- Title
- Joint Modelling Inference for Longitudinal and Time To Event Data with Application to Biomarkers in Medical and Clinical Studies
- Creator
- Azeez, Adeboye Nurudeen
- Subject
- Biochemical markers Bayesian statistical decision theory
- Date
- 2020
- Type
- Thesis
- Type
- Doctoral
- Type
- PhD (Biostatistics)
- Identifier
- http://hdl.handle.net/10353/18476
- Identifier
- vital:42543
- Description
- In the past couple of decades, longitudinal and survival data analysis have emerged as important and popular concepts of biostatistics and statistics for disease modelling. In recent years, these two statistics concepts have been combined to develop a joint model for longitudinal and survival data analysis. The Joint model is a simultaneous modelling application of longitudinal and survival data while taking into account a possible association between them. In this thesis, three sub-topics (Conditional score approach, estimating equation approach, and modified Cholesky decomposition approach) are utilised to model the association if the independence assumption is violated. Using the conditional score approach, the study investigated the association between longitudinal covariates and the time-to-event process to examine the within-subject measurement error that could influence estimation when the assumption of normality and mutual independence is violated. Given the assumption violation, I proposed an estimating equation approach based on the conditional score to relax parametric distributional assumptions for repeated measures of random effects. I jointly modelled the time-dependent biomarkers and event times using the Cox model with intermittent time-dependent covariates measure, in which the longitudinal model was used to characterize the biomarker underlying (unobservable) trajectory and incorporated as a latent time-dependent covariate in the survival model to predict failure times. Estimates of the parameters were obtained by a restricted maximum likelihood estimate (REML). A modified Cholesky decomposition method was used to capture the within-subject covariance for a positive definite and symmetric matrix, with the assumption that the observed data from different subjects are independent. I illustrated the proposed method by a real data set from a lung study and simulation. An extension to the joint model of longitudinal-survival data was also proposed, in which the longitudinal data has a cumulative and weighted effect on the hazard event function. Using a Bayesian parametric method, I proposed a skewed weighted probability density function to estimate the parameters. The weighted cumulative effect used enabled different longitudinal profiles to be incorporated over time in calculating the hazard ratio between the subjects. The proposed functions provide greater flexibility for modelling the association structure of different longitudinal and survival sub-model. The focus was on the association between the biomarker (serum creatinine, sCr) and the development of end-stage renal disease (ESRD). Since the effect of sCr biomarker is anticipated to be a cumulative effect, with the development of sCr biomarker over time leading to progressively higher damage of the kidney. The approach was applied a simulation for validation of the proposed method
- Format
- 148 leaves
- Format
- Publisher
- University of Fort Hare
- Publisher
- Faculty of Science and Agriculture
- Language
- English
- Rights
- University of Fort Hare
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