Multiscale detection of localized anomalous structure in aggregate disease incidence data.

We present a modelling framework for detection of potentially anomalous structure in aggregate spatial disease incidence data in a manner sensitive to localization at multiple scales and/or positions. The key technical contribution is the re-casting of the components of a multiscale disease mapping methodology, recently introduced by the authors in an earlier paper, into a form appropriate for hypothesis testing. In particular, we describe how hypotheses of spatially clustered variations in disease incidence may be linked in one-to-one correspondence with collections of hypotheses on the values of certain multiscale parameters associated with a user-defined hierarchy of nested partitions of an overall spatial region. A Bayesian hypothesis testing methodology is developed in the context of a standard Poisson measurement model, over the collection of possible multiscale hypotheses. We discuss the specification of hyper parameters and prior distributions on the space of models. The methodology is illustrated on both simulated and real data.