On-line Supplementary Material
An agent-based model of child sugar-sweetened beverage consumption: implications for
policies and practices
Authors: Matt Kasman1, Ross A. Hammond1,2,3, Rob Purcell1, Benjamin Heuberger1, Travis R.
Moore4, Anna H. Grummon6,7, Allison J. Wu6,8, Jason Block6, Marie-France Hivert6,9, Emily
Oken6,7, Ken Kleinman10
1 Center on Social Dynamics and Policy, Brookings Institution, Washington, DC, USA (MK,
RAH, RP, BH)
2 Brown School at Washington University in St. Louis, MO, USA (RAH)
3 The Santa Fe Institute, Santa Fe, NM (RAH)
4 ChildObesity180, Gerald J. and Dorothy R. Friedman School of Nutrition Science and Policy,
Tufts University, Boston, MA, USA. (TRM)
5 Department of Community Health, School of Arts and Sciences, Tufts University, Medford,
MA, USA. (TRM)
6 Division of Chronic Disease Research Across the Lifecourse, Department of Population
Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, MA,
USA (AHG, AJW, JB, MH, EO)
7 Department of Nutrition, Harvard TH Chan School of Public Health, Boston, MA, USA (AHG,
EO)
8 Division of Gastroenterology, Hepatology and Nutrition, Boston Children’s Hospital, Boston,
MA, USA (AJW)
9 Diabetes Unit, Massachusetts General Hospital, Boston, MA, USA (MH)
10 Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences,
University of Massachusetts—Amherst, MA, USA (KK)
Supplementary Materials and Methods
Model Description
The ABM model simulates young children’s sugar-sweetened beverage (SSB) consumption over
time, with consumption being driven by the time that children spend in different settings.
Parental behavior plays an active role in this model, making decisions that determine children’s
SSB availability in the home.
The model uses a weekly time resolution: each model step represents one week of real-life time.
One model one represents five years, and such is comprised of 260 model steps.
Agent Properties
The model is populated by a set of agents 𝐶𝑖 for 𝑖 ∈ {1, … , 𝑛}, representing a cohort of young
children, who age through early childhood and elementary school during the model. Each agent
object 𝐶𝑖 is associated with properties describing the represented child, as well as those
describing that child’s parents; parents are not represented by separate object, but by certain
properties and behaviors of the child agent. The model population is 1014 children.
Each agent has the following properties:
Individual Properties
- Age, 𝑎𝑖 ∈ [2,7]. Each child begins at age 2 and the simulation ends when they are age 7.
- BMI z-score, 𝐵𝑀𝐼(𝐶𝑖 ), intended to approximately reflect the contribution to BMI from
consumption of sugar-sweetened beverages. The BMI z-score is relative to the CDC
growth chart for the current age of the child.
Household Properties
- Race, 𝑟𝑖 ∈ [𝑤, 𝑏, ℎ]. We limit our racial groups to white, Black, and Hispanic, which
represent most of the Viva cohort. Several other properties and distributions in the model
are correlated with race.
- SES (socio-economic status), 𝑠𝑒𝑠𝑖 ∈ [low,high]. We define low SES as a family income
under $55,000. We use the notation low_ses to denote the Boolean variable 𝑠𝑒𝑠 = low.
- Maternal employment status. This is used while drawing simulated values for childcare
time.
Setting Association
- Each child is associated with one of each of the three model settings: a home, a school,
and a child-care type. At any step of the model, each child has a vector of weekly times
⃗ = [𝑇𝐻 , 𝑇𝑆 , 𝑇𝐾 ].
spent in each setting, 𝑇
Agents also take several actions which may bring about changes to their and settings’ properties.
Here we summarize agents’ actions, and more detail is found below in the ‘Update Rules’
section.
Actions
- Consume SSBs: each unit of time, the child consumers some amount of SSB, equal to the
sum of the amount consumed in each setting. For each setting, this is equal to the hourly
consumption rate times the weekly hours spent in that setting. This also leads to changes
in BMI z-score.
- Update time distribution: at age 5, the child begins attending school. This reduces the
amount of time spent in childcare and at home.
- Visit pediatrician: once per year, each agent potentially visits a pediatrician, with a
probability depending on agent properties.
- Update home beverage distribution: each unit of time, each child’s parents update the
home SSB offering.
Model Environment
The model includes three simulated settings.
Homes, 𝐻𝑖 for 𝑖 ∈ {1, … , 𝑛}, represent each separate agent’s home environment. That is, no two
agents share a home environment. We use 𝐵 𝐻 to denote the beverage offering of an agent’s
home environment; all beverage offerings are in units of servings of SSB per hour of time in that
setting.
