Personal Belief Exemptions to
Vaccination in California:
A Spatial Analysis
Margaret Carrel, PhDa,b, Patrick Bitterman, BSa
abstract
BACKGROUND: School
vaccination rates in California have fallen as more parents opt for personal
belief exemptions (PBEs) for their children. Our goals were to (1) spatially analyze PBE
patterns over time, (2) determine correlates of PBEs, and (3) examine their spatial overlap
with personal medical exemptions (PMEs).
METHODS:
PBE and PME data for California kindergarten classes from the 2001/2002 to
2013/2014 school years were matched to the locations of schools. Nonspatial clustering
algorithms were implemented to group 5147 schools according to their trends in PBE
percentages among kindergartners. Cluster assignments were mapped and hotspot analysis
was performed to find areas in California where schools sharing trends in PBEs over time
were colocated. Schools were further associated both with school-level data on minority
enrollment and free and reduced price lunch participation and with charter/private and
rural/urban status. Spatial regression was implemented to determine which school-level
variables were correlated with PBE rates in the 2013/2014 school year.
RESULTS: Distinct spatial patterns are observed in California when PBE cluster assignments are
mapped. Results indicate that schools belonging to the “high PBE” cluster are spatially buffered
from those in “low PBE” areas by “medium PBE” schools. Further, PBE rates are positively
associated with the percentage of white students, charter status, and private schools.
CONCLUSIONS:
Hotspots of high PBE schools are in some cases colocated with schools that have
elevated PME rates, prompting concern that herd immunity is diminished for school
populations where students have no choice but to remain unvaccinated.
WHAT’S KNOWN ON THIS SUBJECT: An increasing
number of children are unvaccinated at entry
into public schools, potentially endangering
children who cannot be vaccinated for medical
reasons and threatening herd immunity.
Voluntary exemptions from immunizations vary
geographically and by parental characteristics.
Departments of aGeographical and Sustainability Sciences, and bEpidemiology, University of Iowa, Iowa City, Iowa
WHAT THIS STUDY ADDS: We find that exemption
behavior is highest in peripheral areas of cities
and that specific types of student populations
are associated with high exemption rates.
Additionally, there is spatial overlap between
clusters of high personal exemption and medical
exemption populations.
Accepted for publication Apr 15, 2015
Dr Carrel conceptualized and designed the study, performed statistical and spatial analysis, and
drafted the initial manuscript; Mr Bitterman developed the dataset, carried out spatial and
statistical analyses, and reviewed and revised the manuscript; and both authors approved the final
manuscript as submitted.
www.pediatrics.org/cgi/doi/10.1542/peds.2015-0831
DOI: 10.1542/peds.2015-0831
Address correspondence to Margaret Carrel, PhD, 303 Jessup Hall, University of Iowa, Iowa City, IA
52242. E-mail: [email protected]
PEDIATRICS (ISSN Numbers: Print, 0031-4005; Online, 1098-4275).
Copyright © 2015 by the American Academy of Pediatrics
FINANCIAL DISCLOSURE: The authors have indicated they have no financial relationships relevant to
this article to disclose.
FUNDING: No external funding.
POTENTIAL CONFLICT OF INTEREST: The authors have indicated they have no potential conflicts of
interest to disclose.
ARTICLE
PEDIATRICS Volume 136, number 1, July 2015
An ongoing measles outbreak has
sparked heated debate about vaccinepreventable diseases (VPDs) and the
choice of parents to not vaccinate
their children. Parents who choose to
not vaccinate their children are
primarily motivated by concerns over
vaccine safety or feelings that
children are not at risk for these VPDs
due to their geographic location.1–6
Measles elimination was maintained
via high rates of vaccination coverage,
and there is concern that the
protective effect of herd immunity
will wane as large numbers of
children remain un- or
underimmunized, resulting in the
reemergence of VPDs in the United
States.7,8 Studies find that when belief
exemptions to vaccination guidelines
are permitted, vaccination rates
decrease.9,10 Additionally, vaccination
refusal is associated with increased
infection with and transmission of
VPDs in unvaccinated children.11–15
In 2003, May and Silverman16
warned against the rise in families
claiming personal belief or other
nonmedical exemptions to public
school requirements for vaccination
and their tendency to cluster
geographically. Data have indicated
that clusters of high exemption
rates are spatially congruent with
outbreak clusters of pertussis and
measles.17–20 Within California, there
is high heterogeneity in the rates of
personal belief exemptions (PBEs),
with northern and southern coastal
regions exhibiting higher PBE
proportions.21,22 This spatial
heterogeneity exists at higher
geographic scales as well, with high
variation in exemption rates among
US states.23 High exemption rates
have been correlated with schools
that have higher numbers of white
students and greater wealth, and with
charter and private schools.17,24
The current study examines PBE
data from California between the
2001/2002 and 2014/2015 school
years to determine spatial patterns of
PBEs in kindergartners as well as the
PEDIATRICS Volume 136, number 1, July 2015
type of school populations associated
with higher rates of PBEs. We explore
the spatial overlap between schools
with high PBE rates and high rates of
personal medical exemptions (PMEs)
for students who are unable to
receive childhood immunizations.
