Estimating the Baseline and Threshold for the Incidence of Diseases with Seasonal and Long-Term Trends.

In epidemiology, it is very important to estimate the baseline incidence of infectious diseases. From this baseline, the epidemic threshold can be derived as a clue to recognize an excess incidence, i.e. to detect an epidemic by mathematical methods. Nevertheless, a problem is posed by the fact that the incidence may vary during the year, as a rule, in a season dependent manner. To model the incidence of a disease, some authors use seasonal trend models. For instance, Serfling applies the sine function with a phase shift and amplitude. A similar model based on the analysis of variance with kernel smoothing and Serfling's higher order models, i.e. models composed of multiple sine-cosine function pairs with a variably long period, will be presented below. Serfling's model uses a long-term linear trend, but the linearity may not be always acceptable. Therefore, a more complex, long-term trend estimation will also be addressed, using different smoothing methods. In addition, the issue of the time unit (mostly a week) used in describing the incidence is discussed.