Pathogen seasonality and links with weather in England and Wales: a big data time series analysis

Cherrie, Mark P. C.; Nichols, Gordon; Iacono, Gianni Lo; Sarran, Christophe; Hajat, Shakoor; Fleming, Lora E.

Descriptive statistics were generated for the organisms including total count, crude prevalence rate per month, peak month and plots of time-series patterns (for gastro-intestinally acquired infections and those from respiratory transmission). We applied a two stage automated analysis to: a) detect seasonality and b) identify correlations with weather variables. The first stage was the seasonality detection analysis, undertaken in Rstudio (ver 0.98.507). Description of the forecast package, which was used extensively in the analysis to automatically detect seasonal patterns, has been detailed elsewhere [18] . Briefly, the pathogen time series data were decomposed via Box Cox Transformations into trend, seasonal and irregular components, which were used to forecast the time series into the future [18] . The algorithm automatically selects model parameters such as trend (with or without a dampening parameter) and noise (ARMA (p,q) process) using model fit statistics (i.e. minimising Akaike Information Criteria (AIC)). A TBATS model, as described above, was fitted for each organism serotype (with a non-zero count) using the weekly periodicity (i.e. the most granular temporal resolution available). The models were re-run with data aggregated at monthly and quarterly periodicities to investigate seasonality at different temporal aggregations [19] . Each time the model would provide a logical output (i.e. true/false) as to whether the model fit improved with the inclusion of the seasonal component (i.e. consistent repeating pattern over time). This is because the algorithm fits two models, seasonal and non-seasonal, and selects the seasonal model if the AIC is lower than the non-seasonal model (heuristically, it selects the model that results in the best combination of good fit and lower number of parameters). To limit the seasonality definition to those whose model fit was significantly better with the addition of the seasonal component, we calculated the difference between the seasonal and non-seasonal AIC (Δ i = AIC nonseasonal − AIC seasonal ) and excluded organisms with AIC difference greater than 10, as suggested as a suitable cut-off by Burnham and Anderson [20] . The pathogens at a monthly resolution with AIC difference greater than 10 were used in subsequent analysis with weather variables.