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\begin{document}

\title{Predicting virologically-confirmed influenza using school absences in
Allegheny County, Pennsylvania, USA during the 2007-2015 influenza
seasons}



\author[1]{Talia Quandelacy}%
\author[2]{Shanta Zimmer}%
\author[3]{Justin Lessler}%
\author[4]{Charles VUKOTICH}%
\author[4]{Rachel Bieltz}%
\author[5]{Kyra Grantz}%
\author[4]{David Galloway}%
\author[6]{Jonathan Read}%
\author[7]{Yenlik Zheteyeva}%
\author[7]{Hongjiang  Gao}%
\author[8]{Amra Uzicanin}%
\author[5]{Derek Cummings}%
\affil[1]{Johns Hopkins University Bloomberg School of Public Health}%
\affil[2]{University of Pittsburgh School of Medicine}%
\affil[3]{Johns Hopkins Bloomberg School of Public Health}%
\affil[4]{University of Pittsburgh}%
\affil[5]{University of Florida}%
\affil[6]{University of Liverpool}%
\affil[7]{Centers for Disease Control and Prevention}%
\affil[8]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
Background Children are important in community-level influenza
transmission. School-based monitoring may inform influenza surveillance.
Methods We used reported weekly confirmed influenza in Allegheny County
during the 2007, and 2010-2015 influenza seasons using Pennsylvania's
Allegheny County Health Department all-age influenza cases from health
facilities, and all-cause and influenza-like illness (ILI)-specific
absences from nine county school districts. Negative binomial regression
predicted influenza cases using all-cause and illness-specific absence
rates, calendar week, average weekly temperature and relative humidity,
using four cross-validations. Results School districts reported
2,184,220 all-cause absences (2010-2015). Three one-season studies
reported 19,577 all-cause and 3,012 ILI-related absences (2007, 2012,
2015). Over seven seasons, 11,946 confirmed influenza cases were
reported. Absences improved seasonal model fits and predictions.
Multivariate models using elementary school absences outperformed middle
and high school models (relative mean absolute error (relMAE)=0.94,
0.98, 0.99). K-5 grade-specific absence models had lowest mean absolute
errors (MAE) in cross-validations. ILI-specific absences performed
marginally better than all-cause absences in two years, adjusting for
other covariates, but markedly worse one year. Conclusions Our findings
suggest seasonal models including K-5th grade absences predict all-age
confirmed influenza and may serve as a useful surveillance tool.%
\end{abstract}%



\sloppy


\textbf{Predicting virologically-confirmed influenza using school
absences in Allegheny County, Pennsylvania, USA during the 2007-2015
influenza seasons}

\textbf{Running Title:} School absences predicting county influenza

Talia M. Quandelacy\textsuperscript{1,2}, Shanta
Zimmer\textsuperscript{3,4}, Justin Lessler\textsuperscript{1}, Charles
Vukotich\textsuperscript{3}, Rachel Bieltz\textsuperscript{3}, Kyra H.
Grantz\textsuperscript{5}, David Galloway\textsuperscript{3}, Jonathan
M. Read\textsuperscript{6}, Yenlik Zheteyeva\textsuperscript{7},
Hongjiang Gao\textsuperscript{7}, Amra Uzicanin\textsuperscript{7},
Derek A.T. Cummings\textsuperscript{1,5}

\textbf{Affiliations:}

1. Johns Hopkins University, Baltimore, MD, USA (TMQ
taliaquandelacy@jhu.edu, JL justin@jhu.edu, DATC datc@ufl.edu)

2. University of Colorado, Anschutz Medical Campus, Aurora, CO (TMQ
talia.quandelacy@cuanschutz.edu)

3. University of Pittsburgh, Pittsburgh, PA, USA (CV charlesv@pitt.edu,
RB rlb105@pitt.edu, DG ddg5@pitt.edu)

4. University of Colorado, Denver, CO, USA (SMZ
shanta.zimmer@ucdenver.edu)

5. University of Florida, Gainesville, FL, USA (KHG kgrantz@ufl.edu,
DATC datc@ufl.edu)

6. Lancaster University, Lancaster, United Kingdom (JMR
jonathan.read@lancaster.ac.uk)

7. Centers for Disease Control and Prevention, Atlanta, GA, USA (YZ
igg0@cdc.gov, HG uxi7@cdc.gov, AU aau5@cdc.gov)

\textbf{Corresponding Author:} Talia Quandelacy
(talia.quandelacy@cuanschutz.edu)

