Associations between illness-related absences and ventilation and indoor PM 2.5 in elementary schools of the Midwestern United States

This study monitored indoor environmental data in 144 classrooms in 31 schools in the Midwestern United States for two consecutive days every fall, winter, and spring during a two-year period; 3,105 pupils attended class-rooms where the measurements were conducted. All classrooms were ventilated with mechanical systems that had recirculation; there were no operable exterior windows or doors. The daily absence rate at the student level and demographic data at the classroom level were collected. The overall mean ventilation rate, using outdoor air, was 5.5 L/s per person (the corresponding mean carbon dioxide concentrations were < 2,000 ppm), and the mean indoor PM 2.5 was 3.6 μ g/m 3 . The annual illness-related absence rate at the classroom level was extracted from the student-level absence data and regressed on measured indoor environmental parameters. Significant associations were found. Every 1 L/s per person increase in ventilation rate was associated with a 5.59 decrease in days with absences per year. This corresponds to a 0.15% increase in the annual daily attendance rate. Every additional 1 μ g/m 3 of indoor PM 2.5 was associated with a 7.37 increase in days with absences per year. This corresponds to a 0.19% decrease in the annual daily attendance rate. No other relationships were significant. Present results agree with the previously demonstrated benefits of reduced absence rates when classroom ventilation is improved and provide additional evidence on the potential benefits of reducing indoor inhalable particles. Overall, reduced absence rates are expected to provide socioeconomic benefits and benefits for academic achievements, while higher ventilation rates and reduced particle levels will also contribute to reduced health risks, including those related to airborne respiratory pathogens.


Introduction
The indoor environment of elementary schools has been identified as a major environmental concern and risk factor (Daisey et al., 2003;Mendell and Heath, 2005).Children spend 8 to 10 h per day and approximately 200 days a year in elementary schools, and many children are more vulnerable to adverse indoor environmental conditions because (a) children have higher breathing rates than adults and (b) their bodies are still growing and many organs are developing (Chen et al., 2015).An adverse classroom environment could lead to aggravated health conditions and decreased academic achievement (Mendell and Heath, 2005), which causes overall public concern among parents, teachers, and school officials.
Absenteeism caused by pupils missing school days because of medical conditions or illnesses that make it impossible to attend classes has been used in previous research as a proxy for pupils' health and classroom conditions.One of the leading causes of illness-related school absences has been attributed to asthma or asthma-related respiratory illnesses and symptoms (Meng et al., 2012;Tinkelman and Schwartz, 2004).Other common health problems associated with school absenteeism have been identified and incude among others allergic rhinitis (Blaiss, 2004), chronic illness and pain (Sato, 2007), influenza (Neuzil et al., 2002), obesity and sickle cell anemia (Taras and Potts-Datema, 2005), and diabetes (Kearney, 2008).Illness-related absenteeism has also been considered a risk factor for the academic performance of pupils in schools.Studies have reported that pupils with better attendance records have better grade point averages (GPA) and perform better on standardized reading and math tests (Gottfried, 2010), mathematics sections of college entrance examinations (Balfanz and Byrnes, 2006), standardized achievement tests (Lamdin, 1996;Douglas and Ross, 1965), and high school graduation examinations (Nichols, 2003).
Increased school absence has been found to be correlated with teacher evaluations of academic performance in higher education courses (Marburger, 2001;Rodgers, 2001;Andrietti and Velasco, 2015;Buechele, 2021) and with standardized test scores of children with asthma (Silverstein, 2001).Some health problems that cause increased absence rates, like respiratory illnesses and allergic rhinitis, have been associated with indoor environmental conditions in classrooms (Mendell and Heath, 2005).Moreover, previous studies have also documented that pupils' health symptoms and illness relapse have been associated with indoor environmental conditions in classrooms.The health symptoms comprised sick building syndrome symptoms (Apte et al., 2000), respiratory infections (Pilotto et al., 1997), allergic reactions (Carreiro-Martins, 2014), and asthma relapse (Smedje et al., 1997).
The indoor classroom environment is characterized by different factors and conditions, including the building and its condition (building envelopes, floor and ceiling materials, painting of interior walls, etc.), building maintenance, air quality (pollution sources and ventilation), thermal environment (air temperature and relative humidity), and acoustic and visual environment (Wargocki, 2021).These conditions affect the health and learning of pupils in schools differentially (Wargocki).For many of these environmental parameters, the causal paths are unknown, and a better understanding of pathways would allow improved delineation of solutions that benefit pupils in schools.
The current literature has limited evidence that classroom air quality and thermal environment affect the absence rate of pupils in elementary schools.Two studies conducted in the U.S. significantly associated the indoor ventilation rate and mean CO 2 concentration with absence rates (Shendell, 2004;Mendell, 2013), while another study performed in Scotland showed a similar association between indoor CO 2 concentration and absence rates (Gaihre et al., 2014).Other than those two indoor variables, no other indoor environmental variables, like indoor PM 2.5 , have been previously examined in association with absence rates of elementary schools worldwide.
Providing new evidence on the problems presented above is essential.Therefore, a large-scale research project was launched to target the relationship between school indoor environmental quality and pupils' absenteeism and performance in K-12 schools in the Midwestern United States (Lau et al., 2016;Deng and Lau, 2019;Kuhlenengel et al., 2021;Kabirikopaei et al., 2021;Wang and Brill, 2021).Results of this project suggest that comprehensive indoor environmental quality monitoring is necessary to adequately represent the exposure to and measure the seasonal variations in indoor air, thermal conditions, and visual and acoustic environment (Lau et al., 2016).Results also suggest that indoor acoustical conditions were associated with the standardized test scores of pupils (Brill and Wang, 2021).Present analyses were performed to examine the effects of indoor classroom environmental quality on shortterm illness-related absences in the examined elementary schools.

