Development and application of methodology for the parametric analysis of complex survival and joint longitudinal-survival data in biomedical research

摘要

The occurrence of survival, or time-to-event, data is commonplace in medical research,\udwhere interest lies in the time it takes from a given baseline, for an event of interest\udto occur, and the factors that are associated with it. For example, this could be the\udeffect of a treatment on the time to death since diagnosis of cardiovascular disease. The\udprimary aim of this thesis is to develop parametric methods for the analysis of complex\udsurvival data, including the extension to joint models of longitudinal and survival data,\udto provide a number of advantages over the commonly used semi-parametric Cox model.\udNew and current methodology is often assessed using simulation studies; however, often\udin the field of survival analysis they are simplistic and fail to reflect biologically plausible\udscenarios. In this thesis a general algorithm for simulating complex survival data,\udfrom any given hazard function, is proposed and assessed. A general framework for the\udparametric analysis of survival data is then developed, utilising numerical quadrature,\udillustrated in detail using the special case of restricted cubic splines to model the baseline\udhazard and time-dependent effects. Extensions to the framework including cluster\udrobust standard errors and excess mortality models are also considered. Finally, the\udjoint longitudinal-survival modelling framework is extended to incorporate the Royston-\udParmar survival model, and a mixture of two parametric distributions, both evaluated\udthrough simulation, utilising the proposed simulation algorithm, showing advantages\udover more simple parametric approaches. The estimation of joint models, using Gaussian\udquadrature, is also evaluated through an extensive simulation study. Throughout\udthe thesis, user friendly software is developed to implement the methodological components, allowing statisticians and non-statisticians alike, to apply the methods directly.\udA variety of clinical datasets in the areas of cancer, cardiovascular disease and liver\udcirrhosis are used to exemplify the proposals.