This analysis identifies locations of
children who are unprotected from
VPDs not by choice and are
surrounded by other students who
remain unprotected because of
parental choice.
or reduced price lunch (FRL) during
the 2013/2014 school year for each
of the public schools in the dataset.
Also available from the CDE are
indicators of whether the school is
a charter school, a private school, or
religiously affiliated. Private schools
do not have race/ethnicity or FRL
data available. Rural-urban
commuting area codes for schools
were obtained for the census tract in
which the school is located, and
schools were assigned as either
suburban or nonsuburban.28,29
METHODS
Descriptive maps of PBEs and PMEs
in 2001/2002 and 2013/2014 were
generated to visualize how rates have
changed over both space and time.
Interpolation methods create
a continuous surface over space
based on observed measurements at
specific points. Inverse distanceweighted methodology was used to
interpolate PBE and PBE rates in
these 2 school years, where
estimations of PBEs and PMEs at
unsampled points were more strongly
influenced by nearby schools rather
than those far away.
The California Department of Public
Health (CDPH) records the total
number of PBEs and PMEs for
individual schools. PBEs recorded
before the 2014/2015 year represent
both philosophical and religious
exemptions. Data were acquired from
the CDPH on the number of PBEs and
PMEs and total enrollments in
kindergarten classes from the
2001/2002 through the 2014/2015
school years.25 CDPH suppresses data
from schools with fewer than 10
kindergartners. Proportions of
kindergartners claiming a PBE or
PME were calculated for each school
in each school year.
Using unique school codes, we
then matched CDPH data to the
locations of schools and their
sociodemographic characteristics
from California Department of
Education (CDE) data.26 School
locations were geocoded by using
latitude and longitude coordinates
from (1) the CDE dataset, (2)
geoprocessing services provided by
Texas A&M University,27 and (3)
Google Earth. Ninety-eight schools
were excluded from the dataset
because of missing or mismatched
data. The processed dataset includes
7283 kindergartens geocoded to the
accuracy of either parcel or street
segment.
By using data from the CDE, we then
calculated the rates of white students
and students receiving (adjusted) free
PBE proportions within individual
schools are likely to be highly
correlated over time, given that the
population of students (and their
parents) who attend each school does
not dramatically change year to year.
The nonspatial clustering algorithm
mclust (Model-Based Clustering,
Classification, and Density
Estimation)30,31 was used to group
schools according shared PBE
characteristics across the years of
the study. Model clustering
algorithmically partitions
observations into groups based on
similarity of n characteristics; in this
case, annual proportions of PBEs,
varying the size and shape
constraints and total number of
clusters detected. A reverse-scored
Bayesian information criterion (BIC)
was used to determine which number
of clusters and which size/shape
clusters best fit the data, where the
highest BIC is selected. In addition to
81
accounting for correspondence in the
behavior of schools’ PBE rates over
the 2001/2002 to 2013/2014 school
years, the clustering algorithm
reduced the complexity of our
outcome variable of interest, from
individual PBE proportions for 13
separate years to a multinomial
indicator of cluster membership. As
mclust will not execute on datasets
containing missing values, only
schools with PBE data in all years of
the study (ie, not schools that
open/closed during the duration of
the study) were included in the
cluster and subsequent regression
analysis (n = 5147).
predictors.32,33 Spatial models
control for spatial dependence among
the variables (ie, that people live near
people who are like them). This
allows us to understand how factors
such as the percentage of students
who are white are correlated with
PBE percentages without the inflating
effect of spatial autocorrelation.
Spatial weights were calculated based
on the nearest neighbors to a school,
3 sets of weights were generated
(knn = 3, 5, 7).
