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Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity

Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Key Points Question Is social contagion associated IMPORTANCE Childhood obesity is a principal public health concern. Understanding the geographic with spatial patterns in childhood distribution of childhood obesity can inform the design and delivery of interventions. obesity rates across neighborhoods in Arkansas? OBJECTIVE To better understand the causes of spatial dependence in rates of childhood obesity Findings In this cohort study of across neighborhoods. 935 800 children, after controlling for neighborhood fixed effects, positive and DESIGN, SETTING, AND PARTICIPANTS This cohort study used data from a legislatively mandated significant spatial autocorrelation was body mass index screening program for public school children in Arkansas from the 2003-2004 detected using spatial panel models through 2014-2015 academic years. Spatial autoregressive moving average (SARMA) models for when obesity rates were computed for panel data were used to estimate spatial dependency in childhood obesity at 2 levels of spatial larger census tracts but not when aggregation. Data were analyzed from August 2017 to February 2018. computed for smaller census block groups, indicating that neighborhood EXPOSURES The SARMA models included geographic fixed effects to capture time-invariant contextual factors, rather than social differences in neighborhood characteristics along with controls for the mean age of children and the contagion, appeared to better explain proportion of children by race/ethnicity, school meal status, and sex. observed spatial patterns in obesity rates across neighborhoods. MAIN OUTCOMES AND MEASURES The proportion of obese schoolchildren in Arkansas neighborhoods by year, defined at larger (census tract) and smaller (census block group) Meaning Spatial analysis may be used spatial scales. in epidemic studies, but researchers should use caution when interpreting a RESULTS The geographic aggregations were based on 935 800 children with a mean (SD) age of 132 positive spatial autocorrelation as (39) months. Of these children, 51% were male; 65% were white, 21% were black, 10% were evidence for contagion, especially in a Hispanic, 2% were Asian, and the remainder were of other or unidentified race/ethnicity. In models social context. without geographic fixed effects, there was evidence of positive and significant spatial autocorrelation in obesity rates across tracts (ρ = 0.511; 95% CI, 0.469-0.553) and block groups (ρ = Supplemental content 0.569; 95% CI, 0.543-0.595). When geographic fixed effects were included, spatial autocorrelation diminished at the census tract level (ρ = 0.271; 95% CI, 0.147-0.396) and disappeared at the census Author affiliations and article information are listed at the end of this article. block group level (ρ = −0.075; 95% CI, −0.264 to 0.114). CONCLUSIONS AND RELEVANCE Because block groups are smaller than tracts, children in neighboring block groups were more likely to attend the same schools and interact through neighborhood play. Thus, geographic-based social networks were more likely to span block group boundaries. The lack of evidence of spatial autocorrelation in block group–level models suggests that social contagion may be less important than differences in neighborhood context across space. Caution should be used in interpreting significant spatial autocorrelation as evidence of social contagion in obesity. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 Open Access. This is an open access article distributed under the terms of the CC-BY License. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 1/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Introduction Childhood obesity is a persistent problem in the United States, with 17% of children having obesity. 2,3 A finding in the literature is that the incidence of obesity can cluster through social networks. Although obesity is not a disease that can be transmitted through contact, the analog remains that children who reside in close proximity are more likely to form friendships, which in turn can lead to the spread of obesity through the development of common habits or by altering one’s body type to identify with peers. This phenomenon could be defined broadly as social contagion and could be associated with spatial dependency similar to that found in studies of contagious diseases. According to Datar and Nicosia, social contagion means that any member of a social network who becomes obese affects the likelihood that others in the network will also become obese through social influences. Social contagion, if present, would manifest in spillovers in obesity rates across geographic units or, more specifically, in positive spatial autocorrelation, because of children being likely to form neighborhood-based friendship networks. Geographic location is the primary factor in assignment of children to public schools, which are an important venue for the formation of childhood friendship networks. Spatial autocorrelation emerges in the presence of social contagion because social network relationships, although dependent on geography, do not necessarily respect arbitrary geographic boundaries. Support for this argument can be found in studies of infectious diseases, in which the mechanism of spread is through contact between infected individuals, and there is 5-13 evidence of positive spatial autocorrelation in rates of infection across geographic units. There is 14,15 also evidence of positive spatial autocorrelation in rates of childhood obesity and adult 16,17 obesity across geographic units. The existence of spatial autocorrelation, however, cannot be taken as prima facie evidence of social contagion. The problem is that obesity can show spatial clustering for reasons unrelated to socialization. Manski elucidates the problems associated with separating endogenous peer effects arising from a process such as social contagion from contextual effects and correlated effects. Contextual effects result from characteristics common to members of a social network, such as neighborhood safety, access to green space, and annual days with weather conducive to outside play. Correlated effects emerge from the tendency of a group to behave similarly not because of socialization but because they share similar personal characteristics or institutional environments. To the extent that children in nearby geographic areas are subject to similar environmental features or share common personal or familial characteristics that impact diet or physical activity, spatial autocorrelation arises if these features are dependent on space but are not adequately captured in the statistical model. In short, spatial autocorrelation could be evidence of social contagion, but as shown by McMillen, can also reflect an inadequate model specification. In this study, we used