A spatially-adaptive dynamic conditionally autoregressive model for longitudinal periodontal data

Attachment loss (AL), the distance down a tooth′s root that is no longer attached to surrounding bone by periodontal ligament, is a common measure of periodontal disease. In this paper, we develop a spatiotemporal model to monitor progression of AL. Our model is an extension of the conditionally autoregressive (CAR) prior, which spatially smooths estimates towards their neighbors. However, since AL often exhibits burst of large values in space and time, we develop a non-stationary spatiotemporal CAR model that allows the degree of spatial and temporal smoothing to vary in different regions of the mouth. To do this, we assign each AL measurement site its own set of variance parameters and spatially smooth the variances with spatial priors. A heuristic is developed to measure the complexity of the site-specific variances which is used to select priors that ensure that all the parameters in the model will be well identified. This model is shown to improve the fit compared to the usual dynamic CAR model for one patient′s AL measurements at four visits separated by three-month intervals.