\emph{Conflict of interest}

The authors declare that they have no conflicts

\emph{Authorship}

DATC, and JL contributed to concept and design of analysis. TMQ
contributed to analyses. TMQ, DATC, JMR, and JL drafted and revised
manuscript. TMQ, DATC, JL, CV, SZ, KG, RB, DG, YZ, BD, HG, and AU gave
final approval.

\emph{Acknowledgments}

This work was supported by the US Centers for Disease Control and
Prevention (Cooperative Agreement 1 U01 CK000337-01 to DATC), and the
Engineering and Physical Sciences Research Council (grant EP/N014499/1
to JMR). We would like to thank the Allegheny County Department of
Health (Dr. Luanne Brink and Steve Forest) for providing their data; and
the schools, staff, students, and parents who participated in PIPP,
SMART, and SMART\textsuperscript{2}.~We also thank Rahaan Gangat of the
National Weather Service Pittsburgh for his assistance with climate
data. We thank Scott Zeger for helpful discussions regarding analyses.

\textbf{Word count: 3,204}

\textbf{Abstract word count: 184}

\textbf{Abstract}

\textbf{Background}

Children are important in community-level influenza transmission.
School-based monitoring may inform influenza surveillance.

\textbf{Methods}

We used reported weekly confirmed influenza in Allegheny County during
the 2007, and 2010-2015 influenza seasons using Pennsylvania's Allegheny
County Health Department all-age influenza cases from health facilities,
and all-cause and influenza-like illness (ILI)-specific absences from
nine county school districts. Negative binomial regression predicted
influenza cases using all-cause and illness-specific absence rates,
calendar week, average weekly temperature and relative humidity, using
four cross-validations.

\textbf{Results}

School districts reported 2,184,220 all-cause absences (2010-2015).
Three one-season studies reported 19,577 all-cause and 3,012 ILI-related
absences (2007, 2012, 2015). Over seven seasons, 11,946 confirmed
influenza cases were reported. Absences improved seasonal model fits and
predictions. Multivariate models using elementary school absences
outperformed middle and high school models (relative mean absolute error
(relMAE)=0.94, 0.98, 0.99). K-5 grade-specific absence models had lowest
mean absolute errors (MAE) in cross-validations. ILI-specific absences
performed marginally better than all-cause absences in two years,
adjusting for other covariates, but markedly worse one year.

\textbf{Conclusions}

Our findings suggest seasonal models including
K-5\textsuperscript{th}grade absences predict all-age confirmed
influenza and may serve as a useful surveillance tool.

\textbf{Keywords: human influenza, surveillance, prediction, school-aged
children}

\textbf{Introduction}

Influenza surveillance utilizes multiple data sources, including
syndromic indicators, laboratory-confirmed cases, and deaths(1).
Non-clinical sources have the potential to complement clinical and
laboratory data and improve influenza prediction efforts(2). Student
absenteeism is a real-time school-based indicator for influenza
surveillance tool. It is advantageous for being widely available in
real-time, having minimal reporting delays, and being relatively low
cost and is a reasonable proxy for influenza infections since school-age
children (5-17 year olds) experience higher infections compared to other
age-groups(3) and contribute to household and community-level
transmission(4).

Previous studies used school-based surveillance (i.e. absence
duration(5) or causes(6, 7)) to identify patterns correlated with
influenza- or ILI-related cases, primarily at a city-level, but
usefulness of school absenteeism as a surveillance indicator in these
studies has been mixed. Using ILI-specific absence duration predicted
2005-2008 outbreaks well in Japan with high sensitivity and
specificity(5), but a similar approach using city-level all-cause
absences from 2005-2009 had low predictive ability when predicting
outbreaks in New York City(6). Absence patterns correlated well with
sentinel surveillance in Hong Kong showing similar peaks in absenteeism
and ILI consultation and influenza detection rates, but ILI-specific
absences had low specificity(8). The varied conclusions of these studies
could be from differing school- and absence-types captured, and short
surveillance periods, but other types of absence data could have
utility.

