Farrington Flexible Algorithm

Arguments	Description
Start Year	Insert the start year of the data
Start Month	Insert the start month of the data
Start Day	Insert the data start date
Frequency	If the time unite is weekly, select the number 52 and if the time unite is monthly, select the number 12
Range of Data(min)	Insert the beginning of the range under review
Range of Data(max)	Insert the end of the range under review
b	How many years back in time to include when forming the base counts.
w )windows size(	Windows size, i.e. number of weeks to include before and after the current week
alpha	An approximate (two-sided) (1 − α) prediction interval is calculated
weightsThreshold	A scalar indicating when observations are seen as outlier. In the original Farrington proposal the value was 1 (default value), in the improved version this value is suggested to be 2.58
Choose xlsx File	In this section, upload the data file. The data format should be according to the data structure

Flexible Algorithm Farrington

The Farrington Flexible algorithm is one of the algorithms based on generalized linear models (GLM), and the improved method of the Farrington algorithm, which was developed by Nuofaily et al. (2013). This model estimates the number of infections in the previous week and includes a linear trend and a ten-level annual factor. The annual factor encompasses a reference period of seven weeks, including one recent week, three past weeks, and three future weeks (), as well as nine five-week periods per year. Additionally, the model takes into account the number of corresponding weeks in previous years by considering b years in the past. The corresponding linear logarithmic model is expressed as follows:

where represents the seasonal factor corresponding to week ; assuming , . In this model a trend is always fitted, except in cases of sparse data for specific infections.
REFERENCE
Noufaily A, Enki DG, Farrington P, Garthwaite P, Andrews N, Charlett A. An improved algorithm for outbreak detection in multiple surveillance systems. Statistics in medicine. 2013
Mar 30;32(7):1206-22.
Zareie, B., Poorolajal, J., Roshani, A. et al. Outbreak detection algorithms based on generalized linear model: a review with new practical examples. BMC Med Res Methodol 23, 235 (2023).
https://doi.org/10.1186/s12874-023-02050-z