Eletti, Alessia; (2024) General flexible modelling frameworks for multivariate and multi-state survival outcomes. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Health data often give rise to complex survival outcomes, which cannot be dealt with using traditional methods without incurring a loss of crucial information. We consider four such cases, motivated by different clinical settings, and present, for each, a general and flexible modelling framework, with the aim of achieving a better understanding of disease patterns and more accurate predictions. We first focus on diseases which manifest through multiple organs, resulting in dependent time-to-events. We propose a copula-based framework for the joint modelling of bivariate survival outcomes, specified as flexible functions of time and the covariates of interest, with a mixed censoring scheme. When interest lies in the progression of a disease, multi-state processes represent a powerful modelling approach. For the second case, we consider a continuously observed process, and propose a unified framework that exploits the simplification implied by the exact knowledge of the times-to-events. It combines the flexible specification of each transition, with a simulation-based approach to compute the transition probabilities, posing no limitations on the processes supported. When constant monitoring of the process is not possible, existing models do not allow the information contained in the intermittently-observed data thus limiting the specifications supported to be fully exploited. The third framework proposed overcomes this challenge by exploiting a novel development, i.e. a closed-form expression for the local curvature information of the transition probability matrix, and supports flexible modelling for virtually any type of process. Finally, we develop an approach to model two dependent multi-state processes. This is motivated by clinical applications which give rise to two (or more) associated diseases, making the modelling of their joint progression of interest. The frameworks described are implemented in the R packages GJRM and flexmsm and are exemplified through case studies based on clinical data.

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