School selection and description
Analyses are based on data collected in K-12 schools located in the Midwestern United States.The research team contacted school districts from the state of Nebraska and Iowa, and five districts, labeled Districts 1-5 in this study, agreed to participate.Elementary schools providing the first six years of formal education (grades 1-6) and secondary schools providing middle and high school education (grades 7-12) were included.In each school district, data was collected from 3rd and 5thgrade elementary school classrooms and from 8th-grade math and 11th-grade language arts middle and high school classrooms.The present analyses only used data from elementary classrooms because pupils in elementary schools stay in their primary classrooms for the majority of the school day, while pupils in middle and high schools migrate between different classrooms for various class sessions.In each school district, up to three 3rd and 5th-grade classrooms were selected from each of the elementary schools.This yielded a total of 144 classrooms from 31 schools within five school districts.All participating schools were located in Climate Zone 5A, which is defined as "Cold" by the Department of Energy.Detailed school selection was described previously (Deng and Lau, 2019).
All participating classrooms were ventilated with mechanical ventilation systems that included recirculation.They were equipped with either heat pumps, unit ventilators, or multi-zone air conditioning systems.All classrooms were without operable exterior windows or doors.
The total number of pupils in selected classrooms was N = 3,105, representing approximately 20% of all elementary school pupils from the participating school districts.Individual class sizes ranged from 16 to 27 pupils, with an average of 21.5.De-identified student-level data was provided by the school districts and aggregated to the classroom level.The percentage of white pupils was calculated in each classroom to represent classroom ethnicity, and the percentage of pupils enrolled in the free or reduced price lunch program was calculated to represent classroom family economic status.Table 2 in the Results section provides additional information.

