Introduction

This report outlines the work I have completed and the projects I have been developing during my first year as a PhD student at the Department of Health Sciences, University of Leicester, under the supervision of Dr. Michael Crowther and Prof. Keith Abrams. An online version of this report can be accessed at https://ellessenne.github.io/prr/.

I will begin by briefly introducing some terminology and notation that I will be using throughout this report in Chapter 1. Second, I will introduce survival models with random effects (e.g. frailties, in the simplest form) and joint models for longitudinal and time-to-event data in Chapters 2 and 3, respectively. Some of the computational challenges that survival models with random effects and joint models pose are presented in Chapter 4. I will then present the results of two simulation studies in Chapters 5 and 6; the first simulation study investigates the accuracy of quadrature methods when approximating analytically intractable terms, while the second simulation study investigates the impact of model misspecification in survival models with shared frailty terms. I will introduce an interactive tool I have been developing to aid dissemination of results from simulation studies and motivated by the simulation studies of Chapter 5 and 6 in Chapter 7. Next, I will introduce the problem of informative visiting process in clinical research using healthcare consumption data in Chapter 8, and how I aim to evaluate and compare the different approaches that have been proposed and utilised in literature to tackle such problem in Chapter 9. Chapter 9 will also include further research goals for the second and third year of my PhD. Finally, I will summarise the training and personal development activities I attended to during my first year in Chapter 10.