Abstract
Introduction:
The Supplemental Nutrition Assistance Program (SNAP), Free and Reduced Priced Lunch program (FRPL), and Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) reduce food insecurity for millions of Americans with lower incomes. However, critics of the programs have questioned whether they increase obesity. This study examined whether participating in each program was associated with child BMI z-score (BMIz) from kindergarten to fifth grade.
Methods:
Data from 4,457 primary grade students whose household incomes were equal to or below 200% of the federal poverty level from kindergarten to fifth grade as part of the Early Childhood Longitudinal Study (ECLS-K:2011) were analyzed. Marginal structural models with inverse probability of treatment/censoring weights were used to estimate the association between parent-reported SNAP/FRPL participation over time and fifth grade BMIz, accounting for loss-to-follow-up and time-varying confounders. Weighted generalized estimating equations were used to examine the association between WIC participation and BMIz trends. All analyses incorporated ECLS-K sampling weights. ECLS-K:2011 data were collected from 2010 to 2016, and analyses were conducted in 2021 and 2022.
Results:
At baseline, 2,419 (54.3%) ECLS-K participants in this sample used SNAP, 3,993 (89.6%) participated in FRPL, and 3,755 (84.2%) reported past WIC participation. No associations were found between any program and BMIz at the end of fifth grade or between WIC participation and BMIz trend.
Conclusions:
Prior findings of a relationship between program participation and BMI may have been due to weaker study designs and uncontrolled confounding. SNAP, FRPL, and WIC were not associated with increased risk of childhood obesity in this recently conducted longitudinal study.
INTRODUCTION
Childhood obesity, which impacts millions of children in the U.S., is associated with adverse health outcomes including cardiometabolic diseases, diabetes, and all-cause mortality.1–3 The burden of childhood obesity is not equitably borne – children from families with low-income or those that identify as Black and Latinx are more likely to have obesity and severe obesity compared to other groups. These children are also at higher risk for food insecurity, or inadequate access to food.4 Children born to individuals experiencing food insecurity have increased risk of birth defects, anemia, malnutrition, and reduced cognitive functioning.5
The Supplemental Nutrition Assistance Program (SNAP), the Free and Reduced Priced Lunch Program (FRPL), and the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) are the largest programs nationwide that successfully reduce food insecurity among children.6–8 However, some have raised concerns that these programs might inadvertently exacerbate obesity risk, under the theory that increasing purchasing power or access to food could lead to excess calories.9–12 Yet research on participation and childhood obesity is mixed, especially among studies using cross-sectional data from the National Health and Nutrition Examination Survey (NHANES).13–18 Among adults, another cross-sectional NHANES analysis found SNAP participation was positively associated with obesity.19
Meanwhile, longitudinal studies with control for time-invariant sources of confounding have found predominantly null or negative associations with obesity risk, though potential effect measure modification has been reported by child age, sex, and neighborhood,20–23 with 1 earlier study reporting positive associations between food stamp participation and overweight risk for girls.24
Few studies have examined these relationships using prospective data with adequate control for time-varying sources of confounding. Time-varying confounding could obscure relationships between program participation and child obesity over time. For example, food insecurity may increase obesity risk while being both a cause and consequence of future and prior participation. Food insecurity itself might both confound and mediate the effect of participation on childhood obesity, and simply adjusting for food security status at one time point may be inadequate. Another source of time-varying confounding may include variables such as household resources, if programs alleviate financial burdens by offsetting food costs and change household income and program eligibility status over time. To address these gaps, marginal structural models (MSMs) were used to estimate the association of SNAP, FRPL, and WIC participation on childhood BMI in a nationally-representative cohort of students followed from kindergarten to fifth grade in the Early Childhood Longitudinal Study, Kindergarten Class of 2010‒2011 (ECLS-K:2011). Associations between WIC and BMI trend were also estimated using weighted generalized estimating equations (WGEE). Questions of interest were: is any exposure, even at one time point, to SNAP/FRPL associated with increased childhood BMI z-score (BMIz) at the end of fifth grade (RQ1); is consistent exposure to SNAP or FRPL associated with increased BMIz at the end of fifth grade compared to no exposure (RQ2); and is there a dose-response association of cumulative program participation and child fifth grade BMIz (RQ3)? For WIC, questions were: is exposure to WIC in early childhood associated with obesity risk at the end of fifth grade (RQ4), and is WIC participation associated with trend in BMIz (RQ5).