Grade-specific differences in absences have not been explored as a
predictor of influenza but may correlate better to high-risk
infections-groups. Given the variation of infection burden and
proportion of illness-related absences by age, particular individual
school levels and grades may serve as a proxy for these high-risk
infection groups. School absenteeism may also be useful for detecting
underlying viral changes in transmission. Unusual patterns of school
absences arising across different periods of time have also been
correlated to detecting changes in influenza A and B viruses(9) and have
been attributed to detecting the re-emergence of an influenza B/Victoria
antigenic group antigenic group(10). The varied study findings of school
absenteeism suggest further assessment is needed.

Here, we evaluated how school absences models predicted weekly confirmed
influenza cases in Allegheny County, Pennsylvania over multiple
influenza seasons. We compared predictions from all-cause absence models
for the 2010-2015 influenza seasons at varying administrative levels. We
also compared predictions for individual influenza seasons (2007-2008,
2012-2013, and 2015-2016) from models including all-cause and
ILI-related absences from three school-based cohort studies.

\textbf{Methods}

\emph{Ethics}

Our analyses used only de-identified data. We obtained Institutional
Research Board approval from University of Pittsburgh (PRO13100580),
Johns Hopkins Bloomberg School of Public Health (IRB \#5474), Centers
for Disease Control and Prevention (IRB\#00000319), and the Allegheny
County Department of Health.

\emph{Data}

Allegheny County Health Department (ACHD) provided
virologically-confirmed influenza case data (N=11,946) for 2007-2008,
and 2010-2015 influenza seasons. A reported confirmed influenza case was
a positive laboratory-confirmed test (i.e., rapid diagnostic test,
reverse-transcriptase polymerase chain reaction, or viral culture)
reported by hospital emergency departments or sentinel medical providers
in Allegheny Country from any individual experiencing influenza-like
illness. Weekly all-cause absences and school enrollment data for
2010-2015 came from nine Allegheny County school districts. Six
districts provided grade-specific absences (Supplemental Text and
Supplemental Table 1). Grade-level served as an age-proxy, since student
demographics (i.e., age, gender, or vaccination status) were
unavailable. Additional all-cause and cause-specific absences came from
three school-based cohort studies (Pittsburgh Influenza Prevention
Project (PIPP) during the 2007-2008 season (10 K-5 schools), Social
Mixing and Respiratory Transmission in School study (SMART) during the
2012-2013 season (eight K-12 schools), and Surveillance Monitoring of
Absences and Respiratory Transmission (SMART\textsuperscript{2}) study
during the 2015-2016 season (nine K-12 schools)). Cohort studies used
similar absence collection protocols(11).

Greater Pittsburgh area daily minimum and maximum temperature and
relative humidity data came from the National Oceanographic and
Atmospheric Administration's National Climatic Data Center(12). We used
temperature and relative humidity (a proxy for absolute humidity) given
their effects on influenza transmission (i.e., viral dispersal and
survival)(13, 14). Allegheny County population data came from US Census
Bureau's yearly estimates for 2007, 2008, and 2010-2015(15).

Our primary outcome was weekly confirmed influenza infections reported
in Allegheny County during 2007-2008 and 2010-2015 seasons. Influenza
infection was defined as any virologically-confirmed case reported by a
health provider in Allegheny County during CDC-defined influenza seasons
(i.e., 40\textsuperscript{th} calendar week to the
20\textsuperscript{th} calendar week of the subsequent year)(16) Weekly
influenza cases were the total cases reported each week, excluding cases
occurring during school closures (e.g., spring break, federal holidays,
weekends).

All-cause absences were defined as a full or partial school day missed
for any reason. Cause-specific absences were a full or partial school
day missed due to influenza-like illness (i.e., fever
(\textgreater{}37C) and either cough, sore throat, runny nose, or
congestion). We restricted school absences to periods overlapping the
influenza seasons to examine absence patterns during influenza
circulation, and excluded weekends, observed federal holidays, and
school breaks. Weekly school absences were the total absences reported
in one school week (i.e., if no observed holidays, five days in a school
week). Weekly absence rates were total absences in a week, divided by
the total students enrolled times the number of school days in a given
week.