Schools, 𝑆𝑗 for 𝑗 ∈ {1, … , 𝑚}, represent agent’s school environments, but only abstractly
correspond to specific schools. That is, we do not simulate social interaction between agents
assigned to the same school. Agents are associated with schools such that segregation by race
and SES approximately matches reality. Each school entity has its own beverage offering, which
we denote by 𝐵𝑆 .
Childcare types, 𝐾𝑙 for 𝑙 ∈ {1, … , 𝑝}, represent the different settings in which children receive
childcare. Childcare types are even further abstracted than schools, and each type of childcare is
represented by a single object. The model contains four types: center-based, own home care,
outside home-based care, and none. We represent the childcare offering for a given agent by 𝐵𝐾 .
Model Initialization
Here we describe the rules for initializing agent properties:
Agent Properties
Agent race is chosen by selecting from the options white, Black, and Hispanic weighted by Viva
cohort population. SES is initialized second using probability conditional on race. Age is
initialized to 2 years (104 weeks).
Child BMI conditional on both race and SES, and is simulated from the coefficients of regression
bmiz ~ race + low_ses +race*low_ses.
Beverage Offering Distributions
Home beverage offering is initially drawn from a gamma distribution whose parameters depend
on the agent’s race and SES: 𝐵𝐻,𝑖 ~ Γ(𝛼(𝑟𝑖 , 𝑆𝐸𝑆𝑖 ), 𝛽(𝑟𝑖 , 𝑆𝐸𝑆𝑖 )).
The beverage offering for each school is drawn from a folded (positive, about zero) normal
distribution, 𝐵𝑠,𝑗 ~ |𝑁(𝜇𝑆 , 𝜎𝑆 )|.
The beverage offerings for each childcare type are fixed.
Agent Setting Association
Each household is associated by definition with a unique agent. Childcare-types are assigned
simply by using probability weighted by cohort incidence of each type.
School association is accomplished by an algorithm that uses matrices exposure coefficient
matrices to attempt to recreate real world levels of school segregation, described in pseudocode
below. Here, “race-ses group” refers to one of the six combinations of race and SES: white-high,
white-low, black-high, etc., which we notate w_h, w_l, b_h, etc.
Objects:
- child_list: list of all child agents
- school_list: list of all schools
- exposure_matrix: matrix of exposure coefficients, with rows and
columns indexed by race-ses groups; i.e.,
exposure_matrix[h_h,w_l] is the exposure coefficient of a
Hispanic, high-SES child to white, low-SES children.
Classes:
- child: a child agent
o child.group: race-ses combination of the child agent
- school: a model school
o school.children: list of children assigned to this school
for school in school_list:
initialize school.children as empty list
uniformly sample child c1 from child_list
add c1 to school.children
remove c1 from school_list
for i in [2,...,school.size]:
randomly select a race-ses combination, weighted by
exposure_matrix[c1.group,] (the exposure coefficents to the
race-ses combination of child c1)
try:
uniformly sample child cn from subset of child_list
matching the chosen race-ses combination
if subset is empty:
uniformly sample cn from child_list
add cn to school.children
remove cn from child_list
Setting Time Distribution
Agent’s childcare time is initialized is set to zero if their childcare-type is “none”, and otherwise
it is initialized by simulation from the coefficients of regression for the formula childcare_time ~
mother_part_time + mother_stay_at_home + childcare_own_home + childcare_other_home,
where each of the regressors is a self-explanatory Boolean variable. The weekly childcare time
TK is equal to five times the simulation draw.
Agent school time is initialized to zero at age 2, and home time is equal to remaining time in the
week, 𝑇𝐻 = 24 × 7 − 𝑇𝐾 .
Model Dynamics
Each agent’s age increments by one week each time step, and its other properties vary according
to several rules.
Child SSB Consumption
At each time step, the amount of SSB consumed is:
SSB(𝐶𝑖 , 𝑡) = 𝑇𝑆 (𝐶𝑖 , 𝑡) × 𝐵𝑆 (𝑆(𝐶𝑖 )) + 𝑇𝐻 (𝐶𝑖 , 𝑡) × 𝐵𝐻 (𝐻𝑖 ) + 𝑇𝐾 (𝐶𝑖 , 𝑡) ×
𝐵𝐾 (𝐾(𝐶𝑖 ))
This is added to the total SSB consumption, and used to calculate instantaneous BMI change for
this time step.
Child Time Distribution Update
At ages 2 through 4, children attend only child-case and not school. At age 5, children begin
attending school. Each child Ci begins attending school at a random model step 𝑡𝑆 (𝐶𝑖 ) between
the ages of 4.5 and 5.5, at which point their weekly time at school is set to 5 times the length of
the school day (in the main policy sweep, 6 hours).