METHODS
Study Population
This study used nationally-representative panel data from students selected from public/private schools who attended full- or part-day kindergarten in 2010–2011.25 Students, parents, and teachers were asked to complete questionnaires in the Fall/Spring for kindergarten through second grade, and in the Spring thereafter.
Because nutrition assistance program participants typically have lower household incomes than non-participants, and because income is a very strong determinant of childhood obesity,26 the analytic sample was restricted to those with household incomes ≤200% FPL at baseline to reduce the potential for residual confounding (N=4,457 at baseline). Failure to account for income differences may otherwise lead to bias in isolating the association between participation and obesity. On the other hand, restrictions that correspond exactly to eligibility thresholds (i.e., 130% FPL for SNAP or 185% for WIC), may be too conservative and result in the exclusion of individuals who are eligible by other criteria. A 200% FPL threshold has been applied previously and is likely to capture those around the cut-off who would be eligible to participate.27
Measures
Exposures of interest were participation in SNAP and FRPL (measured at 3 time points), and in WIC (measured retrospectively at baseline). Parents reported household SNAP exposure via the question, “In the past 12 months, have you or anyone in your household received food stamps, also called SNAP, or food benefits on EBT (Electronic Benefit Transfer)?’”, FRPL via the question, “Does [child] receive complete school lunches for free or reduced price at school?”; and WIC via the questions, “Did [child] receive any WIC benefits as an infant or child” or “When (you were/[child]’s mother was) pregnant with [child], did (you/she) receive any benefits from the Special Supplemental Food Program for Women, Infants, and Children, or WIC?”28
The outcome, child BMIz, was computed from measured height and weight, age, and sex taken at each wave,29 using WHO Growth Reference Standards using the zscorer R package.30,31
Covariates included parent-reported Temporary Assistance for Needy Families (TANF) participation in the past year, past WIC participation, child disability status, child sex, food security status (18-item USDA Household Food Security Module32), income as %FPL, highest maternal education, parental marital status, child race/ethnicity, and age.
Statistical Analysis
Stratification-based methods, including conventional regression modeling, will result in bias in the presence of time-dependent confounders (e.g., food insecurity) that both affect and are affected by exposure (e.g., program participation), since controlling for these covariates may prevent unbiased estimation of the effect of prior exposure on an outcome (e.g., child BMIz) that is mediated through these variables (Appendix Section 1 Figure 1).33 For example, food insecurity might be affected by past participation in SNAP while simultaneously influencing whether families decide to participate in these programs in the future, and analyses of the relationship between repeated measures of participation and child BMIz may be biased if these mediating variables are conditioned on an outcome in a regression model. MSMs adjust for time-varying confounding via a 2-stage modeling procedure where predicted probabilities of treatment or exposure for each individual are first estimated conditional on covariates at each time, then outcome models that are weighted by the inverse of these probabilities are fit to the data. This allows for confounder control without necessitating the inclusion of variables that are on the causal pathway in the outcome regression itself. MSMs with treatment and censoring (defined by any missing data at the next time point) weights were used to account for time varying/invariant confounding, as well as for loss-to-follow-up. Attrition in cohort studies that is differential between those who participate and do not participate in nutrition assistance programs may otherwise result in bias if those who remain in the study differ with respect to the outcome (i.e., BMI).34 Stabilized weights, which help to improve the efficiency of MSM estimators, were estimated from logistic models for program participation and censoring at each time and included survey weight, sampling unit, and stratum in addition to prior participation status and covariates.35 Outcome weighted regression models for child BMIz at the end of fifth-grade were fit using generalized estimating equations accounting for the repeated measurements with bootstrapped SEs. Analyses of SNAP and FRPL included baseline adjustment for participation in other food assistance programs (i.e., FRPL where SNAP was the exposure, and SNAP for FRPL models), as well as for all covariates listed above. Adjustment for time-varying confounding was made for FRPL participation (or SNAP exposure for FRPL models), TANF status, child disability status, maternal education, food security, poverty, parental marital status, and intermediary BMIz, since this may be associated with both program participation and future BMIz.
