The use of transfer function models, intervention analysis and related time series methods in epidemiology

In epidemiology, data often arise in the form of time series e.g. notifications of diseases, entries to a hospital, mortality rates etc. are frequently collected at weekly or monthly intervals. Usual statistical methods assume that the observed data are realizations of independent random variables. However, if data which arise in a time sequence have to be analysed, it is possible that consecutive observations are dependent. In environmental epidemiology, where series such as daily concentrations of pollutants were collected and analysed, it became clear that stochastic dependence of consecutive measurements may be important. A high concentration of a pollutant today e.g. has a certain inertia i.e. a tendency to be high tomorrow as well. Since the early 1970s, time series methods, in particular ARIMA models (autoregressive integrated moving average models) which have the ability to cope with stochastic dependence of consecutive data, have become well established in such fields as industry and economics. Recently, time series methods are of increasing interest in epidemiology. Since these methods are not generally familiar to epidemiologists this article presents their basic concepts in a condensed form. This may encourage readers to consider the methods described and enable them to avoid pitfalls inherent in time series data. In particular, the following topics are discussed: Assessment of relations between time series (transfer function models). Assessment of changes of time series (intervention analysis), forecasting and some related time series methods.