If a child’s initial childcare time is less than six hours per weekday, their childcare time after
starting school is set to zero; otherwise, their school time is subtracted from their childcare time:
𝑇𝐾 (𝐶𝑖 , 𝑡𝑆 (𝐶𝑖 )) = max(0, 𝑇𝐾 (𝐶𝑖 , 𝑡0 ) − 𝑇𝑆 (𝐶𝑖 , 𝑡𝑆 (𝐶𝑖 ))
After the child attends school, the new home time is 𝑇𝐻 (𝐶𝑖 , 𝑡𝑆 (𝐶𝑖 )) = 24 × 7 − 𝑇𝐾 (𝐶𝑖 , 𝑡𝑆 (𝐶𝑖 )) −
𝑇𝑆 (𝐶𝑖 , 𝑡𝑆 (𝐶𝑖 )).
BMI Update
Each agent’s BMIz updates using a simple linear update function,
𝐵𝑀𝐼(𝐶𝑖 , 𝑡 + 1) = 𝐵𝑀𝐼(𝐶𝑖 , 𝑡) + 𝑆𝑆𝐵(𝐶𝑖 , 𝑡) ∗ 𝐾𝐵𝑀𝐼 𝑆𝑆𝐵 ,
where 𝐾𝐵𝑀𝐼 𝑆𝑆𝐵 is a parameter drawn at each time step from the BMI update coefficient
distribution, 𝐾𝐵𝑀𝐼 𝑆𝑆𝐵 ~ 𝑁(𝜇𝐵𝑀𝐼 𝑆𝑆𝐵 , 𝜎𝐵𝑀𝐼 𝑆𝑆𝐵 ).
Home SSB Offering Update
Each time step, each agent’s home SSB offering updates by the formula:
𝐵𝐻 (𝐻𝑖 , 𝑡 + 1) = 𝐵𝐻 (𝐻𝑖 ) + 𝑊(𝑡) + 𝐹(𝐵𝐻 (𝐻1 , 𝑡), 𝐵𝐻 (𝐻2 , 𝑡), … 𝐵𝐻 (𝐻𝑛 , 𝑡))
The marginal change in SSB offering has two terms. 𝑊(𝑡)~ 𝑁(𝜇𝑊 𝜎𝑤 ) is a normally distributed
weekly increase term that represents a constant linear increase with random variation.
The function F is a “follow the average” function that depends on the current home beverage
offerings of the entire model cohort. Parents move their home beverage offering towards the
mean offering by a certain portion (a free parameter) of the distance. Parents within a satisficing
threshold (another free parameter) do not update their offering.
Pediatrician Visit
Once a year (at a random calendar point per child) each child may have a simulated pediatrician
visit. The visit occurs with a probability that is dependent on each agent’s race and SES; if they
miss a probability draw one year, they may still succeed in other years.
If the visit occurs in a model year, parents of a child with high BMI receive a signal to reduce
home SSB offering. This occurs if the agent’s BMIz is greater than 1, and the amount of
reduction is a variable free parameter. The parameter represents the fractional reduction to home
SSB offering if the signal is received; i.e., a signal of 0.25 immediately lowers home SSB
offering by 25%.
Model Usage
We test several policy interventions, which are represented as alterations to several model rules.
Beverage Multipliers
The model includes four multiplier interventions: home beverage multiplier, school beverage
multiplier, childcare beverage multiplier, and childcare center beverage multiplier. These can be
used to test setting-wise reductions to SSB availability.
Home and school multipliers simply multiply all beverages in those settings by a fixed
coefficient. For home, this includes both the initialization and yearly update terms, but does not
alter social and pediatrician mechanics. The school multiplier alters each school’s fixed beverage
amount.
The childcare multiplier effects the initial and update terms for all childcare settings. There is
also a childcare center multiplier, which if set to a value other than 1 will override the general
childcare multiplier and multiply the childcare setting beverage value instead by the childcare
center multiplier.
Pediatrician Signal Strength
The baseline pediatrician signal strength is determined through model calibration, as described in
below. The effect of the pediatrician signal can be increased by using larger values for the
pediatrician signal parameter.
Pediatrician Access Boost
Improved pediatrician access is represented in the model by increasing agents’ probability of a
yearly pediatrician visit occurring. This is accomplished by a “pediatrician access boost”
parameter. Altering the value of this parameter increases pediatrician signal probability such that
an access boost of zero yields baseline probabilities, and a boost of one ensures each agent will
see the doctor every year.
Specifically, the boost decreases the probability that individual agents do not see a pediatrician.
