter 4, we develop a more general JLCM in Chapter 5, in which the heterogeneous random covariance matrix is also modelled. In particular, regression submodels for the decomposed variance-covariance matrix of the multivariate random effects are added to the time-varying JLCM. This model can guard from misspecification of the random effects covariance and also allows us to determine any effects of covariates on this covariance. We compare the performance of our general JLCM to the time-varying probability JLCM through both simulation and real data analysis of the aids dataset, to find that our general JLCM outperforms the time-varying JLCM, in terms of both DIC and estimation accuracy. What is more, in the dynamic prediction of survival probabilities, our general JLCM can predict survival probabilities more accurately compared to the time-varying JLCM.
Date of Award1 Aug 2023
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPeter Foster (Supervisor) & Christiana Charalambous (Supervisor)


  • Dynamic predictions
  • MCMC algorithm
  • Shared multivariate normal distribution
  • Shared parameter model
  • Latent random effects
  • Heterogenous random
  • Time-varying probability
  • Covariance modelling
  • Survival analysis
  • Longitudinal measurements
  • Latent class
  • Joint latent class model
  • Cholesky decomposition

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