Although 2014/2015 data were not
included in the model clustering or
spatial regression, the current PBE
rates in schools are highly relevant
to the ongoing measles outbreak.
Scatterplots of PBE versus PME
proportions were generated and
schools that fell below the 90%
to 95% thresholds generally
considered necessary for herd
immunity to measles to be effective
were mapped.34,35 High PBE
hotspots as determined by local
Moran I were overlaid with
interpolated data on school-level
PMEs to evaluate spatial
concordance.
Cluster assignments were mapped
and a local Moran I test determined
whether cluster assignments were
spatially autocorrelated and the
location of significant hotspots of
cluster membership. Local Moran I
tests indicate areas of significantly
high density of schools with the same
cluster assignment. “High-high”
schools are those with elevated
PBEs surrounded by other high
PBE schools, “low-low” are low PBE
schools surrounded by low PBE
schools, and “transitional” schools are
those that are dissimilar from their
neighbors.
To determine if cluster membership
varied significantly according to
hypothesized covariates, x2 tests
were performed. Within the x2 tests,
a percentage deviation also was
calculated to indicate the degree to
which the observed frequency of
cluster membership within that
covariate category (eg, charter versus
noncharter) deviated from what is
expected under a null hypothesis of
even cluster membership across
categories.
Spatial multivariable linear models
were run in the spdep (Spatial
Dependence: Weighting Schemes,
Statistics and Models) package in R,
by using 2013/2014 PBE proportion
as the outcome variable and the
previously mentioned
sociodemographic variables as
82
FIGURE 1
Interpolated rates of PBEs and PMEs in California schools during the 2001/2002 and 2013/2014
school years. Darker shading indicates higher rates of exemptions.
CARREL and BITTERMAN
RESULTS
PBE percentages in the 2013/2014
school year ranged from 0% to
79.1%, and PMEs ranged from 0% to
17.3%. In contrast, PBE percentages
in the 2001/2002 school year had
a range of 0% to 63.2% and PMEs
ranged from 0% to 19.23%. PBE rates
increased across much of the state,
with the exception of persistently low
rates in the Central Valley (Fig 1).
Although PMEs do not increase as
much as PBEs do, areas reporting no
PMEs decreased between 2001/2002
and 2013/2014.
A 3-cluster option best fit the PBE
data, as determined by the highest
BIC score. The mclust model choice
and the number of clusters were
robust for samples down to
approximately 20% of the full
dataset. The mean proportion of PBEs
among schools in each cluster across
years was calculated and provides an
indication of how schools were
assigned to each cluster (Fig 2).
Cluster 1 is composed of schools with
low average PBE proportions across
all years of the study. Cluster 2
schools have higher PBE proportions
than those in cluster 1, with an
increase observed staring in the
2008/2009 school year. Cluster 3
schools have high PBE proportions in
the 2001/2002 school year and these
PBE proportions climb over time.
Thus, the clustering algorithm has
divided schools into “low,” “medium,”
and “high” PBE schools (Fig 3).
Local Moran I tests show locations of
significantly nonrandom hotspots of
cluster membership. A map focused
on Southern California shows that
statistically significant high-high
hotspots (meaning schools sharing
a cluster 3 designation) are located
primarily along the coast (Fig 4).
Transitional hotspot schools
(meaning schools that belong to
either the medium PBE cluster
[cluster 2] or are neighbored by
schools with higher or lower cluster
assignments) are located between
PEDIATRICS Volume 136, number 1, July 2015
FIGURE 2
Mean PBE rates in schools assigned to each cluster over the years of the study.
these high-high hotspots and the
central urban area of Los Angeles,
primarily composed of low-low
hotspots (all schools in cluster 1
neighbored by schools in cluster 1).
School profiles by cluster assignment
are shown in Table 1. The x2 tests
indicate that sociodemographics in
schools vary significantly by cluster
assignment (Table 2). Higher
FIGURE 3
Schools mapped by cluster assignment, where cluster 1 schools have consistently low PBE rates
(“low”), cluster 2 schools have low but increasing PBE rates (“medium”), and cluster 3 schools have
high rates of PBE (“high”).
83
More suburban schools are assigned
to the high PBE cluster than expected.
Public schools with high proportions
of white students had higher than
expected membership in the low and
medium PBE clusters and lower than
expected membership in the high PBE
cluster, whereas schools with low
proportions of white students had
higher than expected membership in
the low PBE cluster and lower than
expected membership in the medium
and high PBE clusters.