Environmental parameters
The research team continuously monitored numerous indoor environmental parameters in each classroom, including indoor carbon dioxide concentration (CO 2 ), classroom ventilation rate (Vent), optical particles with diameters ranging from 0.3 μm to 2.5 μm (PM 2.5 ) and from 0.3 μm to 10 μm (PM 10 ), indoor air temperature (T), and relative humidity (R.H.).The measurement campaign utilized four absorption infrared CO 2 sensors (Telaire 7001 by GE Sensing), an optical particle counter (Handheld 3016 by Lighthouse Worldwide Solutions), and four temperature and relative humidity sensors (HOBO U12-012 by Onset) for one classroom.The instruments were all calibrated before measurements.For research purposes, four instrument sets with measuring equipment were placed in different locations in classrooms: one was placed next to the teacher's desk, two were hung from the classroom ceiling next to the air supply diffuser and return air grill of the mechanical ventilation system, and the last one was placed in a secured

Table 1
List of variables used in the analyses.
outdoor location next to the monitored classroom.The equipment was caged so the pupils could not access it (Fig. 1).Fig. 2 shows the schedule of the measurement campaign.
The classroom ventilation rate was estimated based on the 95th percentile of the 15-minute moving average of the monitored indoor CO 2 concentration, the method adopted from the ASTM D6245-12 standard (ASTM International, 2012) and the literature (Mendell, 2013;Mendell et al., 2016).Previous analyses showed that using the steady-state measurements (represented here by the 95th percentile) resulted in the lowest uncertainty (Kabirikopaei et al., 2021).Therefore, a similar approach was used in the present analyses; outdoor CO 2 concentration was also measured and used in the calculations.The CO 2 generation rate was assumed to be 0.0043 L/s per pupil in the 3rd and 5th grades and 0.0052 L/s per adult, assuming there was only one teacher in a classroom; these CO 2 generation rates were also used in previous studies (Kabirikopaei et al., 2021;Batterman, 2017).Detailed information on ventilation rate estimation is reported in the Supplementary Material (SM).The concentration of indoor PM was converted to mass concentration based on the centroid of the area of the count distribution and based on the assumption of the PM density (1.65 g/cm 3 ) of elementary classrooms (Tittarelli, 2008).
In each classroom, the measurements were made for two consecutive school days, from approximately 7:00 a.m. on the first day until around 5:30p.m. on the second day.These measurements were repeated three times per year in each classroom: during the fall, the winter, and the spring (Fig. 2).The repeated measurement campaigns were evenly allocated from the beginning of semester one to the end of semester two and to represent the three seasons.Because many schools and classrooms participated, the entire measuring campaign lasted two years, with half of the classrooms monitored in the first year and the other half in the second year.
Only the data from occupied hours were used in the analyses.The occupied hours were defined as the time between the start of the first class and the end of the last class of each school day according to the schedules provided by the school districts.
The environmental data collected from the different locations in a single classroom were averaged since the research team did not observe  S. Deng et al. a significant difference in measurements between these locations which additionally suggested good mixing conditions inside the classroom.Also, daily means were calculated by aggregating environmental data collected during the occupied hours.Finally, all daily-mean environmental data were then averaged across the three seasons for analysis.
Previously, seasonal variations of various indoor environmental parameters were observed except for indoor air temperature (Deng and Lau, 2019), but no significance tests were performed.In the present analyses, they were not included because the focus was on annual absence rates, and aggregate average conditions across seasons were expected to best predict year-round conditions in classrooms.In addition, since indoor measurements were only performed during a 2-day period for each season, aggregating data collected during the three seasons could provide a better parameter to represent general classroom conditions.This is based on the hypothesis that the classroom environmental conditions might have a long-term impact instead of an acute influence on illness-related absences.This is also observed and suggested by the previous study (Mendell, 2013).Further details on measurements and data processing can be found in previously published papers (Deng et al., 2021;Deng and Lau, 2019;Kabirikopaei et al., 2021).

