Comparing CAR and P-spline models in spatial disease mapping

Smoothing risks is one of the main goals in disease mapping as classical measures, such as standardized mortality ratios, can be extremely variable. However, smoothing risks might hinder the detection of high risk areas, since these two objectives are somewhat contradictory. Most of the work on smoothing risks and detection of high risk areas has been derived using conditional autoregressive (CAR) models. In this work, penalized splines (P-splines) models are also investigated. Confidence intervals for the log-relative risk predictor will be derived as a tool to detect high-risk areas. The performance of P-spline and CAR models will be compared in terms of smoothing (relative bias), sensitivity (ability to detect high risk areas), and specificity (ability to discard false patterns created by noise) through a simulation study based on the well-known Scottish lip cancer data.