On Bayesian prediction under nonparametric transformation models with doubly censored data

Abstract

This MPhil thesis extends, in two main ways, a previous framework on the predictions of right censored survival outcomes under nonparametric transformation models. The first extension is regarding censoring scheme complexity. Specifically, we extend from right censoring to double censoring, which contains both left and right censoring. The previous work relied on proposing a weakly informative prior for the transformation function to mitigate model unidentifiability, and we heavily modify this prior so that nonparametric transformation models can be implemented under both random and fixed double censoring. By comparing our predictions results to two leading methods, we demonstrate that the proposed approach is computationally effective under double censoring and successfully utilizes a robust and flexible nonparametric transformation model. The second extension is regarding model complexity. Specifically, we extend from nonparametric transformation models, which contain two unidentified infinite-dimensional parameters to a certain model with more than two such parameters. For this more sophisticated model, we attempt to adjust priors to control posterior Markov Chain Monte Carlo (MCMC) mixing. Numerical illustrations show that carefully chosen priors can indeed mitigate poor mixing under the more complex model. Subsequently, we consider how weak a prior can be to still allow for well-mixed MCMC chains. Driven by this question, we explore the concept of informativeness further and speculate to quantify it through a mathematical definition. This definition may contribute to a criterion for identifying priors that are sufficiently informative, as to potentially help address poor mixing generally for models with more than two unidentified infinite-dimensional parameters.