Because WIC participation was measured retrospectively at baseline, a single time-point MSM comparing WIC participation to BMIz at the end of fifth grade was used. Longitudinal MSMs could not be used to assess the association between WIC participation and BMIz trend. Thus, weighted GEE (WGEE), which account for the clustering of repeated BMIz observations within study participants over time, was used for this question where models were weighted by ECLS-K:2011 survey weights.36 WIC models were adjusted for baseline child disability, food security, poverty, maternal education, child race/ethnicity, child age, child sex, and parental marital status.
Analyses were conducted in R 3.6.1 (R Core Team, Vienna, Austria). Based on the existing literature, potential interaction by child sex was assessed.14,20 MSM analyses were limited to the occasions where all variables were collected: kindergarten, first, and fifth grades. For WGEE, BMIz at all time points was used. Secondary analyses explored MSM and WGEE models using a dichotomous indicator for obesity status, defined as greater than or equal to the 95th percentile of sex- and age-specific BMI. Additional details on the analytic approach are available in the Appendix. This research was considered exempt by the Harvard Committee on the Use of Human Subjects; de-identified data from a publicly available data set was used.
RESULTS
After restricting to children whose household incomes were ≤200% FPL and those with complete data, the final sample size was 4,457 students at baseline, 4,204 at first grade, and 2,828 at fifth grade. Compared to those excluded, those in the final analytic sample were significantly more likely to participate in SNAP, FRPL, TANF, and WIC, to be food insecure, to have lower household incomes and lower maternal educational attainment, to identify as non-Hispanic Black or Hispanic, and to have higher baseline BMIz. Reductions in the sample-size were likely driven by declines in response rates between 2012‒2016, which were especially large for non-White groups.37,38 At baseline, 84.2% of parents recalled participation in WIC, 54.3% participated in SNAP, and 89.6% participated in FRPL. Mean BMIz at baseline was 0.85 (SD=1.31). Distributions of covariates differed at each wave, except for child sex (Table 1). In particular, between kindergarten and fifth grade, the proportion participating in SNAP, FRPL, and TANF decreased. Food security improved over time, with 75.9% food secure in kindergarten and 83.7% food secure at the end of fifth grade. A smaller proportion of households had incomes ≤100% FPL in 2016, and maternal education generally increased.
Table 1.
Characteristics of Children in Households With Income ≤200% of the Federal Poverty Level (FPL) in the ECLS-K:2011 Analytic Sample, 2012–2016
| Measurement occasion |
||||
|---|---|---|---|---|
| Characteristic | Spring 2012 (N=4,457) n (%) |
Spring 2013 (N=4,204) n (%) |
Spring 2016 (N=2,828) n (%) |
p-valuea |
|
| ||||
| Age, years, mean (SD) | 6.04 (0.37) | 7.02 (0.37) | 10.92 (0.37) | <0.001 |
| BMIz, mean (SD) | 0.85 (1.31) | 0.89 (1.40) | 1.15 (1.43) | <0.001 |
| Child race/ethnicity | <0.001 | |||
| Non-Hispanic White | 1,328 (29.8) | 1,268 (30.2) | 876 (31.0) | |
| Non-Hispanic Black | 824 (18.5) | 668 (15.9) | 363 (12.8) | |
| Hispanic | 1,779 (39.9) | 1,768 (42.1) | 1,284 (45.4) | |
| Non-Hispanic Asian | 271 (6.1) | 257 (6.1) | 178 (6.3) | |
| Non-Hispanic Other/Multiple | 255 (5.7) | 243 (5.8) | 127 (4.5) | |
| Child sex | 0.953 | |||
| Male | 2,264 (50.8) | 2,140 (50.9) | 1,447 (51.2) | |
| Female | 2,193 (49.2) | 2,064 (49.1) | 1,381 (48.8) | |
| Program participation | ||||
| SNAP in past 12 months | 2,419 (54.3) | 2,281 (54.3) | 1,220 (43.1) | <0.001 |
| FRPL | 3,993 (89.6) | 3,811 (90.7) | 2,414 (85.4) | <0.001 |
| WIC while pregnant or during childhood | 3,755 (84.2) | 3,513 (83.6) | 2,252 (79.6) | <0.001 |
