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.

Department of Biostatistics National Institute of Public Health Prague Czech Republic

Department of Infectious Diseases Epidemiology Centre for Epidemiology and Microbiology National Institute of Public Health Prague CzechRepublic

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