Sensitivity analysis for correlated survival models
In this thesis we introduce a model for informative censoring. We assume that the joint distribution of the failure and the censored times depends on a parameter δ, which is actually a measure of the possible dependence, and a bias function B(t,θ). Knowledge of δ means that the joint distribution is fully specified, while B(t,θ) can be any function of the failure times. Being unable to draw inferences about δ, we perform a sensitivity analysis on the parameters of interest for small values of δ, based on a first order approximation. This will give us an idea of how robust our estimates are in the presence of small dependencies, and whether the ignorability assumption can lead to misleading results. Initially we propose the model for the general parametric case. This is the simplest possible case and we explore the different choices for the standardized bias function. After choosing a suitable function for B(t,θ) we explore the potential interpretation of δ through it's relation to the correlation between quantities of the failure and the censoring processes. Generalizing our parametric model we propose a proportional hazards structure, allowing the presence of covariates. At this stage we present a data set from a leukemia study in which the knowledge, under some certain assumptions, of the censored and the death times of a number of patients allows us to explore the impact of informative censoring to our estimates. Following the analysis of the above data we introduce an extension to Cox's partial likelihood, which will call "modified Cox's partial likelihood", based on the assumptions that censored times do contribute information about the parameters of interest. Finally we perform parametric bootstraps to assess the validity of our model and to explore up to what values of parameter δ our approximation holds.