Influenza predictions using county-level absences
We evaluated negative binomial models of seasonal variables (i.e., calendar week, average weekly temperature, and relative humidity) alone, and including weekly all-cause county-level school absences at one-, two-, and three-week lags. One- and third-week lagged absences had similar model performance (Supplemental Table 2), therefore, we used one-week lagged absences in all models to better reflect influenza’s infectious period (i.e. one-week spread)(25). Compared to seasonal models, AICs of in-sample models including calendar week, average weekly temperature, average weekly relative humidity, and one-week lagged weekly county-level all-cause absences either stayed the same or slightly worsened ( AICc=2, 1, and 0, Table 1), whereas models of calendar week, average weekly temperature, and one-week lagged weekly absences had slightly improved fits ( AICc=-4, -4, -4, Table 1). For prediction performance, MAEs either stayed the same or decreased when including one-week lagged weekly absences in models of calendar week, average weekly temperature and relative humidity relative to seasonal-only models (relMAE=0.95, 1.0, & 0.95, Table 1).
For individual influenza seasons, weekly-lagged country-level absence multivariate models predicted atypical seasons poorly, but predicted more typical seasons (i.e., 2013-2014, 2014-2015) with relatively high accuracy (R2 of 0.91 and 0.57) (Figure 2A). Predicted seasonal peaks were earlier and over-predicted during low transmission seasons (i.e., 2010-2011 and 2011-2012), whereas during high transmission seasons (2014-2015) had later predicted peaks, but of equal magnitude (Figure 2A & 2C). Compared to seasonal models, predicted cases from all-cause absence models varied (either increased or decreased) over the five seasons (Figure 2B), with seasonal peak timing varying most (Figure 2B). Calendar week, average weekly temperature, and absence models varied the most across seasons (Figure 2B). The model containing all seasonal variables and weekly absences had the smallest changes in predicted cases. Lowest MAE models depended on the withheld validation season (Supplemental Table 5). Given the consistently low MAEs of the model including calendar week, average weekly temperature, average weekly relative humidity and school absence, we present results from this model.