| TANF in the past 12 months | 462 (10.4) | 409 (9.7) | 172 (6.1) | <0.001 |
| Child disability status | 877 (19.7) | 628 (14.9) | 404 (14.3) | <0.001 |
| Food security status | <0.001 | |||
| Food secure | 3,383 (75.9) | 3,266 (77.7) | 2,367 (83.7) | |
| Low food security | 809 (18.2) | 708 (16.8) | 331 (11.7) | |
| Very low food security | 265 (5.9) | 230 (5.5) | 130 (4.6) | |
| Household income | <0.001 | |||
| <100%FPL | 2,553 (57.3) | 2,441 (58.1) | 1,327 (46.9) | |
| 100%–200% FPL | 1,904 (42.7) | 1,763 (41.9) | 1,501 (53.1) | |
| Maternal education | 0.006 | |||
| Less than high school | 1,187 (26.6) | 1,107 (26.3) | 753 (26.6) | |
| High school/GED | 1,399 (31.4) | 1,339 (31.9) | 860 (30.4) | |
| Some college/vocational | 1,471 (33.0) | 1,377 (32.8) | 886 (31.3) | |
| College or higher | 400 (9.0) | 381 (9.1) | 329 (11.6) | |
| Parental current marital status | <0.001 | |||
| Married | 2,325 (52.2) | 2,324 (55.3) | 1,648 (58.3) | |
| Separated | 298 (6.7) | 264 (6.3) | 173 (6.1) | |
| Divorced/widowed | 414 (9.3) | 415 (9.9) | 348 (12.3) | |
| Never | 1,205 (27.0) | 1,029 (24.5) | 570 (20.2) | |
| Civil union/Domestic partnership | 215 (4.8) | 172 (4.1) | 89 (3.1) | |
Note: Boldface indicates statistical significance (p<0.05).
p-values are from continuity-corrected chi-squared tests for categorical variables, and from 3-group analysis of variance for continuous variables.
FRPL, Free/Reduced Priced Lunch; SNAP, Supplemental Nutrition Assistance Program; TANF, Temporary Assistance for Needy Families; WIC, Special Supplemental Nutrition Program for Women, Infants, and Children.
Estimates, 95% CIs, and p-values from MSMs testing the associations between SNAP, FRPL, and WIC, and BMIz are shown in Table 2. No associations between SNAP or FRPL participation and child BMIz were found in any model. In addition, there was no association between recalled WIC participation and fifth-grade BMIz, and no evidence for interaction by child sex in any analyses. No association between WIC and BMIz trend was found in WGEE analyses (Table 3). Results did not differ when an indicator for obesity was used instead of continuous BMIz (Appendix Section 3).
Table 2.
Adjusted Differences in Mean BMIz by SNAP, FRPL, and WIC Participation, From Survey-Weighted MSMs
| Program | Estimate (95% CI) | Bootstrapped p-value |
|---|---|---|
|
| ||
| SNAPa: Difference in mean BMIz at 5th grade... | ||
| ...Per each additional year of program participation from kindergarten to 5th grade (dose-response) | −0.037 (−0.097, 0.023) | 0.191 |
| ...Between those with any exposure compared to those with none from kindergarten to 5th grade | −0.047 (−0.195, 0.102) | 0.492 |
| ...Between those who were continuously exposed and those who were never exposed from kindergarten to 5th grade | −0.107 (−0.315, 0.110) | 0.267 |
| FRPLa: Difference in mean BMIz at 5th grade... | ||
| ...Per each additional year of program participation from kindergarten to 5th grade (dose-response) | 0.082 (−0.013, 0.177) | 0.072 |
| ...Between those with any exposure compared to those with none from kindergarten to 5th grade | 0.171 (−0.065, 0.406) | 0.156 |
| ...Between those who were continuously exposed and those who were never exposed from kindergarten to 5th grade | 0.219 (−0.023, 0.466) | 0.077 |
| WICb: Difference in mean BMIz at 5th grade... | ||
| ...Between those exposed to WIC compared to those who were not exposed to WIC reported at baseline | −0.015 (−0.230, 0.199) | 0.862 |
SNAP (FRPL) MSMs include IPW adjustment for baseline FRPL (SNAP), TANF, and WIC participation, child disability status, child sex, categorical food security status, income as a percent of the FPL, highest maternal education, parental marital status, child race/ethnicity, and continuous child age and BMIz, and time-varying FRPL (SNAP) and TANF participation, disability status, maternal education, food security, poverty level, parental marital status, and BMIz.