Absence rates
Each school district provided the number of daily absences for each pupil throughout an academic year.The count was available with a code describing the reason for each absence, such as illness, medical condition, family vacation or trip, or other reasons like suspension or inschool activities.The research team only focused on the absence rates related to illness or medical conditions (illness-related absences, IRAs) as the primary outcome in the present analyses, as they could be caused or exacerbated by classroom environmental conditions.We used annual absences per class to ensure pupil anonymity and to avoid acquiring approvals from the Institutional Review Board (IRB).
The codes defining the reason for absence were different among the school districts.District 1 recorded the absence and defined them as excused, unexcused, or unverified twice a day: a.m. and p.m.According to the district administrators, an "excused" absence was normally related to a pupil's illness or medical condition and was usually confirmed by doctoral approval, while an "unverified" absence was related to a family-requested absence such as a family trip or vacation.An "unexcused" absence was defined as an absence that was not communicated to schools or teachers.The research team consequently used the "excused" count of absences for IRA from District 1.
District 2 used a four-code system to record absences."A" was used to define an absence caused by family business, while "D" and "E" defined absences caused by illness or medical conditions."U" was used to describe absences with no proper reason.Absences were recorded twice a day.The research team used the absences coded "D" and "E" to determine the IRA in District 2.
District 3 divided a typical school day into eight periods from the morning preparation to the last classes and recorded the absence rate in each period.Each absence was coded clearly, especially any absence related to illness or medical conditions.The codes "illness" and "medical" were combined and designated as IRA in the case of District 3.
District 4 used a similar coding system to District 3. The only difference was that a school day was divided into four periods instead of eight.Absences related to illnesses and medical conditions were used as IRA for District 4.
District 5 recorded absences once a day using various codes, whereas illness and medical conditions were clearly marked and were used as IRA.
The IRA of each classroom was defined as the total count of days absent of the class through a whole academic year among all enrolled pupils.
In addition to absence rate data, class size and the socioeconomic data of pupils, including ethnicity and economic status of the families of pupils, were also collected at the classroom level and included in the models.

Analyses
The IBM Statistical Product and Service Solutions Statistics 26 (SPSS) package was used to develop a multilevel model to describe the association between absence rates (IRAs) and indoor environmental data (Table 1).Multilevel models are commonly used in clustered data, and the school data is classic clustered data as pupils were clustered in a classroom and classrooms were clustered in a school (Gaihre et al., 2014;Guthold et al., 2020;Krull and MacKinnon, 2001;Rumberger, 1995).The school and district IDs were added to the model as random effects, S. Deng et al. and the indoor environment variables and demographic variables as a fixed effect.All the variables described in Table 1 were included in the model, with IRA as the criterion (at the classroom level) and grade, enrollment, ethnicity, family economic status, average indoor CO 2 concentration, ventilation rate (estimated from the 95th percentile CO 2 concentration), indoor PM 2.5 concentration, indoor air temperature, and relative humidity as predictor variables.The variable indoor CO 2 was not used to calculate the ventilation rate and is the arithmetic mean of the indoor CO 2 concentration.The research team hypothesizes that this variable may represent the chronic effects of exposure to other pollutants.Using both CO 2 and ventilation rate (which represent the nearpeak concentration of indoor CO 2 ) in the model might consequently have some benefits.Outliers were detected by the 3σ law and excluded before the multilevel model analysis.A nominal alpha level of α = 0.05 was used to determine statistical significance.A multivariant linear regression model that used the same independent variables and dependent variables as the multilevel model was also performed without considering the clustering issue.Results were similar to the multilevel model but with a reduced regression effect; these were reported in the Supplementary Material for reference.

Absence rates
The average IRA was 97.3 days of absence per classroom per year, with an annual average daily attendance rate of 97.5%.Table 2 shows the average IRA among districts, while the variation is illustrated in Fig. 3.

Conditions in classrooms
Fig. 4 and Table 3 show annual averages of measured classroom environmental parameters.

