One-dimensional, two-dimensional, and three dimensional B-splines to specify space -time interactions in Bayesian disease mapping: Model fitting and model identifiability

In recent years, models incorporating splines have been considered for smoothing risks in disease mapping. Although these models are very flexible, they can be computationally demanding in certain cases. In this work, one, two, and three-dimensional B-splines (penalized or unpenalized) are considered to model space-time interactions. Model identifiability issues are discussed and appropriate constraints are clearly established. As computing time could be a limitation in real practice, integrated nested Laplace approximations are used for model fitting and inference. The complete set of proposed models are illustrated using cancer mortality data in small areas. We conclude that if the number of small areas is not big, one dimensional P-splines for the space-time interaction could be a good choice. When the number of small areas increases substantially, two-dimensional and mainly three dimensional splines are computationally better alternatives.