WIC MSMs include IPW adjustment for baseline child disability, food security, poverty level, maternal education, child race/ethnicity, child age, child sex, and parental marital status.
BMIz, BMI z-score; FRPL, Free/Reduced Priced Lunch; MSMs, marginal structural models; SNAP, Supplemental Nutrition Assistance Program; TANF, Temporary Assistance for Needy Families; WIC, Special Supplemental Nutrition Program for Women, Infants, and Children.
Table 3.
Adjusted Associations Between Recalled WIC Participation and BMIz Trend From Weighted Generalized Estimation Equations (WGEE)
| Contrast | Estimatea (95% CI) | p-value |
|---|---|---|
|
| ||
| Difference in mean BMIz, WIC participants vs WIC non-participants at baseline (kindergarten) | 0.133 (−0.005, 0.270) | 0.060 |
| Yearly BMIz slope change among those who did not participate in WIC, from kindergarten to 5th grade | 0.053 (0.038, 0.069) | <0.0001 |
| Yearly BMIz slope change from kindergarten to 5th grade, WIC participants vs WIC non-participants (the WIC-BMIz trend association) | 0.007 (−0.011, 0.025) | 0.441 |
Note: Boldface indicates statistical significance (p<0.05).
WIC WGEE models include regression adjustment for baseline child disability, food security, poverty level, maternal education, child race/ethnicity, child age, child sex, and parental marital status.
BMIz, BMI z-score; FRPL, Free/Reduced Priced Lunch; SNAP, Supplemental Nutrition Assistance Program; TANF, Temporary Assistance for Needy Families; WIC, Special Supplemental Nutrition Program for Women, Infants, and Children.
DISCUSSION
In this nationally representative sample of U.S. primary-school children living in households with lower income from the ECLS-K:2011, neither participation in SNAP nor in FRPL – regardless of whether participation at any time point vs. none (RQ1), participation at all 3 time points vs. none (RQ2), or in a dose-response manner (RQ3) was considered – were associated with differences in mean fifth-grade BMI z-score after adjustment for time-dependent confounding and loss to follow up. No evidence was found for interaction by child sex. Last, no association between WIC and fifth-grade BMIz (RQ4), or between WIC and BMIz trends over time in WGEE models (RQ5) were found. This is the first study to assess the association between food assistance program participation and child BMI in longitudinal settings with control for time-varying confounding and loss to follow up. Overall, these findings re-affirm those presented by Kreider et al. (2012), who demonstrate no relationship between SNAP and poor health after accounting for unmeasured confounding and participation misreport,39 and those presented by Millimet et al. (2010), who demonstrate no relationship between school lunch participation and long-run measures of weight gain after similar adjustments.40 Findings of no evidence for interaction by child sex is consistent with work from the prior ECLS-K cohort demonstrating no relationship between school lunch participation and obesity or weight by student sex.41,42
Findings of no association between WIC and BMI trajectory or to BMI at the end of fifth grade are consistent with studies of WIC prior to 2009 that also found no association between participation and child or infant weight.43–45 For example, Foster et al. (2010) examined data from the Panel Study of Income Dynamics (PSID) in 1997 and found that while children born to WIC recipients were more likely to be low birth-weight and small-for-gestational age in crude models, these associations were not significant after confounder adjustment using propensity-score matching.44 In 2009, changes were made to the WIC package including increased allowances for fruits and vegetables and that aimed to improve household diet quality.46 Recent work suggests that among the WIC participant population, these changes have had positive impacts to child obesity trends compared to earlier years.47 However, less is known about the policy’s comparative impacts relative to those who are income-eligible non-participants. Similarly, while improvements to NSLP’s nutrition standards have been shown to improve diet quality and possibly reduce obesity, changes to obesity risk when comparing participants and non-participants is less clear. The present study does examine differences in BMIz between participants and non-participants who are income-eligible for these programs but does not directly evaluate the policy changes to WIC and NSLP. Future work should leverage quasi-experimental designs in order to better isolate the effect of these policies on child health.