Association between absence rates and conditions in classrooms
Table 4 summarizes the model output where eight of ten variables were not statistically significantly associated with the outcome.Ventilation rate and concentration of PM 2.5 were statistically significantly associated with IRA.Increasing the ventilation rate reduced the absence rate; each additional 1 L/s per person was associated with 5.59 fewer days absent at the classroom level annually, while each 1 μg/m 3 lower PM 2.5 reduced the annual absence rate by 7.37 days.The variance inflation factors (VIFs) were checked to ensure that multicollinearity among predictors was not a contributing factor to model results.
Fig. 5 shows the linear relationship between IRA and ventilation rate and PM 2.5 .The scatterplots for other variables and partial regression plots for ventilation rate and indoor PM 2.5 are shown in the Supplementary Material.

Discussion
The annual average daily attendance rate of 97.5% in the study was slightly higher than the total attendance rate from studies across the United States (96.43% for the 3rd and 5th grades combined (Ansari and Pianta, 2019), the southern Nevada region (95.01%for all elementary grades (Coughenour, 2021), the state of Utah (approximately 95.7% for rural areas, and 90.21% for metropolitan areas for all elementary school grades (Hales et al., 2016), the states of Washington and Idaho (95% for attendance across states and grades of elementary schools (Shendell, 2004), and a state in the southern United States (approximately 96% for the 5th grade (Haverinen-Shaughnessy et al., 2015).The reason is probably that the research team only included illness-related absenteeism.Should the attendance rate be generated for illness-related absences, the annual attendance rate in this study would be similar to what was observed in the state of California (97.6% for the 3rd to 5th grades (Mendell, 2013), and in the southern United States (approximately 98% for all illness-related attendance rate of the 5th grade (Haverinen-Shaughnessy et al., 2015).

Absence rates and ventilation
Ventilation refers to bringing fresh outdoor air indoors to ensure the outdoor air requirements for occupants are met and to dilute indoor air pollutants (Fisk, 2017).Various standards recommend minimum ventilation rates to fulfill those needs, specifically for different buildings or space types.As for the classroom setting, the minimum ventilation rate recommended in the United States is approximately 7 L/s per person (ANSI/ASHRAE, 2019).The European standard recommended a slightly higher number, which is approximately 8 L/s per person.
In this study, ventilation rates were estimated using the 95th percentile moving average CO 2 concentration.Similar estimations were made in previous studies (Mendell, 2013;ASTM International, 2012;Mendell et al., 2016).The mean ventilation rate was estimated to be 5.5 L/s per person, and about 73% of classrooms had ventilation rates lower    , 2019) and lower than the rates normally observed in offices where low ventilation rates were also observed to increase absence rates (Milton et al., 2000).
Besides the effects on absence rates examined in this study, these low ventilation rates would also reduce academic achievements and negatively impact school work (Wargocki et al., 2020).This study showed a significant association between ventilation rate and IRA.This result confirms previous work in the US (Shendell, 2004;Mendell, 2013) and Scotland (Gaihre et al., 2014).The effect, approximately a 5.8% reduction in absence rate for each additional 1 L/s per person, was higher than in the study of Mendell et al., where the effect was a 1.4-1.6%lower illness absence rate for each additional 1 L/s per person (Mendell, 2013).In the other two studies, the effect was compared to the changes in CO 2 : Shendell et al. found a 1,000 ppm increase in CO 2 to be associated with a 0.5-0.9%decrease in annual attendance in a cross-sectional study in the United States (Shendell, 2004), while Gaihre et al. showed that annual absence rates were reduced by 0.2% for each 100 ppm reduction in CO 2 (Gaihre et al., 2014).In this study, annual daily attendance increased by 0.15% for each additional 1 L/s per person.Wargocki et al. summarized the existing evidence of the effects of classroom air quality and absence rates and created relationships suggesting that doubling ventilation rates to 2 to 4 L/s per person will increase attendance by 1% and an additional 0.5% increase would be expected from doubling ventilation rates from 4 to 8 L/s per person (Wargocki et al., 2020).Wargocki et al. also implied that reducing CO 2 from 4,100 to 1,000 ppm would increase daily attendance by 2.5%.Present results are comparable with previous studies, suggesting that the effects of increased ventilation rates on absenteeism in schools are not nontrivial.
Wargocki et al. estimated that the annual benefit from reduced teacher absences in Danish schools as a result of increasing the ventilation rate from 6 to 8.4 L/s per person would be around €6 million (Wargocki et al., 2014).A longitudinal study performed by Mendell et al. estimated that increasing ventilation rates from 4 to 7.1 L/s per person would produce benefits from decreased costs for time caregivers stayed at home with a sick child amounting to $80 million (Mendell, 2013).