For example, a boost of 0.2 reduces the probability of not seeing a doctor by a factor of 0.8 = 1 –
0.2, for each agent each year.
Model Parameterization
Model parameters are initialized based on analysis of several data sources. The primary data set
is the Project Viva cohort data; to characterize the distribution of SSBs across different settings
in more detail we use data from NHANES, PSID, and some other literature.
Data sources:
Viva (Supplemental Figure 1): Between 1999 and 2002, Project Viva recruited 2,128 pregnant
women from obstetric offices in Eastern Massachusetts. Mothers who delivered a singleton
infant attended in-person study visits during the first and second trimester of pregnancy, in the
days following delivery, infancy (median age = 6.6 months), early childhood (median age 3.4
years), and mid-childhood (median age 8.0 years). They also completed mailed questionnaires on
the anthropometry, diet, and health behaviors of their children on an annual basis extending
through adolescence. Maternal data included daily SSB (including non-diet soda and fruit drinks
with added sugar), fruit juice, and diet soda consumption during pregnancy, as well as prepregnancy BMI, pregnancy weight change, education, smoking status, income, and
race/ethnicity. Child data included daily physical activity, height, weight, and sugar-sweetened
beverage consumption.
Supplementary Figure 1: Flow of participant involvement in Project Viva through the mid-
childhood visit
NHANES: The National Health and Nutrition Examination Survey (NHANES) is a program of
studies designed to assess the health and nutritional status of adults and children in the United
States. NHANES, a major program of the National Center for Health Statistics (NCHS),
combines interviews and physical examinations. The survey examines a nationally representative
sample of about 5,000 persons each year. These persons are located in counties across the
country, 15 of which are visited each year. The NHANES interview includes demographic,
socioeconomic, dietary, and health-related questions. In particular, we use the 24-hour dietary
recall portion of NHANES data to help characterize consumption amounts and settings We use
the data from the 2003-2004 and 2005-2006 survey cycles, pooled with appropriate adjustment
of the survey weights, which approximately corresponds to the time period of Viva data
collection for the relevant age of the cohort.
PSID: “The PSID began as a longitudinal study that focused on the transfer of capital within
families. In 1997, it was expanded to include a host of measures that are pertinent to children
aged 12 and younger. These measures ranged from parenting, children’s academic achievement,
behavior, and time use. Of the families in the PSID with children younger than 12 years, 2380
participated.” We use the Child Development Supplement (CDS) within the PSID, which has
child time use data.
NCES: NCES data is used to calculate exposure coefficients for school segregation by race and
SES.
Hourly SSB Consumption by Setting
We use the NHANES 24-hour recall dietary survey data along with the PSID time use data to
produce a data set of hourly SSB availability rates by setting, race, and SES. We restrict the
analysis to consumption events of SSBs by the definition used by the Viva study: sugar-added
soda (soft drinks) and fruit drinks (specifically, soda at USDA food code 924 but removing diet
and unsweetened soda, and fruit drinks at code 925 but removing artificially sweetened lowcalorie drinks). We refer to this below as the NHANES-derived dataset.
The NHANES data set allows us to classify consumption events for home and school. We then
use the daily time use data from PSID to assign child time by setting for each age and surveyed
day of the week, and then calculate the expected hourly consumption by setting for each
NHANES survey respondent. We use a similar approach to calculate average daily servings at
school per school day.
Parameter Values from Data
Below we list model parameters along with the data sources and analysis techniques used to
calculate them.
Cohort Demographics
Cohort demographics are calculated using the Viva dataset only. Race is simulated using
population probability, low SES status using a logistic regression based on race, and BMIz using
a linear regression with the interaction terms listed. We use a simple value for the simulation
error, equal to one fifth of a z-score SD.
Supplementary Table 1: agent attribute initialization parameters
Race probabilities
probability white
0.78
probability Black
0.14
probability Hispanic 0.08
SES probability coefficients
(logistic)
low SES
-0.89
low SES * Black
1.77
low SES * Hispanic 1.37
BMIz coefficients
constant
-0.04
Black
0.18
Hispanic
-0.02
low SES
0.004
Black * low SES
0.21
Hispanic * low SES 0.52
Error
0.2
Home Beverage Distribution
We parameterize the initial hourly home beverage rates using a gamma distribution which
captures the long-tailed structure of SSB availability amounts found in both the Viva cohort data
and the NHANES 24-hour dietary recall. Using the NHANES-derived hourly consumption data
set described above, and for each race-SES grouping we parameterize a gamma distribution
using by moment matching.