Daily average minimum and maximum temperatures and relative humidity
were used to estimate weekly average temperature and relative humidity
for each influenza season.

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).

\emph{Model validation and predictions}

Using in-sample data for model training and out-of-sample data for model
testing, we used the following four validations: 1) randomly sampled
80\% of weeks without replacement; 2) leave out 52 non-contiguous
randomly sampled weeks; 3) leave out 20\% of randomly sampled schools,
and 4) leave one influenza season out (i.e., model training used all but
one season and the out-of-sample season was used for model testing) to
account for influenzas' seasonal variation. Estimated
R\textsuperscript{2} used linear regressions of out-of-sample observed
influenza cases (outcome) and predicted cases (independent variable).
Prediction metrics used mean absolute error (MAE) and relative mean
absolute error (relMAE). Mean absolute error was defined as the mean of
the absolute value of model prediction errors(18). Relative MAE is the
ratio comparing a model's MAE to a reference MAE (i.e., from a model
including calendar week, and average weekly temperature, and relative
humidity), where relMAE of 1.0 indicated the same prediction error for
two models. We visually compared observed and predicted cumulative
distributions and time-series of influenza cases.

\textbf{Results}

\emph{Characteristics of influenza and school absences}

Over seven influenza seasons, 11,946 confirmed influenza cases were
reported to ACHD (Supplemental Table 1). Influenza type A predominated
most seasons, similar to national patterns(19-24). Overall, 9,350 type A
(1,397 A/H3N2 and 1,115 A/H1N1 subtypes) cases, 2,453 type B cases and
143 un-typed cases were reported. The 2011-2012 and 2014-2015 seasons
were the lowest (301 cases) and highest (3,150 cases) transmission
seasons in Allegheny Country, like national trends. Within seasons,
cases peaked in the winter whereas county-level absences varied
throughout the year (Figure 1).

During the 2010-2015 seasons, county school districts reported 2,184,200
total absences (Figure1), averaging 6.5 weekly absences/100 students
(interquartile range {[}IQR: 5.6, 7.7{]}) (Supplemental Table 1). High
schools had the highest average absence rates (9.4 weekly absences/100
students, IQR: 8.1,10.8), followed by middle schools (6.3 weekly
absences/100 students, IQR: 5.4, 7.7) and elementary schools (5.3 weekly
absences/100 students, IQR: 4.0, 6.6). Study schools reported 20,128
all-cause and 3,012 ILI-specific absences among 11,660 students
(Supplemental Table 1). The SMART\textsuperscript{2} study had the
highest average weekly all-cause absence rates (2.2 weekly absences/100
students (IQR: 1.8, 2.5)), while the SMART study had the highest
ILI-specific absence rates (1.1 weekly absences/100 students (IQR: 0.7,
1.4)).

\emph{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 (\textbf{[?]} 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 (\textbf{[?]} 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 (R\textsuperscript{2} 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.

\emph{Influenza predictions using school-type and grade-specific
absences}

We compared the performance of different school-types (elementary,
middle, and high school) and grade-specific absences in seasonal models.
Elementary school models had lower relMAEs compared to middle and high
school models across validations (Supplemental Table 6). Given varied
model performance across school types, we also considered one-week
lagged grade-specific all-cause absences in seasonal models to assess
heterogeneity in predictions by grades.

Univariate analyses found K, 1, 2, 3,4\textsuperscript{th} and
5\textsuperscript{th} grade absence models had lower MAEs than
(individual) middle school and high school grade-specific absence
models, particularly in leave 20\% of schools' out validation (Figure
3A). Multivariate grade-specific absence models also had lower MAEs
relative to seasonal models across three cross-validations (Figure 3B).
We observed consistently lower relMAEs for kindergarten-specific
absences (relMAE: 0.91, 0.98. 0.92 in three validations). Overall,
middle and high school grade-specific absence models did not decrease
MAEs relative to seasonal models, although 8, 9, \&
10\textsuperscript{th} grade models in leave 20\% of weeks out and
6\textsuperscript{th} grade models in leave 20\% schools out had lower
MAEs.