information from a unique longitudinal data set resulting from a legislatively mandated body mass index (BMI) (measured as weight in kilograms divided by height in meters squared) screening program to investigate whether spatial autocorrelation could be better explained by social contagion or by shared environmental and personal characteristics. Although the data do not provide information on social networks, they permit us to examine obesity rates over time using 2 different levels of spatial aggregation that represent a division into larger (more aggregate) and smaller (less aggregate) geographic units. Because of the longitudinal nature of these data, geographic fixed effects could be used to account for time-invariant, unobservable neighborhood-level or community-level characteristics that may not have been adequately controlled in earlier cross-sectional studies. If social contagion better explains spatial autocorrelation, it should be most pronounced across the smaller geographic units because these reflect divisions over which childhood social networks are most likely to span. Moreover, spatial autocorrelation that is associated with social contagion should continue to be present even after inclusion of fixed effects to account for contextual, personal, and family characteristics that characterize the geographic unit. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 2/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Methods This study used data collected from a legislatively mandated BMI screening program of public school children in Arkansas (Act 1220 of 2003). Parents or children could opt out of this program. The use of these data for this research project was reviewed by the institutional review board at the University of Arkansas and was determined to meet exemption 4 for “research involving the collection or study of existing data or specimens if publicly available or information recorded such that subjects cannot be identified.” The University of Arkansas Institutional Review Board protocol number is 14-07-026. This study followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guideline. The childhood obesity rate in Arkansas ranks among the highest in the United States, and Arkansas became the first US state to institute a BMI screening program for public school children. All schoolchildren were measured annually from the 2003-2004 academic year through the 2006-2007 academic year. Afterward, children were measured biennially in even-numbered grades (kindergarten and grades 2, 4, 6, 8, and 10). Standard protocols and equipment are used to measure BMI in schools across the state. Data from this program are maintained by the Arkansas Center for Health Improvement (ACHI), and the ACHI compiles annual reports of the screening program by academic year. The ACHI facilitated development of the data set for this research. Participants and Measures We examined obesity rates over a 12-year period (academic year 2003-2004 through academic year 2014-2015) across 2 levels of spatial aggregation: census tracts and census block groups. The census tracts are the larger of the 2 units and, according to the US Census Bureau, are designed to optimally contain approximately 4000 people. Census block groups are subdivisions of tracts and are the smallest unit at which we can feasibly characterize geography in this study. In the 2010 census geography, there are 686 tracts and 2147 block groups in Arkansas. The 2010 census geography was used for all 12 years of our sample. We calculated the proportion of obese schoolchildren in each census block group and in each tract in Arkansas for each academic year. The obesity rate was defined as the proportion of children in the tract or block group with a BMI z score above the 95th percentile using the standard reference growth curves from the Centers for Disease Control and Prevention. We also computed the mean age in years of children by tract or block group along with proportions of children by race/ethnicity and school meal status. The school meal status measures reflect the proportion of low-income children in the tract or block group. Children from households with an income less than 130% of the poverty level qualify for free meals, and children from households with an income less than 185% of the poverty level qualify for reduced-price school meals. After these aggregations, we had two 12-year panel data sets: one for census tracts and another for census block groups. The methods described below require nonmissing values for each tract or block group. Depending on the year, between 1 and 3 of the 686 tracts and between 6 and 9 of the 2147 block groups had missing proportions. To avoid artificially inducing special dependence into these data, the missing values for these few block groups or tracts were replaced with the state averages. Statistical Analysis 24,25 The study used spatial autoregressive moving average (SARMA) models. Details of this model are provided in the eAppendix in the Supplement. The SARMA models may have an advantage because they are able to separate spatial dependency caused by social contagion from that caused by the contextual environment. This is done through the construction of weight matrices that place higher 24-26 weights on neighboring geographic units. There are 2 considerations in the estimation of a SARMA model. First, a study area needs to be divided into nonoverlapping geographic units. A modifiable areal unit problem occurs when studies that use aggregate data do not distinguish between spatial associations created artificially by the aggregation and real associations presented by the individuals within the geographic units. Given JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 3/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity this problem, the estimate of spatial effects could be sensitive to the manner of aggregation. Second, McMillen cautioned that autocorrelation is often produced spuriously by model misspecification, such as omitted variables, and he argued that the high degree of parameterization of spatial lag and spatial error models could induce an incorrect structure for the covariance. A common remedy for the omitted variable issue raised by McMillen is the inclusion of spatial 28 28 fixed effects. According to Anselin and Arribas-Bel, a spatial fixed effects specification is appropriate when individual observations are organized into well-delineated groups and some characteristics of the group are unobserved. For example, when physical education classes vary by school district but no data are available to measure the performance of the schools, a spatial fixed- effects variable can capture how this variation is reflected in the prevalence of obesity. Geographic fixed effects will reduce spatial autocorrelation resulting from inadequate specification of contextual factors. However, Anselin and Arribas-Bel stated that spatial fixed effects could address only a form of spatial