Statistical analysis
We predicted weekly influenza cases over seven influenza seasons using negative binomial regression models. Continuous predictor variables were weekly absence rates (lagged by one-week), calendar week, average weekly temperature, and relative humidity. Models used predictors individually and in combination. The offset term represented the estimated annual Allegheny Country population for 2007 and 2010-2015 influenza seasons. Seasonal variables (calendar week, temperature, and relative humidity) accounted for temporal and climatic variation of influenza. We modeled calendar week, average weekly temperature, and average weekly relative humidity as nonlinear terms using thin-plate penalized splines in generalized additive models (mgcv R package)(17). Models including school- (i.e., elementary, middle and high school) and grade-specific absences (alone and in combination) were evaluated to determine if finer administrative-level absences improved model fits and predictions. From three school-based cohort studies, we compared all-cause and cause-specific absence model performance for single seasons (2007, 2012, and 2015), and pooled over these seasons.
Sensitivity analyses examined absence duration, and lagged influenza, and kindergarten-specific absences. We used one-day and two-day or longer absences to assess the impact of absence duration on weekly influenza predictions from 2010 to 2015. Models used one-day absences, and absences two days or longer individually, together, and in models containing average temperature, relative humidity, and calendar week. We also assessed weekly influenza predictions from models including one-week lagged influenza cases, and county-level and kindergarten-specific all-cause absences.
We compared nested and non-nested models using Akaike’s Information Criterion corrected for small sample sizes (AICc). Decreased AICc signified improved model fits. Two-sided 5% alpha-level determined statistical significance. Analyses used R version 3.1.3 (R Foundation for Statistical Computing, Vienna, Austria, 2016).