The methodology of the NHANES survey differs significantly, and further it is conducted on a
nationally representative population rather than the specific location of the Viva cohort. To
compare model output to the Viva cohort data, we introduce a multiplicative “Viva adjustment
parameter” to renormalize the model population mean home beverage rate to that observed in the
Viva dataset. The model population is initialized by drawing home beverage rates from each
agent’s appropriate gamma distribution, and then multiplying by the Viva adjustment. The final
value of the Viva adjustment (0.185) is derived by calibrating the resulting model population so
that the average model population mean numerically matches the Viva population mean.
Supplementary Table 2: Home beverage availability initialization parameters
Home SSB hourly servings
Race
Low
Gamma
SES?
shape
white
FALSE
0.30543
Gamma
rate
9.290275
white
Black
Black
Hispanic
Hispanic
TRUE
FALSE
TRUE
FALSE
TRUE
0.333679
0.915161
1.15037
0.596015
0.588847
17.46528
26.16993
31.74052
17.70099
28.61967
Home Beverage Yearly Increase
The yearly update distribution is derived by regressing mean hourly home consumption on year
in the NHANES-derived dataset. In the model, a draw from a normal distribution is added to the
home beverage availability amount each time step, converting the draw from yearly to weekly (*
1/52), and further multiplying the draw by the Viva adjustment parameter above; the mean for
this distribution is 0.00993 and the standard deviation 0.00089.
Childcare Type and Beverage Distribution
Each agent is matched to a single childcare type which they are associated with throughout the
model. The probability of each type association is calculated directly from the Viva data.
Our value for childcare hourly consumption is taken from (Lutzkanin (2015)); we apply a 2.0
“informal care multiplier” to the home-based childcare types based on consultation with subject
matter experts.
Supplementary Table 3: Childcare initialization parameters
Childcare Type
Center-based
0.241
Home-based, own
0.248
home
Home-based, other
0.181
None
0.33
Childcare SSB hourly
servings
Hourly servings
0.0208
Informal care
2
multiplier
Childcare Time Distribution
Probability of maternal employment is calculated directly from the Viva data, and the daily hours
of early childcare time are simulated using a regression with the below coefficients which
depend on maternal employment and childcare type. The error is a naïve estimate equal to one
fifth the population SD.
Supplementary Table 4: childcare time use parameters
Maternal Employment
Probability full time
Probability part time
Probability stay-athome
Childcare time
coefficients
(hours/day)
constant
mother part-time
mother stay-at-home
own home childcare
other home childcare
Error
0.41
0.31
0.29
7.56
-3.48
-6.6
-0.36
0.53
0.1
School Beverage Distribution
Each simulated school has its daily serving rate drawn from a folded normal distribution, which
is then converted to hourly based on a six-hour school day. The parameters are the population
mean (0.0322) and standard deviation (0.155) of the average daily school setting SSB servings
from the NHANES-derived school data.
School Assignment: Exposure Matrices
School assignment is assortative by both SES and race and conducted according to the
pseudocode algorithm above. The exposure coefficients are calculated from NCES data for the
relevant ages from the 04/05 and 05/06 data sets.
These are the separate exposure matrices for race and SES. The race-SES group exposure matrix
is calculated at model run as the Kronecker product of these blocks.
Supplementary Table 5: School assignment parameters
SES
high
SES
low SES
Race
white
Black
Hispanic
high SES
0.919434
low SES
0.080566
0.89711
white
0.488077
0.107941
0.154866
0.10289
Black
0.218915
0.579593
0.334939
Hispanic
0.293008
0.312466
0.510196
Pediatrician Access
We draw yearly probabilities of pediatrician access from (Weinick 2008). Each agent’s yearly
probability of access is to the probability of their racial group in the table below, multiplied by
the “Low SES factor” if they are a low SES agent.
Supplementary Table 6: Pediatrician access parameters
Pediatrician
access
white probability
Black probability
Hispanic
probability
Low SES factor
0.82
0.54
0.52
0.5
Model BMIz Update
We draw our BMIz update coefficients from the RCT in (deRuyter 2012); these per-serving
distribution parameters are renormalized to the US BMI distribution for the relevant age and
converted to a weekly serving format (mean of 0.00161, standard deviation 0.000045).
Calibrated Parameter Values
The model contains several free parameters that are not set by data analysis or taken from
literature. We use these free parameters to calibrate the model baseline to achieve a good match
with the Viva cohort data in the absence of any policy intervention. We do a simple difference of
means of weekly SSB consumption at age 7 between model data and viva data to rank each
parameter combination, and thereby selected the below free parameters as achieving the best fit.
Supplementary Table 7: calibrated parameters
Home beverage social update
Social probability
0.15
Social coefficient
0.15
Social satisficing
0.00275
threshold
0.25
Pediatrician signal
strength
Intervention Parameter Values
As described above, intervention conditions are implemented by adjusting baseline parameter
values by specified amounts.
