Abstract

Recently, there has been an increasing use of flexible parametric survival models to analyse survival outcomes. Much of our work is based on a survival analysis model in which the baseline hazard function is modelled flexibly using an M-spline. Motivated by the analysis of a large kidney transplant data set supplied by NHSBT (NHS Blood and Transplant), we extend this baseline hazard function flexibility in various ways to allow a random effect for each transplant centre.After providing an introduction to survival analysis, we present an exploratory analysis of the NHSBT kidney transplant data. Next, we analyse the data using Bayesian parametric and multilevel Bayesian parametric survival models. Then, we introduce M-splines to model the baseline hazard function. After this, we introduce transplant centre random effects by allowing the M-spline parameters to depend on the centre. This yields a multilevel Bayesian flexible survival model based on M-splines. As inference is performed within the Bayesian framework, we discuss the choice of the prior distribution for unknown model parameters. Our choice encourages the centre specific baseline hazard functions to be similar.Our analysis indicates that the Bayesian flexible and the Bayesian multilevel flexible parametric survival models produce results that are similar to the classic multilevel Cox model in terms of hazard ratios. We also discuss the choice of the knots used to define the M-spline. We use internal-external cross validation to compare model performance.As the NHSBT kidney transplant data has high censoring rates in the transplant centres, we designed a series of predefined censoring rate simulation studies to assess the effect of censoring on model performance. We found that, when the model is 'right' for the data, unbiased parameter estimates are obtained, even when the censoring rate is high. However, as the censoring rate increases, confidence/credible interval widths increase, meaning that it becomes harder to identify a covariate effect. When the model is 'wrong' for the data, higher censoring rates can sometimes lead to better identification of covariate effects.Amongst a range of results, we found that donor age has a strong relationship with kidney transplant outcomes; the older the age group, the worse the survival. We present a visualization that shows how survival curves vary by centre.

Awarding Institution(s)

University of Plymouth

Supervisor

Yinghui Wei, John Eales, Julian Stander

Keywords

Survival Analysis, Bayesian Statistics, Multilevel models, Multiple Centres

Document Type

Thesis

Publication Date

2025

Embargo Period

2025-09-04

Deposit Date

September 2025

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

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