Measuring spatial effects in time to event data: a case study using months from angiography to coronary artery bypass graft (CABG).

The application of Bayesian hierarchical models to measure spatial effects in time to event data has not been widely reported. This case study aims to estimate the effect of area of residence on waiting times to coronary artery bypass graft (CABG) and to assess the role of important individual specific covariates (age, sex and disease severity). The data involved all patients with definite coronary artery disease who were referred to one cardiothoracic unit from five contiguous health authorities covering 488 electoral wards (areas). Time to event was the waiting time in months from angiography (diagnosis) to CABG (event). A number of discrete time survival models were fitted to the data. A discrete baseline hazard was estimated by fitting waiting time non-parametrically into the models. Ward was fitted as a spatial effect using a Gaussian Markov random field prior. Individual specific covariates considered were age, sex and number of diseased vessels. The recently proposed DIC criteria was used for comparing models. Results showed a marked spatial effect on time to bypass surgery after including age, sex and disease severity in the model. Notably this spatial effect was not apparent when these covariates were not included in the model. The observed small area spatial variation in time to CABG warrants further investigation.