We investigated whether absenteeism can be used to create more accurate
predictions of virologically confirmed influenza only in school aged
children, we built models of virologically confirmed influenza only in
those 5-17 years old, rather than of all ages. We found modest
improvements in two of three validations when including absences
compared to not using absences in models that incorporated week of year,
relative humidity and temperature. Predictions were more accurate when
predicting virologically confirmed influenza in children then when
predicting all ages.

\emph{Influenza predictions comparing all-cause and influenza-like
illness-specific absences from cohort data}

Using school-based cohort studies, we compared the performance of
all-cause absences to ILI-specific absences, a better proxy for
influenza infection. Because the cohorts had short time-series (i.e.,
one influenza season), we were unable to examine models containing all
seasonal variables and to include average temperature in some models.
Multivariate ILI absence models had higher R\textsuperscript{2}estimates
and lower relMAEs than all-cause absence models in analyses using PIPP,
2012-2013 SMART, and pooled absence data (Table 2). From the 2015-2016
SMART\textsuperscript{2} data, the all-cause absence model had a lower
relMAE (relMAE: 0.59) than the ILI-specific model (relMAE: 2.17), but
similar R\textsuperscript{2} estimates (Table 2). Pooling across
studies, the ILI-specific absence model had a lower relMAE (relMAE:0.99)
than the all-cause absence model (relMAE: 1.02), and similar
R\textsuperscript{2} estimates (all-cause R\textsuperscript{2}: 0.30 and
ILI-specific R\textsuperscript{2}: 0.37) (Table 2).

\emph{Sensitivity analyses}

In sensitivity analyses, we found using absence duration did not improve
model predictions. One-day absence models and those including both
one-day and absences two-days or more had lower relMAEs compared to
models containing absences two-days or more (Supplemental Table 9), but
predictions from the three model did not substantially vary
(Supplemental Figure 2). Evaluation of models including one-week lagged
influenza cases found little improvement of model prediction and
performance when compared to seasonal models. Higher MAEs were observed
for one-week lagged influenza models, and one-week lagged influenza and
absence models but had similar R\textsuperscript{2} estimates
(Supplemental Table 8). One exception was the one-week lagged influenza
model from the leave 20\% schools' out validation, which had a lower
relMAE (relMAE: 0.97) (Supplemental Table 8). One-week lagged influenza
and one-week lagged influenza and kindergarten absence models performed
similarly to one-week lagged influenza models in three
cross-validations, except in the leave 52-weeks out validation (relMAE:
0.97).

\textbf{Discussion}

We found including school absences in seasonal models improved
community-level confirmed influenza predictions over multiple seasons
within Allegheny County. All-school absence models subtly improved
predictions, reducing MAE by 5\% across multiple validations, but
school- and grade-specific absence models had better predictions,
reflecting underlying age-specific differences in infections. Elementary
school absence (K to 5\textsuperscript{th} grades) models decreased MAEs
by 1-16\% compared to 6-12\textsuperscript{th} grades, suggesting
younger student absences were illness-related and older children's
absences were non-influenza and non-illness related. From school cohort
data, ILI- and all-cause absences performed better in single season
(2007-2008 and 2012-2013) validations and when pooled across seasons.
Elementary school, K-5\textsuperscript{th} grade-specific all-cause
absences, and potentially ILI-specific absences, may serve surveillance
indicators for the larger community.

Compared to seasonal models, those including all-cause absences improved
MAE and R\textsuperscript{2} estimates, and suggests that after
accounting for seasonal factors, school absences improved influenza
predictions. Our analysis is one of few using weekly all-cause absences
at various administrative levels (i.e., school type and grades) to
predict influenza. Whereas other studies used cause-specific absences to
detect elementary school influenza outbreaks(6), ours evaluated how
different school and grade all-cause absences performed as predictors.
As evidenced by higher R\textsuperscript{2} and lower relMAEs from
elementary school absence models, absences from younger school-aged
children better reflect infections during the influenza season and are a
proxy to the younger age groups that experience higher infections and
increased susceptibility(5, 25, 26). In contrast, middle and high
schools' absences were noisier prediction signals, possible because
older students had more non-influenza related absences (consistent with
the overall higher absenteeism rates observed in these schools over
time). Lower relMAEs from lower individual grade
(K-5\textsuperscript{th} grades) absence models from multiple
validations further support our findings. Hence, elementary school
absences could be useful for influenza surveillance.