FIGURE 4
Location of schools designated as belonging to statistically significant hotspots, as determined by
the PBE cluster assignment, within the Los Angeles area. Schools that were not members of
statistically significant hotspots of high-high, low-low, or transitional PBE clusters are not shown.
numbers of private schools and
public charter schools are included in
the high PBE cluster than expected
under a null hypothesis of
nondifferential group membership.
Among public schools, those without
a religious affiliation have higher than
expected membership in the high PBE
cluster (cluster 3), whereas religious
schools have higher than expected
membership in the low (cluster 1)
and medium (cluster 2) PBE clusters.
TABLE 1 Counts of Schools Assigned to Clusters 1 to 3, Stratified by Potential Correlates of PBE
Rates
Cluster
Total, n (%)
Public, n (%)
Charter
Private, n (%)
Nonreligious
Religious
Rural-urban commuting area, n (%)
Suburban
Nonsuburban
2013/2014 white, n (%)
0%–25%
26%–50%
51%–75%
76%–100%
NA
2013/2014 FRL, n (%)
0%–25%
26%–50%
51%–75%
76%–100%
NA
1 (Low)
1186
1040
10
146
12
134
(23)
(87.6)
(0.8)
(12.3)
(1)
(11.3)
2 (Medium)
2849
2460
80
389
67
322
(55.3)
(86.3)
(2.8)
(13.7)
(2.4)
(11.3)
1112
782
63
330
118
212
(21.6)
(70.3)
(5.7)
(29.7)
(10.6)
(19.1)
79 (6.7)
1107 (93.3)
182 (6.4)
2667 (93.6)
169 (15.2)
943 (84.8)
1016
20
4
0
146
(85.7)
(1.7)
(0.3)
(0)
(12.3)
1404
657
369
29
389
(49.3)
(23.1)
(13)
(1)
(13.7)
90
185
377
130
330
(8.1)
(16.6)
(33.9)
(11.7)
(29.7)
8
30
101
901
146
(0.7)
(2.5)
(8.5)
(78)
(12.3)
445
452
582
980
389
(15.6)
(15.9)
(20.4)
(34.4)
(13.7)
269
207
201
105
330
(24.2)
(18.6)
(18.1)
(9.4)
(29.7)
NA, refers to private schools, given that data on race and FRL % were unavailable for private schools.
84
3 (High)
The situation reverses for FRL. Public
schools with high percentages of
students receiving subsidized lunches
have higher than expected
membership in the low PBE cluster
and lower than expected membership
in the medium and high PBE clusters,
whereas schools with few students
receiving FRL have low membership
in the low PBE cluster (cluster 1) and
high medium and high PBE cluster
membership. Relationships among
cluster membership, white
percentages, and FRL percentages are
strongest for the low and high PBE
clusters, with the medium PBE
cluster exhibiting similar but weaker
patterns to the high PBE cluster.
Given the spatial dependence in
cluster membership, spatial
autoregressive multivariable models
were implemented to explore the
association of sociodemographic
characteristics with 2013/2014 PBE
proportions. PBE rates, rather than
cluster assignments, were used
because of methodological limitations
in spatial multinomial modeling;
however, cluster assignments
strongly correlate with 2013/2014
PBE rates. Parameter estimates from
the final models are seen in Table 3.
In public schools, the percentage of
students who are white or on FRL
and being a charter school are
significant positive predictors of PBE
rates. Suburban location is
a significantly negative predictor.
There is a significant interaction
between FRL percentages in a school
and charter status, with charter
CARREL and BITTERMAN
TABLE 2 x2 Tests and Percentage Deviation of Observed From Expected for Sociodemographic
Variables According to Cluster Assignment
School Characteristic
x2
Cluster 1 (Low), %
Cluster 2 (Medium), %
Cluster 3 (High), %
Public
Private
Public noncharter
Public charter
Private nonreligious
Private religious
Suburban
Nonsuburban
2013/2014, % white
0%–25%
76%–100%
2013/2014, % FRL
0%–25%
76%–100%
169.13***
+5.4
226.8
+2.7
273.1
263.9
+18.0
220.3
+0.61
+3.8
218.8
+0.3
29.0
224.4
+7.2
23.63
+1.1
215.5
+76.6
24.6
+125.5
+57.0
216.8
+7.9
22.38
+66.6
2100
22.6
214.3
280.4
+347.6
295.4
+86.7
+7.3
214.1
+104.0
271.1
66.94***
56.03***
86.82***
1832.51***
1127.26***
***All x 2 are significant at the P , .0001 value.
status moderating the positive
relationship between FRL and PBE. In
private schools, religious affiliation is
significantly negatively associated
with elevated PBE rates, whereas
suburban status has a positive but
nonsignificant relationship with PBEs.
rates higher than 5% and 10% are
highlighted because vaccination rates
below 90% to 95% are considered
dangerous to measles herd immunity.
