Flexible Bayesian excess hazard models using low-rank thin plate splines.

Excess hazard models became the preferred modelling tool in population-based cancer survival research. In this setting, the model is commonly formulated as the additive decomposition of the overall hazard into two components: the excess hazard due to the cancer of interest and the population hazard due to all other causes of death. We introduce a flexible Bayesian regression model for the log-excess hazard where the baseline log-excess hazard and any non-linear effects of covariates are modelled using low-rank thin plate splines. Using this type of splines will ensure that the log-likelihood function retains tractability not requiring numerical integration. We demonstrate how to derive posterior distributions for the excess hazard and for net survival, a population-level measure of cancer survival that can be derived from excess hazard models. We illustrate the proposed model using survival data for patients diagnosed with colon cancer during 2009 in London, England.