Development and Application of Joint Modelling of Longitudinal and Event-Time Data in Frequentist and Bayesian Settings: Addressing the Uncertainty of Association Structure Selection

Abstract

Background and aims: Over the last decade, there has been an increasing interest in applying joint models to related longitudinal and time-to-event outcome data due to their ability to reduce bias in the estimated parameters and individual-level patients' risks predictions, and availability of user-friendly software. Joint models consist of two linked submodels; a longitudinal submodel and a time-to-event submodel. These two submodels are connected through an association structure, a function that represents the relationship between the two outcomes. The choice of the association is an important factor for specification of the joint model, and is usually based on the clinical information regarding the application area. However, the current research in this aspect is considerably limited. Often, a single best fit joint model is used to draw the inference from estimated parameters, which overlooks the issue of model uncertainty entirely. The aim of this thesis is to develop appropriate statistical methodologies to improve the inference of the joint model when background knowledge to support the selection of an association structure is unavailable. Method: A comprehensive review of joint models in Bayesian framework is undertaken to understand the approaches of using background knowledge for joint modelling methodologies and limitations of the current approaches, and to identify future directions. Two novel weighted average (WA) approaches are developed to collate information from multiple joint models with different association structures. The first approach is based on the inverse-variance (IV) weighting and the second is on the Monte Carlo (MC) sampling technique. The proposed approaches are investigated through simulation studies in both frequentist and Bayesian settings of the joint model, and illustrated with real-world clinical data. The methods are applied to explore the prediction of longitudinal biomarkers for diagnosing early recurrence after liver resection for hepatocellular carcinoma (HCC). Results: The simulation studies showed the proposed IV WA approach with an adjusted variance and MC WA approach perform well in estimating the parameters of interest close to the true value even when a model with a wrong association structure was included in the weighting process. Further, even when absence of the model with the true association structure, the two WA approaches were capable of estimating the parameters close to the true value. As observed with the illustrative data, the variability of the combined effect estimated from both WA approaches was consistent with the variability of separate model parameter estimates. The two approaches also showed an improved prediction of the biomarker values on risks of HCC recurrence. Conclusion: The weighted average approaches developed within this thesis provide readily accessible methods for joint models when background knowledge to support the selection of a single association structure is unavailable. Incorporating an accurate association structure is a key factor of the joint model specification. The proposed methods may facilitate greater use of the joint models in health research making more transparent estimation of covariate effects.