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).