Supplementary Table 8: intervention condition parameters
Parameter
Pediatrician signal strength
Home beverage multiplier
School beverage multiplier
Childcare beverage multiplier
Childcare center beverage
multiplier
Pediatrician access boost
Baseline
value
Policy values
0.25
1
1
1
0.3
0
0
0
0.375
0.559
0.822
0.559
1
0
0.39
0.2
0.4
0.5
0.7
0.964
0.7
0.8
0.982
0.8
0.912
0.425
0.45
0.456
0.822
Supplementary Results
Supplementary Figure 2: heatmap representing mean cumulative SSB consumption over a
large portion of the parameter space. Outer axes (“faceted” subplots, with labels at top and right)
are school and childcare beverage reductions, and inner axes (labels left and bottom) are the
home beverage reduction and a combined pediatrician boost variable. Pediatrician boost
0.956
incorporates both the access boost and the signal boost. All dimensions have the total number of
axis points reduced for ease of display. The changes brought about by the physician policy are
small relative to direct SSB availability reduction policies.
Supplementary Figure 3: Heatmap plot showing only pediatrician policies. Increasing
frequency and effect of pediatrician visits both decrease mean cumulative SSB availability, but
do not have population-level effects as large as those that affect availability directly.
Supplementary Table 9: Expanded Results Table. Condition impact means and confidence
intervals obtained from Welch Two-Sample t-test comparison of distributions of average weekly
sugar-sweetened beverage (SSB) consumption across 50 repeated runs under each intervention
condition to 50 repeated runs of the baseline condition.
Home
Beverage
Reduction
-
School
Beverage
Reduction
-
Childcare
Beverage
Reduction
-
Home
Beverage
Reduction
100.00%
School
Beverage
Reduction
100.00%
-
Childcare
Beverage
Reduction
100%
100%
100.00%
-
100.00%
-
-
-
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
-
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
4.4%
(10% soda
reduction)
100.00%
100.00%
-
-
-
Pediatrician
Signal
Increase
-
Mean SSB
Consumption
Weekly
2.061548
CI lower
2.047698
CI upper
2.075398
Pediatrician
Access
Increase
-
Pediatrician
Signal
Increase
-
Mean SSB
reduction
weekly
0.768885
1.807694
CI lower
0.756324
1.796599
CI upper
0.781447
1.818789
-
100%
100%
-
-
1.533543
0.516005
0.251382
1.27969
0.517284
0.519132
1.523193
0.502363
0.238495
1.268242
0.503659
0.505524
1.543894
0.529647
0.26427
1.291138
0.530909
0.532739
100%
100%
-
-
0.516811
0.517915
0.503184
0.504305
0.530439
0.531525
100%
-
-
-
0.520568
0.506963
0.534173
100%
-
-
-
0.52509
0.511523
0.538658
100%
-
-
-
0.560961
0.547653
0.574269
-
0.241694
0.246249
0.240776
0.244059
0.314176
0.32104
0.267417
0.271916
0.266498
0.26971
0.339853
0.346741
100%
100.00%
100.00%
Pediatrician
Access
Increase
-
-
-
Childcare
Center
Beverage
Reduction
Childcare
Center
Beverage
Reduction
-
-
-
20%
50%
-
20%
50%
20%
50%
55.00%
60.00%
-
-
0.254555
0.259082
0.253637
0.256885
0.327015
0.33389
20%
50%
20%
30%
-
-
-
0.353204
0.404567
0.340454
0.391864
0.365954
0.417271
100%
-
-
-
0.579401
0.566022
0.59278
4.4%
(10% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
20.00%
20.00%
30.00%
30.00%
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
-
-
100.00%
-
-
100.00%
-
0.31395
0.301342
0.326558
100%
-
-
-
0.642398
0.62921
0.655586
100%
-
-
-
0.376056
0.803116
0.534792
0.363645
0.79046
0.522882
0.388467
0.815772
0.546702
100%
-
-
-
0.944484
0.674652
0.932257
0.663143
0.956711
0.686161
100%
-
-
-
1.136929
1.125199
1.148658
-
-
-
0.865355