heterogeneity and not true spatial dependence. They argued that, if true spatial dependence is present, spatial fixed effects would not remove this dependence, with the only exception being that the spatial autocorrelation takes on a group-wise structure that is the same as the spatial unit. In terms of our study, the implication is that true spatial dependence, such as that associated with social contagion, should still be detectible even if fixed effects successfully account for dependency arising from contextual and correlated effects as described by Manski. As Manski notes, endogenous peer effects, contextual effects, and unobserved correlated effects can all contribute to similar behaviors and are inherently difficult to separate with linear-in- mean models. The panel SARMA model allows for such separation because the endogenous effect is calculated as the association of the weighted average obesity rate of neighboring units (block group or tract) with the obesity rate of the focal unit. Assuming the unobserved effect also follows a spatial pattern, the correlated effect is addressed in part by the geographic fixed effect and in part by applying the spatial weight matrix to the error term. Given these considerations, we estimated SARMA models using both the tract and block group panels described above. If spatial autocorrelation is associated with social contagion, it should be more pronounced across the smaller census block groups. This is because neighborhood-based friendship networks are more likely to extend across block group boundaries than across tract boundaries. Moreover, children in neighboring block groups are more likely to be in the same public school catchment areas and therefore more likely to be in the same school-based social networks than children in neighboring tracts. Using similar reasoning, compared with tract effects, block group effects would better capture characteristics of the microenvironment that could explain geographic differences in obesity rates because children in the same block group are more likely to attend the same schools, have similar school nutrition and physical activity programs, and be homogeneous with respect to access to parks and safe places for vigorous play. Thus, the strongest evidence of social contagion would be indicated by spatial autocorrelation in the block group panel after inclusion of block group effects. The SARMA models were estimated using the spml package in R, version 3.4.3 (R Foundation). The feature of primary interest is the spatial autoregressive term (ρ) obtained from the different model specifications. The models also included a spatial error term (λ), which accounts for unobserved correlated effects not captured in the geographic fixed effects or in other model covariates. A standard z score (normal distribution) was used to calculate P values, and 2-sided distribution was used. P < .05 was considered to be statistically significant. Data were analyzed from August 2017 to February 2018. Results Participants The census tract and block group aggregations used in this study were based on 935 800 children (51% male) with a mean (SD) age of 132 (39) months. At least 1 valid weight status indicator was JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 4/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity available for 689 809 of these children. Sixty-five percent of the children were white, 21% were black, 10% were Hispanic, 2% were Asian, and the remainder (2%) were of other or unidentified race or ethnicity. Descriptive Statistics Summary statistics for the tract and block group aggregate data sets used in the SARMA models are presented in Table 1. The mean values were similar across the 2 samples. There were higher SDs in the block group panel because block groups are smaller geographic units and reflect less aggregation. Primary Analysis Estimates from the tract-level and block group–level spatial models are reported in Table 2. Table 2 presents estimates from a non–spatial panel model as a reference point along with SARMA models estimated with year fixed effects only and with both geographic fixed effects and year fixed effects. Using a conditional Lagrange multiplier (LM) test, we rejected the null hypothesis of a non–spatial panel model in favor of the SARMA model for both the tract and block group data sets. For the tract- level panel, the test statistic was LM = 6.189 (P < .001). For the block group–level panel, the test statistic was LM = 7.920 (P < .001). As discussed above, our focal interest was spatial autocorrelation across the tracts or census block groups. This is captured by the estimate for the spatial autoregressive parameter (ρ). A comparison of ρ across the 2 SARMA models at the tract level revealed positive and significant spatial autocorrelation. The inclusion of tract fixed effects caused the estimate of spatial autocorrelation to decrease by nearly one-half, from ρ = 0.511 (95% CI, 0.469-0.553; P < .001) to ρ = 0.271 (95% CI, 0.147-0.396; P < .001). In contrast, a comparison of ρ across the 2 SARMA models at the block group level showed that there was no longer significant spatial autocorrelation after inclusion of block group effects. The inclusion of block group effects caused the estimate of spatial autocorrelation to decrease from ρ = 0.569 (95% CI, 0.543 to 0.595; P < .001) to ρ = −0.075 (95% CI, −0.264 to 0.114; P = .44). Additional insight is provided by the spatial error term (λ). As noted above, λ accounts for spatial dependence in the model errors. The λ continued to be significant in the tract-level panel even after including fixed tract effects (λ = −0.252; 95% CI, −0.404 to −0.100; P = .001) (Table 2). By contrast, λ was no longer significant in the corresponding model with block group fixed effects (λ = 0.124; 95% CI, −0.052 to 0.3; P = .17). This indicates that the smaller, block group effects better captured unobserved contextual features that influenced obesity rates. Covariate estimates in Table 2 provided additional insights into the importance of the tract and block group fixed effects in the model. A comparison of estimates from the non–spatial models with those from the SARMA models with tract and block group effects revealed similar point estimates. This was expected because the point estimates are unbiased regardless of spatial dependency in the Table 1. Model Variables for Census Tract-Level and Block Group–Level Panels Census Tract-Level Panel Census Block Group–Level Panel Variable (n = 8232) (n = 25 746) Obesity prevalence 0.22 (0.06) 0.22 (0.08) Unless otherwise specified, data are mean (SD) Race/ethnicity proportion of students within the census tract or Black 0.24 (0.29) 0.24 (0.31) census block group. Asian 0.02 (0.03) 0.02 (0.04) Eligibility for free and reduced-price school meals Hispanic 0.07 (0.11) 0.07 (0.12) represents the proportion of children from lower- Other 0.01 (0.02) 0.01 (0.02) income families in the census tract or block group. Female sex 0.49 (0.03) 0.49 (0.05) Children from families with incomes less than 130% of the poverty level are eligible for free meals. Eligible for free school meals 0.50 (0.21) 0.51 (0.23) b Children from families with incomes between 130% Eligible for reduced-price meals 0.10 (0.05) 0.10 (0.07) and 185% of the poverty level are eligible for Mean age, y 11.04 (0.35) 11.03 (0.48) reduced-price meals. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 5/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity model errors. Point estimates from the models without tract or block group fixed effects were similar in sign, but the point estimates diverged, suggesting that the geographic fixed effects were accounting for contextual and correlated factors that were not directly observed. Although these findings were not the central focus of this study, estimates in Table 2 suggested that neighborhoods with a higher proportion of Hispanic children were associated with higher rates of obesity, and neighborhoods with a higher proportion of children qualifying for free school meals were also associated with higher rates of obesity. The finding of a negative association with obesity for neighborhoods with higher proportions of black children was unexpected, but this finding could be explained by regional differences across the state. Statewide, 222 of 2147 block groups and 64 of 686 census tracts were predominantly composed of black children (>80% of the children in these block groups and tracts were black), and these block groups and tracts tended to be concentrated in urban areas, such as Little Rock. There were differences across the tract and block models for estimated associations between the obesity rate and the proportion of Asian children and girls. This reflected the higher variation across block groups compared with tracts. Table 2. Coefficient Estimates for Census Tract-Level and Block Group–Level Models Non–Spatial Panel Data Model With Time and Geographic SARMA Model Without SARMA Model With Time and Variable Fixed Effects Geographic Fixed Effects Geographic Fixed Effects Census tract-level models (n = 8232) Spatial error term, λ NA −0.251 (−0.321 to −0.181) −0.252 (−0.404 to −0.100) Spatial NA 0.511 (0.469 to 0.553) 0.271 (0.147 to 0.396) autoregressive term, ρ Race/ethnicity Black −0.060 (−0.086 to −0.034) −0.011 (−0.015 to −0.007) −0.058 (−0.081 to −0.034) Hispanic 0.096 (0.058 to 0.134) 0.051 (0.043 to 0.06) 0.088 (0.055 to 0.122) Asian −0.074 (−0.162 to 0.013) −0.214 (−0.253 to −0.175) −0.062 (−0.141 to 0.018) Other −0.458 (−0.522 to −0.395) −0.36 (−0.409 to −0.311) −0.447 (−0.506 to −0.388) Female sex 0.006 (−0.023 to 0.035) −0.011 (−0.037 to 0.016) 0.004 (−0.023 to 0.031) Eligible for free 0.027 (0.012 to 0.043) 0.089 (0.082 to 0.096) 0.024 (0.011 to 0.038) school meals Eligible for 0.006 (−0.014 to 0.026) 0.096 (0.08 to 0.113) 0.003 (−0.013 to 0.020) reduced-price school meals Mean age, y 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.005) Year effects Yes Yes Yes Tract effects Yes No Yes Census block group–level models (n = 25 764) Spatial error term, λ NA −0.456 (−0.5 to −0.412) 0.124 (−0.052 to 0.3) Spatial lag term, ρ NA 0.569 (0.543 to 0.595) −0.075 (−0.264 to 0.114) Race/ethnicity Abbreviations: NA, not applicable; SARMA, spatial autoregressive moving average. Black −0.003 (−0.022 to 0.015) −0.007 (−0.009 to −0.004) −0.002 (−0.019 to 0.016) Unless otherwise specified, data are estimated Hispanic 0.087 (0.062 to 0.111) 0.032 (0.026 to 0.038) 0.087 (0.063 to 0.11) proportion of students within the census tract or Asian 0.137 (0.097 to 0.177) −0.06 (−0.081 to −0.039) 0.137 (0.098 to 0.176) census block group (95% CI). The dependent Other −0.208 (−0.271 to −0.145) −0.307 (−0.349 to −0.265) −0.204 (−0.264 to −0.143) variable is proportion of children with obesity in the Female sex −0.062 (−0.079 to −0.044) −0.052 (−0.067 to −0.038) −0.062 (−0.078 to −0.046) census tract or census block group. Eligible for free 0.024 (0.012 to 0.035) 0.074 (0.07 to 0.079) 0.024 (0.012 to 0.035) b Eligibility for free and reduced-price school meals school meals represents the proportion of children from lower- Eligible for 0.008 (−0.007 to 0.023) 0.074 (0.063 to 0.085) 0.009 (−0.007 to 0.024) income families in the census tract or census block reduced-price school meals group. Children from families with incomes less than 130% of the poverty level are eligible for free meals. Mean age, y 0.009 (0.007 to 0.011) 0.006 (0.005 to 0.008) 0.009 (0.008 to 0.011) Children from families with incomes between 130% Year effects Yes Yes Yes and 185% of the poverty level are eligible for Block group effects Yes No Yes reduced-price meals. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 6/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Secondary Analyses The choice of the weight matrix and the resulting specification of distance decay could lead to different spatial effects. In this study, the weight matrix captured the empirical path through which social contagion was associated with obesity rate. The weight matrix used in the models reported in Table 2 was based on queen contiguity, wherein census tracts or block groups sharing a border, even a single point, were assigned nonnegative values in the weight matrix. As alternative specifications, we considered models with weight matrices constructed with the 4 or 8 nearest census tracts or block groups. Estimates from these models are presented in eTables 1 and 2 in the Supplement. Similar to findings reported in Table 2, estimates from models with the alternative weight matrices showed high levels of spatial autocorrelation when census tract or block group fixed effects were not included. Spatial autocorrelation continued to exist in tract-level models after the census tract fixed effects were included, but as in Table 2, there was no evidence of positive spatial autocorrelation in the census block group–level models after including census block group effects. Given the growth in social media participation, it is possible that geographic-based social networks have become less important in recent years. Consequently, we performed alternative estimations after breaking the panels into 2 periods: one covered the 2003-2004 through 2009- 2010 academic years, and the other covered the 2010-2011 through 2014-2015 academic years. Findings (eTables 3 and 4 in the Supplement) from the census tract-level models were similar to those reported in Table 2. There was no evidence of positive spatial autocorrelation in the census block group–level models in either period among estimations that included census block group fixed effects. However, the census block group–level model for the latter 5-year period provided evidence of significant spatial dependency in the model errors (λ = 0.244; 95% CI, 0.219-0.279; P = .002) even after the inclusion of census block group fixed effects. This could be interpreted as evidence of increased heterogeneity that transcends neighborhood, to