Absence rates and particulate matter
The level of particulate matter was identified as one of the key risk factors for human health.The average annual PM 2.5 in the present study was generally below 5 μg/m3 .The new WHO air quality guidelines (issued in 2021) define that the average annual concentration of PM 2.5 should not be higher than 5 μg/m 3 to reduce health risks.Present results suggest that effects could also be observed below this guideline value.
The present study also found a significant association between indoor PM 2.5 and school absence rates.The research team is unaware of any other study showing such an association; therefore, these results would require corroboration in future works.However, other studies showed the relationship between outdoor particulate matter and illnessrelated absence rates.The estimated relative risk of illness-related absences for each additional 42.1 μg/m 3 ambient PM 10 was 1.06 in South Korea (Park, 2002).The estimated percentage of change of illnessrelated absences for each additional 10 μg/m 3 ambient PM 10 was 5.7% in the United States (Gilliland, 2001), while the association between ambient PM 10 and illness-related absences was not significant in some studies (Chen et al., 2000).As for the ambient PM 2.5 , each additional 1 μg/m 3 was estimated of rate ratio as 1.04 in the United States (Mendoza, 2020), and each additional 10 μg/m 3 was associated with a 4.52 percent annual absence rate change in China (Zhang, et al., 2022).
Each additional 10 μg/m 3 was associated with an increased relative risk of 1.28 in Japan (Watanabe et al., 2021), and each additional 1 μg/m 3 increase was associated with a 1.58% increase in the chronic absenteeism rate in the United States (MacNaughton et al., 2017).The effects observed in the present study were comparable, but the levels of particles in the classrooms were lower, and the classrooms had mechanical ventilation and non-operable windows, which significantly reduced the

Table 4
Model results showing an estimate of the effect, p-value, and 95% confidence interval (upper and lower bounds).Significant effects are bolded, and those close to significant are italicized.fewer absent days at the classroom level when controlling the school and district the same.There was an approximately 4.7% reduction of the annual absent days at the classroom level, or approximately 0.15% increase in the annual daily attendance rate for each additional 1 L/s per person of ventilation rate.penetration of ambient particulate matter indoors.
There are no studies in the literature showing the relationship between particulate matter and children's learning.Wargocki et al. performed an intervention study in school classrooms by installing electrostatic air cleaners, and although a significant reduction in PM was observed, no effects on schoolwork were demonstrated (Wargocki et al., 2008).In another study, Wargocki and Wyon observed that children's performance improved when ventilation rates were increased, resulting in lower levels of gaseous pollutants and particulate matter (Wargocki et al., 2008).They consequently attributed the effects on performance to gaseous pollutants.However, a new study by Laurent et al. with adults sheds new light on this matter (Laurent, 2021).They observed that an increase in the concentration of PM 2.5 resulted in slower response times and reduced accuracy; the average PM 2.5 levels were between 2 and 17 μg/m 3 .There are also studies examining the relationship between outdoor (ambient) particulate matter concentration and illness-related absences, but the results are inconsistent (MacNaughton et al., 2017;Park, 2002;Wu, 2022;Zhang, et al., 2022).Further studies would therefore be needed to understand the origin and morphology of particulate matter in connection with the observed effects.

