In this paper, we develop a so-called relative survival analysis that is used to model the excess risk of a certain sub-population relative to the natural mortality risk which is present in the whole population. Such models are typically used in population-based studies that aim at identifying prognostic factors for disease-specific mortality, with data on specific causes of death not being available. This paper combines relative survival with Bayesian geoadditive regression allowing for a flexible semiparametric analysis. Our work has been motivated by continuous-time spatially referenced survival data on breast cancer where causes of death are not known. A detailed analysis of these data is given. The usefulness of the approach is further illustrated by means of a simulated data set.