Exploring time variation in survival models

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The exploration of time-variation in survival models revolves around two key questions: whether the effect of a covariate remains constant over time or changes, and if it changes, what form does that dynamic structure take? This work investigates approaches to address these questions, proposing flexible methods for accurately describing underlying dynamic structures. A crucial aspect of applied statistics is managing model complexity to ensure interpretability, which necessitates model selection by comparing varying complexities. The focus is on identifying a statistical model that balances complexity with parsimony. Two statistical concepts are examined: likelihood-based theory and Bayesian statistics. In the likelihood framework, model estimation involves maximizing likelihood variants, while Bayesian inference relies on posterior distributions of model parameters. Model selection in the likelihood framework utilizes likelihood ratio tests, whereas Bayesian model criteria are used for comparing non-nested models. The nature of the data influences modeling approaches, as survival time can be continuous or discrete. This work employs the dynamic Cox model for continuous survival time and the dynamic logit model for discrete data. Emphasizing practical relevance, the book prioritizes methods that are straightforward to implement and computationally feasible, ensuring ease of understanding for practitioners.