Exploring Time-Variation in Survival Models

The exploration of time-variation in survival models can be summarised in two general questions: First, can the effect of a covariate be assumed to be time-constant, or does it distinctly change over time? Secondly, if the effect changes over time, of which form is the dynamic structure? The book investigates possible approaches to explore these two questions. Flexible methods are proposed, which allow for a precise description of the underlying dynamic structures. An essential task in applied statistics is thereby to limit model complexity in order to maintain interpretable solutions. This implies model selection by comparison of models with different complexity. A major focus pursued in the book is to find a statistical model that is as complex as needed and as parsimonious as possible. Two different statistical concepts are considered: A likelihood based theory and Bayesian statistics. While model estimation in the likelihood framework is realised by maximising variants of the likelihood, in Bayesian statistics inference is based on posterior distributions of the model parameters. In the likelihood framework model selection can then be based on likelihood ratio tests, whereas in the Bayesian framework, Bayesian model criteria are employed to compare different, non-nested models. Beside the theoretical investigations, the particular structure of the data at hand leads to different modelling approaches. This is since survival time can either be continuous or discrete. Both situations are investigated by employing two different models, the dynamic Cox model for continuous survival time and the dynamic logit model for discrete data. Parsimony in modelling is highly relevant in practical work. The book therefore concentrates on methods which are straightforward to implement and use in practice. In particular it is ensured that methods are computationally feasible and easy to understand.