which social media may be a contributing factor. Discussion Although we did not have information on children’s actual social networks, the empirical findings reported above provide indirect evidence that social contagion is unlikely to be associated with high rates of childhood obesity in Arkansas. Of interest, there was no evidence of spatial autocorrelation in models with the smallest geographic units (ie, block groups) after geographic fixed effects were included to account for unobserved and time-invariant contextual factors. If social contagion was associated with high childhood obesity rates, we would have expected to see significant evidence of spatial autocorrelation even after inclusion of these fixed effects. The tract-level models did continue to show positive spatial autocorrelation after the inclusion of fixed effects, but these models also showed significant spatial dependence in the error structure, which could suggest that the larger tract effects may have been too aggregate to accurately reflect key neighborhood features that were associated with obesity. The estimates of spatial autocorrelation in the tract-level models were similar to some of those estimated by Chen and Wen, who examined adult obesity rates across townships in Taiwan, a spatial scale that would be more aggregate than the tracts in our study. Similarly, Christman et al also found evidence of significant autocorrelation at the census tract level in their study of adult BMI. Despite evidence of spatial autocorrelation at the tract level, that spatial correlation was not present at the block group level was the primary finding of this study. If social contagion were important, it would be expected in these block group–level models because geographic-based social networks are more likely to span block boundaries than tract boundaries. Thus, the findings of this study provide little evidence of an association of social contagion with the increase in childhood obesity rates in Arkansas. This is not inconsistent with a recent study by Asirvatham et al that used a natural experiment involving a court decision that resulted in the plausibly exogenous reassignment of some children in Arkansas to different schools. Although their findings provide JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 7/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity significant evidence of social contagion, the effects that they report were small, and the results presented here are consistent with their findings. The implication for policy is that neighborhood contextual environments matter, but geographic-based social networks may not need to be the central focus of interventions. Limitations There are several limitations of our study. Although geographic proximity likely plays a role in the formation of friendship networks, social networks are complex and not based solely on this, especially in the age of social media. To the extent that geographic proximity is less important to social networks, social contagion could play an important role in childhood obesity that would not be reflected in dependency across spatial units. Second, we examined autocorrelation across census- based geographic areas. Use of school-based geographic areas may be more reflective of social networks; however, school catchment areas change with time. Moreover, schools change as children progress through the public school system, with intermediate and high schools drawing children from larger geographic areas than elementary schools. Nevertheless, most children in the same block group attend the same schools, and thus we expect that the geographic controls are adequate. Conclusions Social contagion and environmental factors are inherently different mechanisms that could be associated with the increase in childhood obesity. We found little evidence that geographic-based social contagion is associated with obesity rates across neighborhoods in Arkansas. Contextual factors operating at a neighborhood level were of greater importance in explaining spatial differences in obesity rates. ARTICLE INFORMATION Accepted for Publication: May2,2018. Published: August 3, 2018. doi:10.1001/jamanetworkopen.2018.0954 Open Access: This is an open access article distributed under the terms of the CC-BY License.©2018FangDetal. JAMA Network Open. Corresponding Author: Di Fang, PhD, Department of Agricultural Economics and Agribusiness, University of Arkansas, Fayetteville, AR 72701 (difang@uark.edu). Author Affiliations: Department of Agricultural Economics and Agribusiness, University of Arkansas, Fayetteville (Fang, Thomsen, Nayga); Arkansas Center for Health Improvement, University of Arkansas for Medical Sciences, Little Rock (Goudie). Author Contributions: Dr Fang had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Concept and design: Fang, Thomsen, Nayga. Acquisition, analysis, or interpretation of data: All authors. Drafting of the manuscript: Fang, Thomsen, Nayga. Critical revision of the manuscript for important intellectual content: All authors. Statistical analysis: Fang, Thomsen, Goudie. Obtained funding: Thomsen, Nayga. Administrative, technical, or material support: Nayga, Goudie. Supervision: Nayga. Conflict of Interest Disclosures: Dr Thomsen reported receiving grants from the National Institute of General Medical Sciences of the National Institutes of Health during the conduct of the study and being a project leader on a project funded by the National Institutes of Health Centers of Biomedical Research Excellence Center. No other disclosures were reported. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 8/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Funding/Support: This work was supported in part by P20GM109096 from the National Institute of General Medical Sciences of the National Institutes of Health. Role of the Funder/Sponsor: The National Institutes of Health 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. Disclaimer: The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. REFERENCES 1. Ogden CL, Carroll MD, Lawman HG, et al. Trends in obesity prevalence among children and adolescents in the United States, 1988-1994 through 2013-2014. JAMA. 2016;315(21):2292-2299. doi:10.1001/jama.2016.6361 2. Christakis NA, Fowler JH. The spread of obesity in a large social network over 32 years. N Engl J Med. 2007;357 (4):370-379. doi:10.1056/NEJMsa066082 3. Christakis NA, Fowler JH. Social contagion theory: examining dynamic social networks and human behavior. Stat Med. 2013;32(4):556-577. doi:10.1002/sim.5408 4. 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Cien Saude Colet. 2017;22(3):831-840. 13. Marotta P. Assessing spatial relationships between rates of crime and rates of gonorrhea and chlamydia in Chicago, 2012. J Urban Health. 2017;94(2):276-288. doi:10.1007/s11524-016-0080-7 14. Greves Grow HM, Cook AJ, Arterburn DE, Saelens BE, Drewnowski A, Lozano P. Child obesity associated with social disadvantage of children’s neighborhoods. Soc Sci Med. 2010;71(3):584-591. doi:10.1016/j.socscimed. 