Joint Modelling Of Longitudinal and Survival Data in Presence of Cure Fraction with Application to Cancer Patients’ Data

Analyses involving longitudinal and time-to-event data are quite common in medical research. The primary goal of such studies to simultaneously study the effect of treatment on both the longitudinal covariate and survival. Often in medical research, there are settings in which it is meaningful to consider the existence of a fraction of individuals who have little to no risk of experiencing the event of interest. In this thesis, we focus on such settings with two different data structures. In early part of the thesis, we focus on the use of a cured fraction survival models performed in a population-based cancer registries. The limitations of statistical models which embodied the concept of a cured fraction of patients lack flexibility for modelling the survival distribution of the uncured group; lead to a not good fit when the survival drops rapidly soon after diagnosis and also when the survival is too high. In this study, a cure mixture model is enhanced by developing a dynamic semi-parametric exponential function with a smoothing parameter. The latter (major) part of the thesis focuses on modelling the longitudinal and the survival data in presence of cure fraction jointly. When there are cured patients in the population, the existing methods of joint models would be inappropriate, since they do not account for the plateau in the survival function. We introduce a new class of joint models in presence of cure fraction. In this joint model, the longitudinal submodel is a combination of a random mixed effect model and a stochastic process. A semi-parametric submodel is also proposed to incorporate the true longitudinal trajectories and other baseline time (dependent or independent) covariates. This model accounts for the possibility that a subject is cured, for the unique nature of the longitudinal data, and is capable to accommodating both zero and nonzero cure fractions. We generalize the two submodels to be multidimensional to investigate the relationship between the multivariate longitudinal and survival data. Bayesian approach was applied to the data using a conjugate and non-conjugate prior families to obtain parameter estimates for the proposed models. Gibbs sampling scheme is modified for fitting the joint model. Metropolis Hasting and Adaptive Rejection Sampling steps are used to update the Markov chain to estimate parameter whose full conditional densities can not be sampled efficiently from the existing methods, leading us to propose efficient proposal densities. The simulation studies demonstrate that the joint modelling method results in efficient estimates and good coverage for the population parameters. The analysis of cancer patient’s data indicates that when ignoring the association between the longitudinal and the survival data would lead to biased estimates for the most important parameters.

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