Relaxing Assumptions on the Censoring Mechanism in Survival Link-Based Additive Models

Survival models are frequently encountered in applications. In these models, the response of interest, the time until a particular event occurs, is often right censored. Most estimation methods assume that the event time and the censoring time are stochastically independent and non-informative conditional on covariates. However, these assumptions may be questioned. The aim of this thesis is to relax these assumptions in a class of flexible parametric survival models, called survival link-based additive models. The assumption of non-informative censoring is relaxed by assuming that the marginal survival functions of the event and censoring times have parameters in common. In particular, we provide evidence on the efficiency gains produced by the newly introduced informative estimator when compared to its non-informative counterpart. The independence assumption is relaxed by modelling both the event time and the censoring time simultaneously using copula functions. We provide some preliminary arguments towards model identification although this topic is very challenging and requires more future work. In these survival link-based additive models, the baseline functions are estimated non-parametrically by monotonic P-splines, whereas covariate effects are flexibly determined using additive predictors that allow for a vast variety of effects. Parameter estimation is reliably carried out within a penalised maximum likelihood framework with integrated automatic multiple smoothing parameter selection. We derive the √n-consistency and asymptotic normality of the estimators proposed in this thesis. Their finite sample performance are investigated via Monte Carlo simulation studies, and the approaches illustrated using two cases study based on infants hospitalised for pneumonia as well as prostate cancer data. The R package GJRM has been extended to incorporate the developments discussed in this thesis to facilitate transparent and reproducible researc