ILI-specific absences predicted influenza better than all-cause absences
when evaluating predictions from weekly all-cause and ILI-specific
absence models (using school-based cohort studies), based on lower MAEs
and higher R\textsuperscript{2} for specific seasons and when pooled.
Other studies also found ILI-specific absences were a proxy for
influenza when evaluating vaccine impacts(27), suggesting ILI-specific
absences likely capture actual influenza infections. We could not
conduct cause-specific absence surveillance for more than one influenza
season for each study nor could we perform school-type and
grade-specific comparisons of all-cause and ILI-specific absences due to
small time-period, but these may also be important predictors of
influenza incidence.

Our study has some limitations. We did not evaluate our predictions
during the 2009 pandemic because our county absence data were either
limited to single seasons, or available after 2009 because participating
schools' electronic absence surveillance began after 2009. Similarly,
cohort studies were funded for and conducted during the 2007, 2012, and
2015 seasons, therefore we could not assess predictions during the 2009
pandemic. In the school-based cohort studies, not all absences were
identified due to challenges contacting parents regarding absences and
our studies may underestimate the number of all-cause absences, and
possibly, ILI-specific absences. Our predictions used school-based data
from school districts within Allegheny County only, therefore our
results may not be generalizable to influenza transmission in other US
counties. Additional data from other Pennsylvania counties or a
representative sampling from other state counties would improve the
generalizability of our predictions.

Recently, others, like those participating in the CDC FluSight Challenge
-- an influenza prediction competition -- have used climate data, past
influenza incidence and other data streams in recent efforts. In the CDC
FluSight Challenge, external research teams predict weekly influenza
cases, and evaluation metrics include the mean absolute scaled error, a
measure of forecast accuracy(28, 29). Our MAE decreased by 5\% when
using county-level all-cause absences models and is equivalent an
additional 8 weeks of data included in a nowcast model, like those used
in the FluSight Challenge. This equates to a 5\% reduction in mean
absolute scaled error(30). Our results suggest that models including
lower grades' absences may improve predictions, as seen by the 10\% MAE
decrease, and may improve predictions more when incorporated into
ensemble models, like those used in FluSight(29).

Our findings suggest models using absences of younger students improves
predictive performance. Real-time, day-to-day absence data are easy to
collect, readily available in many schools, and can provide more
accurate predictions than other surveillance mechanisms reliant on
virologic confirmation, and susceptible to laboratory testing delays.
Future studies could apply absence data to other prediction
methodologies, like ensemble methods and machine-learning algorithms,
which may improve prediction accuracy and identify absence-related
patterns not considered here. We demonstrate grade-specific all-cause
absences predict community level influenza one-week forward, when
influenza- or cause-specific absences are unavailable and suggest
elementary school or lower grade absenteeism during the influenza season
can reflect influenza circulation. Using school indicators can inform
influenza surveillance and control efforts, including annual
vaccination; antiviral treatment or prophylaxis; and promotion of
everyday preventive measures (i.e., staying home when sick, respiratory
hygiene, and hand hygiene) to reduce school- and community-level
influenza transmission.