Impact of other demographic and environmental parameters
The age of the pupils (defined by grade level) was initially hypothesized to be a factor associated with IRA; however, the results demonstrated that the age difference selected in the study (about 2-3 years difference) was not significantly related to illness-related absences.The same was true regarding ethnicity and socioeconomic covariates.These results do not necessarily indicate that those variables have no relationship to IRA, just that in the setting of the experiment in the present study, no significant associations between those demographic and environmental parameters and illness-related absences were observed.
The mechanical ventilation system equipped in all enrolled classrooms ensured that the air temperature and relative humidity were maintained at a fixed target range; the insignificant associations of air temperature and relative humidity to illness-related absence might relate to a lack of variations of these two variables.
It is worth mentioning that a study by Toftum et al. did not find a relationship between ventilation type and absence rate (Toftum, 2015).Therefore, future studies are necessary to further examine the underlying reasons behind the effects of ventilation on illness-related school absences of children.

Limitations
One limitation of the present study is that despite the comprehensive and long-term measurement campaign of the indoor classroom environment conditions part of the current study, continuous measurement throughout the academic year was not achieved.Each of the participating classrooms was measured for six school days; however, this number is relatively small compared to the total school days of an academic year.This is a function of the logistical tradeoff between obtaining a large sample of classrooms and the feasibility of the various indoor environment measurements that were collected.Future studies that can feasibly measure the indoor environment every day for an entire school year might provide more powerful results about the association between indoor environmental conditions and illness-related absenteeism of pupils.Another limitation is that only mechanically ventilated elementary schools were included in the study; thus, the differences between naturally ventilated and mechanically ventilated classrooms were not observed.Future studies that have similar designs but include both ventilation types could provide more information for indoor environment research.
The current study repeatedly monitored classroom indoor environments during occupied hours for a 2-year period in 144 classrooms.This was very complicated and required numerous permissions, cooperation, and unpaid help from school districts.This study is among the largest of its type; however, due to privacy agreements between research group the schools, and the funding agency, student-level information was not collected or reported.Thus, we did not have the ability to examine the reasons for the absences of every pupil.Instead, absence data was filtered by excluding all reasons that were not related to the classroom environment such as family vacations, family business, and absence without reason.In addition, the participating schools confirmed that due to the state policy, there would be no penalties for being absent from school, thus, the misclassification of absence codes was not a big concern to the study.
The participating schools and classes were selected based on convenience and proximity; thus, not all school districts in the metropolitan areas were included, and not all metropolitan areas of the Midwestern United States were included.This limitation might affect the results implicated in other areas of the United States and other countries.Also, only 3rd and 5th-grade classrooms were selected; thus, the age variation of pupils that might affect the associations between IRA and environmental parameters was not fully examined.
The current study utilized a multilevel model, but a more sophisticated modeling approach might reveal the nuanced associations between indoor environmental parameters and illness-related absences in future studies.
Finally, the significant associations observed in the present study between indoor environmental parameters and IRA were not directly measured.Ventilation rates were estimated based on the peak of the indoor CO 2 concentration, and indoor PM 2.5 concentration were converted based on the optical particle counter (instead of the gravimetric weight of particles).The assumptions made during the estimation and conversion were carefully selected and compared to the literature; however, these assumptions may have introduced measurement error into the present study.