Figure 5B indicates the location of
schools that do not meet this
threshold.
The maximum rate of PBEs in
California kindergartens increased
from 79.1% in 2013/2014 to 84.21%
in 2014/2015. The colocation of
schools with elevated PBEs and
elevated PMEs is of particular
concern given the rising numbers of
students claiming philosophical
exemptions to immunizations.
Figure 5A shows the rates of
2014/2015 PBEs and PMEs in
schools. Schools with PBE or PME
A local Moran I on PBE rates in
2014/2015 indicates several
statistically significant areas of the
state where schools with high PBE
rates are neighbored by other schools
with high rates. These are overlaid on
interpolated rates of PMEs from the
same school year to indicate where
herd immunity shortfalls may pose
the greatest risk to students who
cannot medically be vaccinated
(Fig 6). There are a few areas of
spatial overlap, including in the areas
south of Los Angeles, near Santa Cruz,
and around Redding in the north.
TABLE 3 Coefficient Estimates for Variables
Associated With PBE Rates in
Multivariable Spatial Regression
Models
Subset
Public schools
Percent white 2013/
2014
Percent FRL 2013/
2014
Charter
Suburban
FRL:Charter
Private schools
Religious
Suburban
school, avoiding assumptions about
whether nearby residents are
reflective of student or parent
characteristics. Additionally, our use
of spatial autoregressive methods
accounts for dependency in the
spatial patterns and more accurately
establishes what characteristics of
a student population are associated
with increased PBEs.
Estimate
SE
P value
0.092 0.004 ,.0001
0.008 0.003
.004
7.180 0.605 ,.0001
20.483 0.214
.024
20.058 0.011 ,.0001
26.140 0.712 ,.0001
3.178 0.743
.101
Only results from knn = 5 are reported, coefficients and P
values were nearly identical in the knn = 3 and knn = 7
models.
PEDIATRICS Volume 136, number 1, July 2015
DISCUSSION
The study addresses gaps in the cited
literature. By using a longer time span
than other studies, we are better able
to elucidate temporal patterns of
PBEs in California.17,18,21,24 Previous
studies primarily use areal (county,
zip code, Census tract) data, which
may not reflect student populations,
particularly when multiple schools
are assigned to the same area or
when considering charter and private
schools.17–19,21,36 Our analysis is at
the level of the individual elementary
Data from the 2013/2014 school year
versus the 2001/2002 school year
indicate that increasing PBEs are not
confined to urban areas but are
widely distributed across the state
(Fig 1). By using trends in PBEs,
California schools can be classified
into 3 types: those that have high
rates of PBEs from 2001/2002
through 2013/2014 (cluster 3), those
with lower PBE rates that experience
an increase during the years of the
study (cluster 2), and those with
consistently low rates of PBEs
(cluster 1). Although cluster
assignments were derived without
consideration of spatial relationships,
these types of schools exhibit
interesting and significantly
nonrandom patterns. The Central
Valley of California, a primarily
agricultural region with small and
medium-size cities, is dominated by
schools in the low and medium PBE
clusters (Fig 3). High PBE cluster
schools appear across much of
northern California and in the
suburban or peripheral areas of large
urban areas. The Los Angeles area
exhibits a distinctive spatial pattern
of cluster assignments, with hotspots
of low PBE schools centrally located,
ringed by transitional hotspots and
high PBE hotspots located along the
coast to the north and south (Fig 4).
This could indicate that (1) belief
exemptions are diffusing from
suburban/peripheral areas of cities
inward toward the urban core, or (2)
that those with specific vaccine
beliefs have left the core and moved
to the periphery.
Sociodemographic characteristics of
students and schools vary
85
FIGURE 5
A, PME versus PBE rates. Schools with PBE and/or PME rates higher than 10% are highlighted with black triangles, those with PBE or PME rates of 5% to
10% are in gray squares. B, Spatial locations of schools that are above this threshold for PBEs or PMEs are indicated.
significantly according to cluster
membership (Table 2). Low PBE
schools are more likely to be public,
noncharter, and nonsuburban, with
lower percentages of white students
and higher percentages of students
on subsidized lunch. High PBE
schools tend to be charter or private
nonreligious schools located in
suburban areas with high percentages
of white students and low
percentages of students receiving
subsidized lunch.