2010.04.018 15. Duncan DT, Castro MC, Gortmaker SL, Aldstadt J, Melly SJ, Bennett GG. Racial differences in the built environment–body mass index relationship? a geospatial analysis of adolescents in urban neighborhoods. Int J Health Geogr. 2012;11(1):11. doi:10.1186/1476-072X-11-11 16. Chen DR, Wen TH. Elucidating the changing socio-spatial dynamics of neighborhood effects on adult obesity risk in Taiwan from 2001 to 2005. Health Place. 2010;16(6):1248-1258. doi:10.1016/j.healthplace.2010.08.013 17. Christman Z, Pruchno R, Cromley E, Wilson-Genderson M, Mir I. A spatial analysis of body mass index and neighborhood factors in community-dwelling older men and women. Int J Aging Hum Dev. 2016;83(1):3-25. doi: 10.1177/0091415016645350 18. Manski CF. Identification of endogenous social effects: the reflection problem. Rev Econ Stud. 1993;60(3): 531-542. doi:10.2307/2298123 19. McMillen DP. Spatial autocorrelation or model misspecification? Int Reg Sci Rev. 2003;26(2):208-217. doi:10. 1177/0160017602250977 JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 9/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity 20. Arkansas Center for Health Improvement. Assessment of Childhood and Adolescent Obesity in Arkansas: Year 13 (Fall 2015 – Spring 2016). Little Rock: Arkansas Center for Health Improvement; 2016. 21. US Census Bureau. 2010 Geographic Terms and Concepts. https://www.census.gov/geo/reference/gtc/gtc_ct.html. Accessed April 30, 2018. 22. Centers for Disease Control and Prevention. About BMI for Children and Teens. http://www.cdc.gov/ healthyweight/assessing/bmi/childrens_bmi/about_childrens_bmi.html. Accessed April 30, 2018. 23. Arkansas Department of Human Services. National School Lunch Program. https://dhs.arkansas.gov/dccece/ snp/NSLPInfoM.aspx. Accessed June 4, 2018. 24. Anselin L. Spatial Econometrics: Methods and Models. London, England: Springer; 2013. 25. Elhorst JP. Spatial panel data models. In: Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. London, England: Springer; 2014:37-93. doi:10.1007/978-3-642-40340-8_3 26. Richards TJ, Hamilton SF, Allender WJ. Social networks and new product choice. Am J Agric Econ. 2014;96(2): 489-516. doi:10.1093/ajae/aat116 27. Openshaw S. Ecological fallacies and the analysis of areal census data. Environ Plan A. 1984;16(1):17-31. doi:10. 1068/a160017 28. Anselin L, Arribas-Bel D. Spatial fixed effects and spatial dependence in a single cross-section. Pap Reg Sci. 2013;92(1):3-17. doi:10.1111/j.1435-5957.2012.00480.x 29. Millo G, Piras G. splm: spatial panel data models in R. J Stat Softw. 2012;47(1):1-38. doi:10.18637/jss.v047.i01 30. Asirvatham J, Thomsen M, Nayga RM Jr, Rouse H. Do peers affect childhood obesity outcomes? peer-effect analysis in public schools. CanJEcon. 2018;51:216-235. doi:10.1111/caje.12321 31. Ugander J, Backstrom L, Marlow C, Kleinberg J. Structural diversity in social contagion. Proc Natl Acad Sci U S A. 2012;109(16):5962-5966. doi:10.1073/pnas.1116502109 SUPPLEMENT. eAppendix. Details on the spatial autoregressive moving average (SARMA) model eTable 1. Census tract-level spatial panel models for alternative spatial weight matrices eTable 2. Census block group–level spatial panel models for alternative spatial weight matrices eTable 3. Census tract-level spatial panel models for alternative time periods eTable 4. Census block group–level spatial panel models for alternative time periods JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 10/10 Supplementary Online Content Fang D, Thomsen MR, Nayga RM, Goudie A. Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity. JAMA Netw Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 Supplement. eAppendix. Details on the spatial autoregressive moving average (SARMA) model eTable 1. Census tract-level spatial panel models for alternative spatial weight matrices eTable 2. Census block group level spatial panel models for alternative spatial weight matrices eTable 3. Census tract-level spatial panel models for alternative time periods eTable 4. Census block group level spatial panel models for alternative time periods This supplementary material has been provided by the authors to give readers additional information about their work. © 2018 Fang D et al. JAMA Network Open. eAppendix Details on the spatial autoregressive moving average (SARMA) model In the equation below, ! denotes the percentage of obese children living in spatial unit i at time "# t, and $ is the matrix of k demographic variables of the school children across time. As shown %"# in Table 1 of the article, these variables include average age, proportion by gender, race or ethnicity, and school meal status. Social contagion across nearby block groups would be captured by &'! , where W is the spatial weight matrix. To exclude the endogenous self- "# influence, the diagonals of W are set to zero. W is also row-standardized to summarize a weighted-average obesity rates of all “neighbors”. Therefore, the spatial autoregressive parameter, &, is the parameter of interest. A positive & indicates spillover (social contagion) in obesity across geographic space. We also assume that obesity can be influenced by the contextual environment, which we capture with census tract or census block group fixed effects denoted by ( . We control for time effects with ) to capture changes in the environment through " # time. As discussed, spatial units are represented by the weight matrix ' at either the census tract level or the census block group level. ! = + + ) + ( + - . $ + &'! + 2 "# # " % %"# "# "# and 2 = 3'2 + 4 "# "# "# Because unobserved factors may not be independent of spatial locations, we assume that 2 "# follows a similar autoregressive pattern, represented by 3'2 . This way we take care of the "# unobserved correlated effects that can contribute to obesity. © 2018 Fang D et al. JAMA Network Open.! ! eTable 1. Census tract-level spatial panel models for alternative spatial weight matrices b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Census tract level models (n = 8,232) -0.077 (-0.142 to -0.012) -0.156 (-0.314 to 0.002) 0.156 (0.082 to 0.230) -0.197 (-0.403 to 0.008) Spatial error term (l) Spatial lag term (r) 0.357 (0.313 to 0.401) 0.203 (0.069 to 0.338) 0.296 (0.241 to 0.351) 0.246 (0.089 to 0.404) African American -0.012 (-0.017 to -0.008) -0.060 (-0.084 to -0.036) -0.011 (-0.016 to -0.006) -0.060 (-0.084 to -0.036) Hispanic 0.047 (0.037 to 0.057) 0.088 (0.053 to 0.123) 0.060 (0.049 to 0.071) 0.087 (0.053 to 0.122) Asian -0.269 (-0.311 to -0.227) -0.070 (-0.151 to 0.011) -0.277 (-0.323 to -0.232) -0.071 (-0.152 to 0.010) Other race -0.389 (-0.441 to -0.337) -0.451 (-0.511 to -0.392) -0.363 (-0.417 to -0.308) -0.452 (-0.511 to -0.392) Female -0.005 (-0.032 to 0.023) 0.005 (-0.022 to 0.032) 0.005 (-0.022 to 0.032) 0.004 (-0.023 to 0.032) Free school meals 0.104 (0.097 to 0.112) 0.026 (0.012 to 0.040) 0.113 (0.106 to 0.121) 