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\textbf{Tables}

\textbf{Table 1. Fit and Performance of Negative Binomial Models of
Seasonal Variables Including and Excluding One-week Lagged County-level
All-cause School Absence Rates to Predict Weekly Confirmed Influenza
Cases in Allegheny County, Pennsylvania During the 2010-2015 Seasons}\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllll@{}}
\toprule
\textbf{Model Validation} & \textbf{Model Validation} & \textbf{Leave
20\% randomly sampled out data (n=124)} & \textbf{Leave 20\% randomly
sampled out data (n=124)} & \textbf{Leave 20\% randomly sampled out data
(n=124)} & \textbf{Leave 52 randomly sampled weeks out (n=106)} &
\textbf{Leave 52 randomly sampled weeks out (n=106)} & \textbf{Leave 52
randomly sampled weeks out (n=106)} & \textbf{Leave 20\% randomly
sampled schools out (n=159)} & \textbf{Leave 20\% randomly sampled
schools out (n=159)} & \textbf{Leave 20\% randomly sampled schools out
(n=159)}\tabularnewline
\midrule
\endhead
\textbf{Model\textsuperscript{+}} & \textbf{Variables} & \textbf{D.f.} &
\textbf{[?]AICc\textsuperscript{++}} & \textbf{Relative
MAE\textsuperscript{++}} & \textbf{D.f.} &
\textbf{[?]AICc\textsuperscript{++}} & \textbf{Relative
MAE\textsuperscript{++}} & \textbf{D.f.} &
\textbf{[?]AICc\textsuperscript{++}} & \textbf{Relative
MAE\textsuperscript{++}}\tabularnewline
1 (Ref.) & Week, temperature, RH & 8.5 & 0.0 & 1.0 & 8.8 & 0.0 & 1.0 &
10.0 & 0.0 & 1.0\tabularnewline
2 & Week, temperature, all-cause absence rates & 7.3 & -4.0 & 0.97 & 7.2
& -4.0 & 1.05 & 7.4 & -4.0 & 1.0\tabularnewline
3 & Week, RH, all-cause absence rates & 7.9 & -1.0 & 1.23 & 8.0 & -1.0 &
1.2 & 9.5 & -1.0 & 1.27\tabularnewline
4 & Week, temperature, RH, all-cause absence rates & 8.8 & 2.0 & 0.95 &
8.9 & 1.0 & 1.0 & 10.3 & 0.0 & 0.95\tabularnewline
\bottomrule
\end{longtable}

\textsuperscript{+}Each model used negative binomial regression and used
generalized additive models to estimate degrees of freedom for
non-linear (i.e. spline) variables. \textsuperscript{++}Changes in AICc
and relMAE compared all models to the reference (model 1), a seasonal
variables-only model that contains calendar week, average weekly
temperature, and average weekly relative humidity. Abbreviations: [?]AICc,
change in Akaike's Information Criterion corrected for small sample
size; RH, relative humidity.

\textbf{Table 2. All-cause and Cause-specific Absences Model Performance
Using Three School-based Cohorts' Data to Predict Confirmed Influenza
Cases in Allegheny County, Pennsylvania, USA During the 2007-2008,
2012-2013, and 2015-2016 Influenza Seasons}\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\textbf{Flu Season} & \textbf{Cohort} & \textbf{Model\textsuperscript{+,
++}} & \textbf{In-sample AICc ([?])} & \textbf{R\textsuperscript{2}} &
\textbf{MAE} & \textbf{Relative MAE}\tabularnewline
\midrule
\endhead
2007-2008 & PIPP & Week-only & 183 (0) & 0.97 & 8.9 & 1.0
(Ref.)\tabularnewline
& & All-cause absence & 215 (32) & 0.44 & 158.6 & 17.8\tabularnewline
& & ILI-specific absence & 185 (2) & 0.49 & 45.1 & 5.07\tabularnewline
2012-2013 & SMART & Week-only & 161 (0) & 0.93 & 14.4 & 1.0
(Ref.)\tabularnewline
& & All-cause absence & 187 (26) & 0.98 & 11.2 & 0.78\tabularnewline
& & ILI-specific absence & 174 (13) & 0.99 & 8.6 & 0.60\tabularnewline
2015-2016 & SMART\textsuperscript{2} & Week-only & 204 (0) & 1.0 & 8.6 &
1.0 (Ref.)\tabularnewline
& & All-cause absence & 214 (10) & 0.82 & 5.0 & 0.59\tabularnewline
& & ILI-specific absence & 206 (2) & 0.84 & 18.6 & 2.17\tabularnewline
Pooled analysis & PIPP, SMART, SMART\textsuperscript{2} & Week-only &
664 (0) & 0.35 & 51.6 & 1.0 (Ref.)\tabularnewline
& & All-cause absence & 665 (1) & 0.30 & 52.4 & 1.02\tabularnewline
& & ILI-specific absence & 667 (3) & 0.37 & 51.5 & 0.99\tabularnewline
\bottomrule
\end{longtable}