1.27969
1.27969
1.27969
1.27969
0.854368
1.268242
1.268242
1.268242
1.268242
0.876342
1.291138
1.291138
1.291138
1.291138
-
-
100.00%
-
-
100.00%
-
-
100.00%
-
-
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
-
-
1.8% (10%
soda
reduction)
-
20%
50%
55.00%
60.00%
20%
50%
-
-
-
1.356641
1.363636
1.385291
1.438091
1.34525
1.352245
1.373984
1.426843
1.368032
1.375028
1.396597
1.449339
-
-
-
-
1.284259
1.27285
1.295668
-
-
-
-
1.288828
1.277458
1.300199
-
-
-
-
1.324876
0.003513
0.00859
0.002653
0.00654
1.313788
-0.0103
-0.00519
-0.01117
-0.00725
1.335963
0.01733
0.022366
0.016479
0.020331
20%
30%
55.00%
60.00%
20%
30%
-
20%
50%
20%
50%
-
-
-
0.075318
0.082275
0.101492
0.152678
0.061561
0.068507
0.087772
0.138997
0.089075
0.096043
0.115212
0.16636
-
-
-
0.004502
-0.00931
0.018316
-
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
-
-
-
-
0.00906
-0.00472
0.02284
-
-
-
-
0.044703
0.031163
0.058244
-
-
-
-
-
0.06239
0.048812
0.075968
-
-
-
-
-
0.124183
0.282399
0.421951
0.110771
0.26946
0.40942
0.137594
0.295339
0.434483
-
-
-
-
-
0.612264
0.600179
0.624349
-
-
-
-
20%
20%
50%
50%
0.006655
0.012308
0.011272
0.017774
0.078574
0.083087
-0.00713
-0.00143
-0.00246
0.004097
0.064847
0.069403
0.020441
0.026043
0.025002
0.031451
0.0923
0.09677
-
-
-
20%
50%
0.077726
0.081222
0.085458
0.089972
0.084683
0.088229
0.064
0.067534
0.071724
0.076282
0.070944
0.074522
0.091451
0.094911
0.099191
0.103662
0.098421
0.101936
-
-
20%
20%
20%
20%
30%
30%
-
-
20%
50%
0.104371
0.108449
0.10355
0.106494
0.155281
0.158969
0.090673
0.094787
0.089858
0.092835
0.141626
0.145349
0.11807
0.122112
0.117241
0.120153
0.168936
0.17259
-
1.8% (10%
soda
reduction)
1.8% (10%
soda
reduction)
1.8% (10%
soda
reduction)
30%
30%
-
-
20%
50%
0.154488
0.157084
0.140834
0.143467
0.168143
0.170702
4.4%
(10% soda
reduction)
8.8%
(20% soda
reduction)
20.00%
30.00%
44.1%
(100%
soda
reduction)
-
-
-
20%
50%
20%
50%
20%
50%
55.00%
55.00%
55.00%
55.00%
60.00%
60.00%
60.00%
60.00%
-
20%
50%
-
-
20%
50%
20%
50%
20%
50%
-
-
-
-
20%
-
0.008025
-0.00575
0.021801
-
-
50%
-
0.013075
-6.66E-04
0.026817
-
-
0.007154
-0.00663
0.020939
-
20%
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1.8% (10%
soda
reduction)
1.8% (10%
soda
reduction)
1.8% (10%
soda
reduction)
1.8% (10%
soda
reduction)
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
-
-
-
50%
0.0111
-0.00264
0.024845
-
55.00%
-
-
0.079825
0.066102
0.093548
-
60.00%
-
-
0.086795
0.073064
0.100526
20%
-
-
-
0.106011
0.092326
0.119697
30%
-
-
-
0.157176
0.143529
0.170822
-
-
20%
-
0.012583
-0.00115
0.026321
-
-
50%
-
0.017644
0.003937
0.031351
-
-
-
20%
0.01172
-0.00203
0.025473
-
-
-
50%
0.015621
0.00191
0.029333
-
55.00%
-
-
0.084422
0.070732
0.098111
-
60.00%
-
-
0.091338
0.077642
0.105034
20%
-
-
-
0.110571
0.096924
0.124217
30%
-
-
-
0.161739
0.148132
0.175346
-
-
20%
-
0.048154
0.034648
0.061659
-
-
50%
-
0.053145
0.039665
0.066626
-
-
-
20%
0.047299
0.033786
0.060812
-
-
-
50%
0.051063
0.037591
0.064535
-
-
-
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
4.4%
(10% soda
reduction)
8.8%
(20% soda
reduction)
17.8%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
-
55.00%
-
-
0.120137
0.106675
0.1336
-
60.00%
-
-
0.127025
0.113565
0.140484
20%
-
-
-
0.146189
0.132771
0.159607
30%
-
-
-
0.197451
0.184073
0.210829
-
-
-
20%
-
0.065651
0.0521
0.079202
-
-
-
50%
-
0.070123
0.056597
0.083649
-
-
-
-
20%
0.064751
0.051203
0.0783
-
-
-
-
50%
0.068235
0.054729
0.081741
-
-
55.00%
-
-
0.137915
0.124421
0.15141
-
-
60.00%
-
-
0.144748
0.131235
0.158262
-