0.026 (0.012 to 0.040) Reduced-price meals 0.107 (0.089 to 0.126) 0.004 (-0.013 to 0.021) 0.127 (0.106 to 0.147) 0.004 (-0.013 to 0.021) Average age (years) 0.005 (0.002 to 0.007) 0.003 (0.000 to 0.006) 0.005 (0.002 to 0.008) 0.003 (0.000 to 0.006) Year effects Yes Yes Yes Yes Census tract effects No Yes No Yes Weight Four nearest neighbors Eight nearest neighbors a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or census block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! ! eTable 2. Census block group–level spatial panel models for alternative spatial weight matrices b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Census block-group level models (n = 25,764) -0.327 (-0.367 to -0.286) 0.196 (0.107 to 0.284) -0.229 (-0.286 to -0.171) 0.009 (-0.247 to 0.265) Spatial error term (l) 0.459 (0.433 to 0.485) -0.166 (-0.267 to -0.065) 0.459 (0.427 to 0.492) 0.070 (-0.176 to 0.316) Spatial lag term (r) African American -0.007 (-0.010 to -0.004) 0.000 (-0.018 to 0.017) -0.008 (-0.011 to -0.005) -0.002 (-0.020 to 0.015) Hispanic 0.027 (0.020 to 0.033) 0.086 (0.062 to 0.11) 0.029 (0.022 to 0.036) 0.085 (0.061 to 0.109) Asian -0.070 (-0.092 to -0.047) 0.138 (0.099 to 0.176) -0.065 (-0.089 to -0.042) 0.137 (0.098 to 0.175) Other race -0.350 (-0.395 to -0.306) -0.206 (-0.267 to -0.146) -0.341 (-0.388 to -0.295) -0.205 (-0.266 to -0.145) Female -0.057 (-0.072 to -0.042) -0.060 (-0.076 to -0.044) -0.058 (-0.073 to -0.043) -0.062 (-0.078 to -0.045) Free school meals 0.086 (0.081 to 0.091) 0.024 (0.013 to 0.036) 0.091 (0.085 to 0.096) 0.023 (0.012 to 0.035) Reduced-price meals 0.080 (0.069 to 0.092) 0.009 (-0.007 to 0.025) 0.085 (0.073 to 0.097) 0.008 (-0.007 to 0.023) Average age (years) 0.007 (0.005 to 0.009) 0.009 (0.008 to 0.011) 0.008 (0.006 to 0.009) 0.009 (0.007 to 0.011) Year effects Yes Yes Yes Yes Census block-group effects No Yes No Yes Weight Four nearest neighbors Eight nearest neighbors a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or census block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! ! eTable 3. Census tract-level spatial panel models for alternative time periods b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Census tract level models 2003/2004 through 2009/2010 Census tract level models 2010/2011 through Academic Years (n = 4,802) 2014/2015 Academic Years (n = 4,802) -0.251 (-0.321 to -0.181) -0.252 (-0.404 to -0.100) -0.251 (-0.321 to -0.181) -0.252 (-0.404 to -0.100) Spatial error term (l) 0.511 (0.469 to 0.553) 0.271 (0.147 to 0.396) 0.511 (0.469 to 0.553) 0.271 (0.147 to 0.396) Spatial lag term (r) African American -0.011 (-0.015 to -0.007) -0.058 (-0.081 to -0.034) -0.011 (-0.015 to -0.007) -0.058 (-0.081 to -0.034) Hispanic 0.051 (0.043 to 0.060) 0.088 (0.055 to 0.122) 0.051 (0.043 to 0.060) 0.088 (0.055 to 0.122) Asian -0.214 (-0.253 to -0.175) -0.062 (-0.141 to 0.018) -0.214 (-0.253 to -0.175) -0.062 (-0.141 to 0.018) Other race -0.360 (-0.409 to -0.311) -0.447 (-0.506 to -0.388) -0.360 (-0.409 to -0.311) -0.447 (-0.506 to -0.388) Female -0.011 (-0.037 to 0.016) 0.004 (-0.023 to 0.031) -0.011 (-0.037 to 0.016) 0.004 (-0.023 to 0.031) Free school meals 0.089 (0.082 to 0.096) 0.024 (0.011 to 0.038) 0.089 (0.082 to 0.096) 0.024 (0.011 to 0.038) Reduced-price meals 0.096 (0.080 to 0.113) 0.003 (-0.013 to 0.020) 0.096 (0.080 to 0.113) 0.003 (-0.013 to 0.020) Average age (years) 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.005) 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.005) Year effects Yes Yes Yes Yes Census tract effects No Yes No Yes a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! ! eTable 4. Census block group–level spatial panel models for alternative time periods b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Block-group level models 2003/2004 through Block-group level models 2010/2011 through 2009/2010 Academic Years (n = 15,029) 2014/2015 Academic Years (n = 15,029) -0.466 (-0.522 to -0.410) -0.084 (-0.297 to 0.128) -0.450 (-0.520 to -0.380) 0.244 (0.086 to 0.401) Spatial error term (l) 0.591 (0.559 to 0.623) 0.113 (-0.084 to 0.311) 0.538 (0.496 to 0.581) -0.208 (-0.393 to -0.022) Spatial lag term (r) African American -0.009 (-0.013 to -0.006) -0.004 (-0.028 to 0.02) 0.000 (-0.005 to 0.004) -0.014 (-0.049 to 0.021) Hispanic 0.026 (0.019 to 0.034) 0.097 (0.065 to 0.129) 0.040 (0.030 to 0.049) 0.043 (-0.005 to 0.091) Asian -0.012 (-0.038 to 0.014) 0.237 (0.19 to 0.284) -0.118 (-0.153 to -0.083) 0.013 (-0.072 to 0.097) Other race -0.352 (-0.408 to -0.295) -0.262 (-0.353 to -0.171) -0.258 (-0.321 to -0.195) 0.002 (-0.105 to 0.108) Female -0.075 (-0.093 to -0.057) -0.092 (-0.114 to -0.071) -0.024 (-0.047 to -0.001) -0.023 (-0.053 to 0.006) Free school meals 0.072 (0.066 to 0.078) 0.006 (-0.008 to 0.021) 0.077 (0.069 to 0.085) 0.027 (0.004 to 0.051) Reduced-price meals 0.055 (0.043 to 0.067) 0.01 (-0.005 to 0.024) 0.129 (0.106 to 0.152) 0.024 (-0.011 to 0.06) Average age (years) 0.005 (0.003 to 0.007) 0.009 (0.007 to 0.012) 0.008 (0.006 to 0.011) 0.011 (0.007 to 0.014) Year effects Yes Yes Yes Yes Census block-group effects No Yes No Yes a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or census block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png JAMA Network Open American Medical Association

Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity

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Abstract

Key Points Question Is social contagion associated IMPORTANCE Childhood obesity is a principal public health concern. Understanding the geographic with spatial patterns in childhood distribution of childhood obesity can inform the design and delivery of interventions. obesity rates across neighborhoods in Arkansas? OBJECTIVE To better understand the causes of spatial dependence in rates of childhood obesity Findings In this cohort study of across neighborhoods. 935 800 children, after controlling for neighborhood fixed effects, positive and DESIGN, SETTING, AND PARTICIPANTS This cohort study used data from a legislatively mandated significant spatial autocorrelation was body mass index screening program for public school children in Arkansas from the 2003-2004 detected using spatial panel models through 2014-2015 academic years. Spatial autoregressive moving average (SARMA) models for when obesity rates were computed for panel data were used to estimate spatial dependency in childhood obesity at 2 levels of spatial larger census tracts but not when aggregation. Data were analyzed from August 2017 to February 2018. computed for smaller census block groups, indicating that neighborhood EXPOSURES The SARMA models included geographic fixed effects to capture time-invariant contextual factors, rather than social differences in neighborhood characteristics along with controls for the mean age of children and the contagion, appeared to better explain proportion of children by race/ethnicity, school meal status, and sex. observed spatial patterns in obesity rates across neighborhoods. MAIN