Implications
The current study is among the largest studies associating indoor environmental variables with illness-related absence rates.The biggest obstacle to such a study is the concern of privacy and leakage of pupils' information.Collecting only classroom-level data is feasible for a normal research team to do to offset this concern and to avoid having to acquire permissions from every parent and from the IRB, which is usually required for student-level data acquisition.School district administrators are usually not interested in sharing information and opening school campuses up for research.Thus, mutual benefits need to be reached.In addition, having a large sample size and measuring many environmental variables could provide power to such research, but this is extremely costly and time-consuming.There was no single off-day for researchers during this 2-year period.
The purpose of ventilation is to bring outdoor air indoors, and outdoor PM is transferred into the indoor environment as well.For mechanically (with MERV 8 filters) ventilated indoor spaces without operable windows or doors, ventilation is the primary connection between indoor and outdoor environments for fresh air and transmitting pollutants.The results of the present study, which highlighted ventilation rates and indoor PM 2.5 improvements, should be considered together.They emphasized the importance of increasing the ventilation rate to at least the levels prescribed by the Standards, filtering outdoor air using the MERV13 filter (as recommended by the ASHRAE epidemic task force for reducing airborne infectious aerosol exposure), and using particle removers.
The newly issued WHO global air quality guidelines adjusted the level of PM 2.5 from 10 μg/m 3 to 5 μg/m 3 annually and the 24-hour guidance level to 15 μg/m 3 .This action was based on the health risk of exposure to low concentration of PM (Strak, 2021;Wu et al., 2020).New research found that only 0.001% of the global population had an annual exposure to PM 2.5 at concentration lower than the new WHO guidelines value (Yu, 2023).The significant association observed between indoor PM 2.5 and IRA in the present study confirmed the health benefits of removing indoor PM and emphasized the effects of indoor PM exposure.
The benefits of retrofitting and upgrading schools to improve ventilation and control PM 2.5 go beyond illness-related absences, as those two interventions also significantly reduce the risk of infection (Morawska, 2021).Outbreaks of COVID-19 through the transmission of virus-laden particles in indoor spaces (which is suspected to be the dominant indoor mode of transmission for respiratory infections) emphasize the importance of healthy indoor environments for public health.Benefits will stretch beyond local epidemic or worldwide pandemic periods.

Conclusions
The indoor environmental data of 144 classrooms in 31 schools in the Midwestern United States were collected along with the related demographic information and absenteeism data.Associations between indoor environmental data and demographic information were made.Results showed that classroom ventilation rates and indoor PM 2.5 levels were significantly associated with illness-related absences.Every 1 L/s per person increase in ventilation rate and every additional 1 μg/m 3 of indoor PM 2.5 were associated with a 5.59 decrease and a 7.37 increase in days with absences per year.This corresponds to a 0.15% increase and a 0.19% decrease in the annual daily attendance rate.These results may have significant socioeconomic implications and provide some justification for upgrading schools with solutions that benefit child health and learning.These upgrades might provide additional benefits during periods with increased risk for infectious diseases transmitted through the air by virus-laden aerosols.

Fig. 3 .
Fig. 3. Illness-related absences (IRA) of participating classrooms separated by district; the figure shows box plots indicating the 25th percentile, median, and 75th percentile in the boxes.Outliers were excluded in the analyses except for the IRA of outlier classes consistent across seasons.

Fig. 4 .
Fig. 4. Average annual classroom indoor environmental conditions separated by districts.

Fig. 5 .
Fig. 5.The relations between IRA and ventilation rate (top, a) and between IRA and indoor PM 2.5 (bottom, b).

Table 2
Information from participating classrooms and absence rates across the five districts participating in this study.
* data only includes the classrooms where the measurements were performed.** the daily attendance rates were calculated based on the average enrollment and 178 school days of the school year, example: the district 1 average daily attendance rate is 1-(106/178/23.5)%=97.5% (106 missed days, 178 school days, and average 23.5 pupils in those classes).

Table 3
Classroom environmental data.
(Deng and Lau, 2019viations.than6.7 L/s per person(Deng and Lau, 2019).These ventilation rates are lower than the 7 L/s per person prescribed by the current version of the American Society of Heating, Refrigerating and Air-conditioning Engineers (ASHRAE) Standard 62.1-2019 (ANSI/ASHRAE