20%
-
-
-
0.16401
0.150522
0.177497
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
30%
-
-
-
0.215342
0.201896
0.228788
-
-
-
-
0.06691
0.053363
0.080456
-
-
-
-
0.071429
0.05792
0.084937
-
-
-
-
0.107244
0.093967
0.120522
-
-
-
0.127151
0.113772
0.14053
-
20%
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
8.8%
(20% soda
reduction)
-
-
-
-
-
-
-
-
-
-
-
-
-
55.00%
-
-
-
60.00%
0.117759
0.14448
20%
0.126243
0.112853
0.139632
50%
0.129273
0.115918
0.142628
-
0.199841
0.186495
0.213187
-
-
0.206861
0.193519
0.220202
-
-
-
0.226157
0.212814
0.239499
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
30%
-
-
-
0.277691
0.264414
0.290969
-
-
-
-
0.128743
0.11537
0.142117
-
-
-
-
0.133336
0.119992
0.146679
-
-
-
-
0.169087
0.155996
0.182178
-
-
-
0.271633
0.274716
0.271
0.273136
0.345663
0.352613
0.297482
0.30052
0.296854
0.298952
0.371396
0.378326
20.00%
20.00%
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
-
20.00%
30.00%
30.00%
30.00%
0.13112
20%
-
20.00%
-
-
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
50%
20%
50%
-
-
0.284558
0.287618
0.283927
0.286044
0.35853
0.365469
-
-
-
0.385167
0.436909
0.372352
0.424127
0.397981
0.449691
-
-
-
-
0.286926
0.274023
0.29983
-
-
-
-
0.291498
0.27863
0.304366
-
-
-
-
0.327344
0.423596
0.425938
0.423098
0.314729
0.411076
0.413432
0.410576
0.339959
0.436116
0.438443
0.435619
55.00%
60.00%
20%
30%
20%
50%
20%
50%
-
20%
30.00%
-
-
30.00%
30.00%
30.00%
30.00%
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
17.8%
(100%
soda
reduction)
-
30.00%
30.00%
30.00%
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
soda
reduction)
44.1%
(100%
-
-
0.424633
0.412124
0.437142
-
-
-
0.498109
0.50508
0.525325
0.577221
0.485642
0.492617
0.512912
0.564846
0.510577
0.517543
0.537739
0.589596
-
-
-
-
0.426502
0.414006
0.438998
-
-
-
-
0.431038
0.418576
0.443501
-
-
-
-
0.466892
0.454695
0.479088
-
-
-
20%
-
0.613317
0.601239
0.625396
-
-
-
50%
-
0.614864
0.602792
0.626936
-
-
-
-
20%
0.61296
0.600878
0.625042
-
-
-
-
50%
0.613953
0.601875
0.62603
-
-
55.00%
-
-
0.688818
0.676804
0.700831
-
-
60.00%
-
-
0.69581
0.683798
0.707821
55.00%
60.00%
20%
30%
50%
-
20%
-
-
-
0.716428
0.704485
0.728372
-
30%
-
-
-
0.768694
0.756809
0.780579
-
-
-
-
0.616812
0.604765
0.628859
-
-
-
-
0.621373
0.609363
0.633383
1.8% (10%
soda
reduction)
3.6% (20%
soda
reduction)
soda
reduction)
44.1%
(100%
soda
reduction)
17.8%
(100%
soda
reduction)
-
-
-
-
0.657257
0.645523
0.668991
Sensitivity Analyses
We performed sensitivity analysis by computing the model on a reduced sweep of the policy
space for several additional “sensitivity conditions”. Conditions of interest include lengthening
and shortening the school day, as well as three alternative sets of calibrated free parameter values
which also scored well in the procedure outlined above.
Supplementary Table 10: Sensitivity analyses parameters
Sensitivity
Condition
School
Day
Pediatrician
Signal
Home Social
Probability
Home Social
Coefficient
Baseline
School day 2 hours
School day
+2 hours
Free params
alt. 1
Free params
alt. 2
Free params
alt. 3
6
4
0.25
0.25
0.15
0.15
0.15
0.15
Home Social
Satisficing
Thresh
0.00275
0.00275
8
0.25
0.15
0.15
0.00275
6
0.2
0.15
0.1
0.0035
6
0.35
0.05
0.1
0.00275
6
0.3
0.05
0.1
0.00325
Overall, results from these analyses were either as expected a priori (e.g., school-based
interventions had greater impact when the school day was long) in the case of school day
adjustment or qualitative similar to our main results, in the case of alternative free parameters.