Box-Jenkins modelling in medical research

Notifications of diseases, entries in a hospital, injuries due to accidents, etc., are frequently collected in fixed equally spaced intervals. Such observations are likely to be dependent. In environmental medicine, where series such as daily concentrations of pollutants are collected and analysed, it is evident that dependence of consecutive measurements may be important. A high concentration of a pollutant today has a certain 'inertia', i.e. a tendency to be high tomorrow as well. Dependence of consecutive observations may be equally important when data such as blood glucose are recorded within a single patient. ARIMA models (autoregressive integrated moving average models, Box-Jenkins models), which allow the stochastic dependence of consecutive data to be modelled, have become well established in such fields as economics. This article reviews basic concepts of Box-Jenkins modelling. The methods are illustrated by applications. In particular, the following topics are presented: the ARIMA model, transfer function models (assessment of relations between time series) and intervention analysis (assessment of changes of time series).