Use of time-series analysis in infectious disease surveillance

This article reviews the practical aspects of the use of ARIMA (autoregressive, integrated, moving average) modelling of time series as applied to the surveillance of reportable infectious diseases, with special reference to the widely available SSS1 package, produced by the Centers for Disease Control and Prevention. The main steps required by ARIMA modelling are the selection of the time series, transformations of the series, model selection, parameter estimation, forecasting and updating of the forecasts. The difficulties most likely to be encountered at each step are described and possible solutions are offered. Examples of successful and unsuccessful modelling are presented and discussed. Other methods, such as INAR modelling or Markov chain analysis, which can be applied to situations where ARIMA modelling fails are also dealt with, but they are less practical. ARIMA modelling can be carried out by adequately trained nonspecialists working for local agencies. Its usefulness resides mostly in providing an estimate of the variability to be expected among future observations. This knowledge is helpful in deciding whether or not an unusual situation, possibly an outbreak, is developing.