Modelling multivariate longitudinal outcomes and time-to-event data

Theletsane, Modiehi

Modelling multivariate longitudinal outcomes and time-to-event data

Thesis / Dissertation

2025

Publisher

University of Cape Town

Department

Department of Statistical Sciences

Faculty

Faculty of Science

Abstract

It is common in clinical or observational studies to record information repeatedly over time while observing a time-to-event outcome among subjects. Joint models for longitudinal and survival data simultaneously analyse repetitively measured outcomes and associated event times. They offer valuable applications in two contexts: accounting for time-varying covariates measured with error when concentrating on survival outcomes, and controlling for informative censoring when focusing on longitudinal outcomes. It has been nearly four decades since joint modelling was first developed. The main aim of this study was to investigate whether there is an association between multivariate longitudinal electrocardiogram (ECG) characteristics; i.e., ECG rate (ECGrate), ECG PR interval (ECGpri), ECG corrected QT interval (ECGqtc), and ECG QRS duration (ECGqrsd) on survival outcomes, death, constriction, and composite outcome (death, constriction, or cardiac tamponade, whichever occurs first) in the investigation of the management of pericarditis (IMPI) in a multi-centre clinical trial. The ECG characteristics from the IMPI trial were weighed on a continuous scale and were converted into categories to be clinically meaningful. Several approaches were taken towards joint modelling, with the first one being a two-stage joint model approach. The shared parameter joint model is another approach to joint modelling. This study considered univariate and multivariate shared parameter joint models of the longitudinal data and time-to-composite, time-to-death, and time- to-constriction event outcomes. Specifically, the study considered these models when the data were non-normal. The univariate analysis results suggested a weak association between the ECGrate and the risk of composite, death, and constriction event outcomes. However, there was a strong association between ECGpri and the risk of death and constriction, but there was no association in the composite event. Furthermore, there was no association between ECGqrs duration and the risk of either composite or death events; however, there was an association with constriction. Finally, there was no association between ECGqtc and the risk of either composite or death events; however, there was an association between the ECGqtc and constriction. The study utilised multivariate shared parameter joint model analysis to understand if there was an association between composite, death, and constriction survival outcomes. The model had four binary ECG longitudinal outcomes, which were modelled based on the binomial assumption using the generalised linear mixed-effects model. Parameter estimation was based on a Bayesian framework utilising the Markov Chain Monte Carlo technique, and convergency estimates were established. It was discovered that the association parameter for the ECGqtc, which determines how the longitudinal ECGqtc is related to the risk of death, showed that there was an association. In contrast, the association parameter for ECGrate, ECGpri, and ECGqrsd was weak for the risk of composite, death, and constriction outcomes. The ECGqtc also revealed no association between the risk of composite and constriction event outcomes, respectively.