Regression results using percent PBEs
in 2013/2014 as the outcome of
interest indicate a more complex story.
Although the general pattern of
findings is consistent with the
literature, controlling for the
inflationary effect of spatial
FIGURE 6
Hotspots of high PBE rates in the 2014/2015 school year overlaid on interpolated PME rates from the same year.
86
autocorrelation on coefficients and
significance values produces
unexpected results. Among public
schools, the correlation between
percentage of students who are white
and charter status had the expected
relationship, both being significant and
positive predictors of increased PBEs
(Table 3). Suburban location had
a negative relationship with PBEs,
opposite of what was anticipated given
the maps of cluster assignments.
However, determining what is and is
not a suburban area is somewhat
subjective, and these findings suggest
that (1) our definition needs to be
revised, (2) that high PBE rates are no
longer confined to a suburban ring
around cities but have also increased in
urban cores, or (3) might be influenced
by the location of high PBE schools in
smaller urban aggregations. The
positive and significant coefficient for
percentage of students receiving
subsidized lunch was unanticipated,
given the literature on philosophical
exemptions being positively associated
with income.24 The coefficient for
percent FRL is small, and a statistically
significant interaction term with
charter status suggests that the lack of
geographically distinct attendance
boundaries for charter schools, with
students drawn from across a school
district and admitted by lottery, may
CARREL and BITTERMAN
generate schools with simultaneously
high FRL and high PBE rates. Among
private schools, those with a religious
affiliation were significantly associated
with decreased PBE rates. Suburban
location was not a significant predictor
of PBEs in private schools, likely
because, similar to charter schools, they
draw in students from a variety of
areas.
The potential for spatial overlap
between schools with high PBE rates
and high PMEs is particularly
concerning, especially where rates of
exemptions exceed 5% to 10% and
threaten the protective effects of
measles herd immunity. There are
more than 800 schools in the
2014/2015 school year that exceeded
this threshold of exemptions, primarily
because of PBEs. These schools are
located principally in the areas
surrounding Los Angeles, San
Francisco, and Sacramento (Fig 5).
Statistical analysis indicates that
significant hotspots of PBEs in
2014/2015 also overlap with areas
of elevated PMEs (Fig 6). When
outbreaks of measles or pertussis do
occur, these are places where students
with PMEs may be at greatest risk.
Our analysis was confined to those
schools with complete PBE and PME
data from 2001/2002 through
2014/2015. We thus are not
capturing trends and correlates of
PBEs and PMEs in schools that either
opened or closed during these years.
Additionally, our analysis of private
schools was limited by data
availability, namely that there is not
a reliable way to determine the
race/ethnicity or FRL profile for these
schools. Finally, it is possible that
exemptions coded as PME in the
dataset actually represent a PBE;
whereas a written statement from
a physician documenting the medical
exemption is required for a PME
classification, there could be cases in
which a philosophical/religious belief
is actually the underlying motivation.
However, given the relative ease of
registering a PBE before January
PEDIATRICS Volume 136, number 1, July 2015
2014, when no consultation with
a health care professional was
required, and the need to consult
a health care provider for either
a PME or PBE designation since that
time, this is likely to characterize
a limited number of observations.37
CONCLUSIONS
PBE rates are increasing across
California. The decrease in the
protective effects of herd immunity are
coupled with an increase in the
potential for children with PBEs and
PMEs to overlap, both within schools
and surrounding communities. This
suggests that clinicians with PME
patients should inquire about the
location and type of school the child
attends. The steady upward trend in
PBEs in schools across cluster
assignments and across the rural/urban
divide in California suggests that public
health departments across the state will
need to spatially target schools with
riskier populations for containment/
quarantine activities in the event of VPD
outbreaks. We identify areas where
high-risk schools are located in close
spatial proximity, indicating key places
where intervention and education
might reduce the incidence of PBEs,
protect herd immunity, and hopefully
limit future outbreaks.
ABBREVIATIONS
BIC: Bayesian information
criterion
CDE: California Department of
Education
CDPH: California Department of
Public Health
FRL: free or reduced price lunch
PBE: personal belief exemption
PME: personal medical exemption
VPD: vaccine-preventable diseases
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CARREL and BITTERMAN