Joint Models for Multivariate Longitudinal Data and Time-to-Event Data

Abstract

Joint models simultaneously model longitudinal covariates and time-to-event data. Modelling more than one longitudinal covariate with time-to-event data is computationally intensive. This thesis compares two packages contributed to the statistical software R, JMbayes and joineRML. The packages differ in terms of estimation approaches and the definition of the association structure within the survival submodel. The package JMbayes uses Bayesian estimation and a two-stage approach where the longitudinal and survival submodels are fit separately. It has been shown that the two-stage approach results in biased estimates. JMbayes uses importance sampling weights to correct for this bias. The package joineRML uses frequentist estimation techniques through the Monte Carlo expectation-maximization (MCEM) algorithm. In this thesis, the two approaches were demonstrated on two datasets. Simulation studies also compared the parameter estimates and variability of the estimates of the packages. Simulation results show joineRML performs well with small bias. However, the importance sampling weights from JMbayes are often highly variable, leading to unreliable results.