\textsuperscript{+}The week-only model included only week of the year
and absence models included weekly lagged absence rates from the
previous week, week of the year, and average
temperature.\textsuperscript{++}SMART models included weekly lagged
absence rates and week of the year. \textsuperscript{c}Cross-validation
used leave 20\% of schools out. Abbreviations: [?]AICc: change in
corrected Akaike's Information Criterion; ILI: influenza-like-illness;
MAE: mean absolute error; PIPP: Pittsburgh Influenza Prevention Project;
SMART: Social Mixing and Respiratory Transmission in Schools study;
SMART2: Surveillance, Monitoring of Absences \& Respiratory Transmission
Study; R\textsuperscript{2}: coefficient of determination.

\textbf{Figure legends}

\textbf{Figure 1. Weekly reported virologically-confirmed influenza
cases, and all-cause and influenza-like-illness (ILI) specific absences
in Allegheny County, Pennsylvania, USA, during influenza seasons from
2007 to 2015} . Surveillance of influenza cases during each influenza
season in Allegheny County occurred from the 40th week of one year to
the 20th week of the following year (solid black lines). All-cause
absences were collected for the entire school year for each school
district, and data were restricted to their respective influenza
seasons. Nine school districts within Allegheny contributed to weekly
counts of all-cause absences. Additionally, all-cause and ILI-specific
absences were collected during independent influenza seasons for three
separate studies: 2007-2008 (PIPP study), 2012-2013 (SMART study), and
2015-2016 (SMART\textsuperscript{2} study). Absence surveillance data
were not collected during the 2008-2009 or 2009-2010 influenza seasons.
White space on the x-axis reflects periods when data were not collected
for this analysis, whereas black lines on the x-axis (in negative y
values) indicate time periods when data is available. The Allegheny
County student population averaged 43,636 students across the nine
school districts, comprising 122 schools (57 elementary, 20 middle, and
18 high schools, and 24 charter/independent schools). County-level data
for 2010-2011 season were not available for 3 school districts.

\textbf{Figure 2. Four model predictions of confirmed influenza in
Allegheny County using leave one season out validations for the 2010 to
2014 influenza seasons.} Model predictions of four negative binomial
models (calendar week, average weekly temperature, average weekly
relative humidity (red), one-week lagged county-level all-cause
absences, temperature, and week model (yellow), one-week lagged
county-level all-cause absences, relative humidity, and week model
(blue), and one-week lagged county-level all-cause absences,
temperature, relative humidity, and week model (purple)) using
leave-one-season-out validation approaches showing model predictions
compared to observed virologically-confirmed influenza cases (black
line) in Allegheny County, Pennsylvania, USA, A) weekly counts during
each of the 2010-2011 to 2014-2015 influenza seasons, B) the change in
predicted cases using modeling including absences compared to a seasonal
model excluding absences (red), and C) the cumulative proportions of
predicted and observed influenza cases for each season.
R\textsuperscript{2} was obtained using a linear regression, where the
observed cases from the left-out season are the dependent variable and
the independent variable were predicted cases from a negative binomial
model of week-lagged county-level all-cause absences, relative humidity,
temperature, and calendar week.

\textbf{Figure 3. Mean and relative absolute errors for predictions
using grade-specific absence models to predict influenza in Allegheny
County Pennsylvania from 2010 to 2014 influenza seasons.} Mean absolute
errors were estimated from univariate grade-specific weekly absences
models (A), and the relative mean absolute error compared models of
grade-specific weekly absences, week of the year, average weekly
relative humidity, average weekly temperature to models of calendar
week, average weekly relative humidity, and average weekly temperature
(B). Colors reflect the three different school types: red is elementary
school, green is middle school, and blue is high school. Solid black
line refers to a relMAE of 1, where mean absolute errors of the
grade-specific absence models and models excluding absences are the
same.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/prediction-figure-1/prediction-figure-1}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/prediction-figure-2/prediction-figure-2}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/prediction-figure-3/prediction-figure-3}

\end{center}
\end{figure}

\selectlanguage{english}
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