Reducing health inequities related to food insecurity, diet, and obesity is a public health priority. Because of the wide reach of nutrition assistance programs like SNAP, FRPL, and WIC, and their documented impact on food insecurity, many have proposed them as potential interventions to improve diet quality and reduce obesity among participants.13,48 Yet this hope for expanding the health benefits of existing food programs, which, in the cases of FRPL and WIC appear to already have been improving the health of program participants,47,49–51 comes in the context of concerns about whether the programs themselves increase obesity. Near-cash benefits could theoretically lead to obesity if they are used to purchase unhealthy foods, if they lead to excess total energy intake, or if freed income is spent on behaviors not conducive to an active lifestyle,15 and some have found that SNAP participants consume more sugar-sweetened beverages (SSBs) than non-participants.17,52 Findings from this study, however, suggest that these concerns about increased obesity risk are unfounded, and policymakers should continue to consider changes to nutrition assistance programs that would improve their reach and quality, including increasing the benefit size and incentivizing spending on healthy foods in SNAP,18,53 maintaining nutrition standards in WIC and the school lunch program and expanding community eligibility provisions (CEP) that would decrease the stigma of FRPL while improving access,50,54 and exploring strategies that would increase participation rates.55,56 Such strategies to leverage the benefits of SNAP, WIC, and FRPL could be promising approaches for helping to reduce nutrition- and obesity-related health inequities.
Limitations
Strengths of this study included the use of rich longitudinal data with repeated measures, valid measures of food security and BMIz, and methods that accounted for potential time-varying confounding and censoring. However, several limitations should be noted. First, misreported (particularly underreported) participation in nutrition assistance programs is a well-documented issue when studying the causal effects of these interventions; this may result in selection bias if documented participants are systematically different than non-reporters of participation.57 In this sample, the extent to which participants may have under-reported program participation in SNAP or FRPL was unknown. However, past WIC participation rates in this study were comparable to those observed nationally based on data from the Current Population Survey.58 Recent work has leveraged natural experiments to estimate effects of SNAP policy changes while circumventing self-reported participation,18 while others have proposed methods for sensitivity analyses that relax assumptions of accurate and complete reporting.39 However, these methods are largely available only for cross-sectional settings, and future work should explore extensions of these methods to longitudinal data and to estimators of causal effects that account for time-confounding, such as MSMs. Second, MSMs may suffer from loss of statistical efficiency without further modifications. To address this concern, stabilized forms of all inverse probability weights (Appendix Section 1) and bootstrapping for SEs with many bootstrap iterations (5,000) were used to improve precision.
It was assumed that program participation assessed at each occasion always occurred after time-varying covariates measured at that occasion, though this assumption is untestable with the data available. Future studies could address this concern by measuring program participation and potential covariates using finer increments of time, particularly given turnover in programs like SNAP, in order to identify the role of participation duration and timing on health outcomes. Lastly, unmeasured or residual confounding is always of concern in observational studies regardless of analytic strategy, and it is possible that other determinants of non-participation among eligible families that influence BMIz exist but were not documented as part of the study. For example, access to healthy and unhealthy food outlets in the neighborhood, availability of green space, and environmental pollution may all be correlated with participation in nutrition assistance programs as well as with weight, but this contextual information was not part of the publicly-available data.
CONCLUSIONS
Obesity remains a pressing issue in the U.S., especially among children. Food insecurity, which has greatly increased due to COVID-19, also threatens child health and development. Understanding how to best leverage public policies to support child health is critical, as is understanding whether programs that are well-positioned to support better diet and reduce food insecurity could be unintentionally exacerbating obesity risk. Using data from the Early Childhood Longitudinal Study, there were no associations between participation in SNAP, FRPL, or WIC on child obesity at the end of fifth grade. In models fit using weighted generalized estimating equations, there were no associations between WIC participation and BMI trend over time. SNAP, WIC, and FRPL remain valuable programs that support food security and do not increase obesity among children.
Supplementary Material
ACKNOWLEDGMENTS
This work was supported by funding from Harvard Catalyst | The Harvard Clinical and Translational Science Center (National Center for Advancing Translational Sciences, NIH Award UL 1TR002541). EWK was supported by a Eunice Kennedy Shriver National Institute of Child Health & Human Development Career Development Award (K99HD101657). ELK was supported by a National Institute of Diabetes and Digestive and Kidney Diseases Career Development Award (K01DK125278). The sponsors had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication. No financial disclosures were reported by the authors of this paper. The authors wish to thank Kelsey Vercammen, PhD for her assistance in developing code.
Footnotes
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