From the Research
For modeling diarrhea admissions seasonality, I recommend using only the sine and cosine terms: sin(2piweekepi/52) + cos(2piweekepi/52) + sin(4piweekepi/52) + cos(4piweekepi/52). This approach is preferable because these Fourier terms specifically capture seasonal patterns - the first pair models annual cycles (52-week periodicity) while the second pair captures semi-annual patterns (26-week periodicity). Including the linear and quadratic terms (weekepi + weekepi*weekepi) would be appropriate only if you expect a long-term trend in admissions beyond seasonality, such as a general increase or parabolic pattern over time. For infectious diarrheal diseases, seasonality is typically the dominant pattern, with peaks often corresponding to specific weather conditions or seasonal behaviors, as observed in studies such as 1 which analyzed the effects of climate variability and seasonal influence on diarrheal disease. The Fourier terms alone provide a more parsimonious model focused specifically on cyclical patterns, making interpretation clearer. You can always evaluate model fit with and without the trend terms to confirm which approach better represents your data.
Some studies, such as 2, have shown that viral infections, particularly norovirus, play a significant role in the seasonality of infectious diarrhea, with winter peaks being mainly due to norovirus and rotavirus. This highlights the importance of capturing seasonal patterns accurately in the model.
In terms of the evidence provided, while studies such as 3 and 4 discuss statistical models for hospital admissions and the diagnosis and management of chronic diarrhea, respectively, they do not directly inform the choice of terms for modeling seasonality in diarrhea admissions. However, they do underscore the complexity of diarrhea as a symptom and the importance of accurate modeling for public health purposes.
Ultimately, the choice of model terms should be guided by the goal of accurately capturing the seasonal patterns in diarrhea admissions, and the sine and cosine terms are well-suited for this purpose, as supported by the most recent and highest quality studies, such as 1 and 2.