BaySTDetect: detecting unusual temporal patterns in small area data via Bayesian model choice

Space-time modeling of small area data is often used in epidemiology for mapping chronic disease rates and by government statistical agencies for producing local estimates of, for example, unemployment or crime rates. Although there is typically a general temporal trend, which affects all areas similarly, abrupt changes may occur in a particular area, e.g. due to emergence of localized predictors/risk factor(s) or impact of a new policy. Detection of areas with "unusual" temporal patterns is therefore important as a screening tool for further investigations. In this paper, we propose BaySTDetect, a novel detection method for short-time series of small area data using Bayesian model choice between two competing space-time models. The first model is a multiplicative decomposition of the area effect and the temporal effect, assuming one common temporal pattern across the whole study region. The second model estimates the time trends independently for each area. For each area, the posterior probability of belonging to the common trend model is calculated, which is then used to classify the local time trend as unusual or not. Crucial to any detection method, we provide a Bayesian estimate of the false discovery rate (FDR). A comprehensive simulation study has demonstrated the consistent good performance of BaySTDetect in detecting various realistic departure patterns in addition to estimating well the FDR. The proposed method is applied retrospectively to mortality data on chronic obstructive pulmonary disease (COPD) in England and Wales between 1990 and 1997 (a) to test a hypothesis that a government policy increased the diagnosis of COPD and (b) to perform surveillance. While results showed no evidence supporting the hypothesis regarding the policy, an identified unusual district (Tower Hamlets in inner London) was later recognized to have higher than national rates of hospital readmission and mortality due to COPD by the National Health Service, which initiated various local enhanced services to tackle the problem. Our method would have led to an early detection of this local health issue.