A Bayesian analysis of the 2009 decline in tuberculosis morbidity in the United States.

Although annual data are commonly used to model linear trends and changes in trends of disease incidence, monthly data could provide additional resolution for statistical inferences. Because monthly data may exhibit seasonal patterns, we need to consider seasonally adjusted models, which can be theoretically complex and computationally intensive. We propose a combination of methods to reduce the complexity of modeling seasonal data and to provide estimates for a change in trend when the timing and magnitude of the change are unknown. To assess potential changes in trend, we first used autoregressive integrated moving average (ARIMA) models to analyze the residuals and forecast errors, followed by multiple ARIMA intervention models to estimate the timing and magnitude of the change. Because the variable corresponding to time of change is not a statistical parameter, its confidence bounds cannot be estimated by intervention models. To model timing of change and its credible interval, we developed a Bayesian technique. We avoided the need for computationally intensive simulations by deriving a closed form for the posterior distribution of the time of change. Using a combination of ARIMA and Bayesian methods, we estimated the timing and magnitude of change in trend for tuberculosis cases in the United States. Published 2012. This article is a US Government work and is in the public domain in the USA.