OUTCOMES AND MEASURES The proportion of obese schoolchildren in Arkansas neighborhoods by year, defined at larger (census tract) and smaller (census block group) Meaning Spatial analysis may be used spatial scales. in epidemic studies, but researchers should use caution when interpreting a RESULTS The geographic aggregations were based on 935 800 children with a mean (SD) age of 132 positive spatial autocorrelation as (39) months. Of these children, 51% were male; 65% were white, 21% were black, 10% were evidence for contagion, especially in a Hispanic, 2% were Asian, and the remainder were of other or unidentified race/ethnicity. In models social context. without geographic fixed effects, there was evidence of positive and significant spatial autocorrelation in obesity rates across tracts (ρ = 0.511; 95% CI, 0.469-0.553) and block groups (ρ = Supplemental content 0.569; 95% CI, 0.543-0.595). When geographic fixed effects were included, spatial autocorrelation diminished at the census tract level (ρ = 0.271; 95% CI, 0.147-0.396) and disappeared at the census Author affiliations and article information are listed at the end of this article. block group level (ρ = −0.075; 95% CI, −0.264 to 0.114). CONCLUSIONS AND RELEVANCE Because block groups are smaller than tracts, children in neighboring block groups were more likely to attend the same schools and interact through neighborhood play. Thus, geographic-based social networks were more likely to span block group boundaries. The lack of evidence of spatial autocorrelation in block group–level models suggests that social contagion may be less important than differences in neighborhood context across space. Caution should be used in interpreting significant spatial autocorrelation as evidence of social contagion in obesity. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 Open Access. This is an open access article distributed under the terms of the CC-BY License. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 1/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Introduction Childhood obesity is a persistent problem in the United States, with 17% of children having obesity. 2,3 A finding in the literature is that the incidence of obesity can cluster through social networks. Although obesity is not a disease that can be transmitted through contact, the analog remains that children who reside in close proximity are more likely to form friendships, which in turn can lead to the spread of obesity through the development of common habits or by altering one’s body type to identify with peers. This phenomenon could be defined broadly as social contagion and could be associated with spatial dependency similar to that found in studies of contagious diseases. According to Datar and Nicosia, social contagion means that any member of a social network who becomes obese affects the likelihood that others in the network will also become obese through social influences. Social contagion, if present, would manifest in spillovers in obesity rates across geographic units or, more specifically, in positive spatial autocorrelation, because of children being likely to form neighborhood-based friendship networks. Geographic location is the primary factor in assignment of children to public schools, which are an important venue for the formation of childhood friendship networks. Spatial autocorrelation emerges in the presence of social contagion because social network relationships, although dependent on geography, do not necessarily respect arbitrary geographic boundaries. Support for this argument can be found in studies of infectious diseases, in which the mechanism of spread is through contact between infected individuals, and there is 5-13 evidence of positive spatial autocorrelation in rates of infection across geographic units. There is 14,15 also evidence of positive spatial autocorrelation in rates of childhood obesity and adult 16,17 obesity across geographic units. The existence of spatial autocorrelation, however, cannot be taken as prima facie evidence of social contagion. The problem is that obesity can show spatial clustering for reasons unrelated to socialization. Manski elucidates the problems associated with separating endogenous peer effects arising from a process such as social contagion from contextual effects and correlated effects. Contextual effects result from characteristics common to members of a social network, such as neighborhood safety, access to green space, and annual days with weather conducive to outside play. Correlated effects emerge from the tendency of a group to behave similarly not because of socialization but because they share similar personal characteristics or institutional environments. To the extent that children in nearby geographic areas are subject to similar environmental features or share common personal or familial characteristics that impact diet or physical activity, spatial autocorrelation arises if these features are dependent on space but are not adequately captured in the statistical model. In short, spatial autocorrelation could be evidence of social contagion, but as shown by McMillen, can also reflect an inadequate model specification. In this study, we used information from a unique longitudinal data set resulting from a legislatively mandated body mass index (BMI) (measured as weight in kilograms divided by height in meters squared) screening program to investigate whether spatial autocorrelation could be better explained by social contagion or by shared environmental and personal characteristics. Although the data do not provide information on social networks, they permit us to examine obesity rates over time using 2 different levels of spatial aggregation that represent a division into larger (more aggregate) and smaller (less aggregate) geographic units. Because of the longitudinal nature of these data, geographic fixed effects could be used to account for time-invariant, unobservable neighborhood-level or community-level characteristics that may not have been adequately controlled in earlier cross-sectional studies. If social contagion better explains spatial autocorrelation, it should be most pronounced across the smaller geographic units because these reflect divisions over which childhood social networks are most likely to span. Moreover, spatial autocorrelation that is associated with social contagion should continue to be present even after inclusion of fixed effects to account for contextual, personal, and family characteristics that characterize the geographic unit. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 2/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Methods This study used data collected from a legislatively mandated BMI screening program of public school children in Arkansas (Act 1220 of 2003). Parents or children could opt out of this program. The use of these data for this research project was reviewed by the institutional review board at the University of Arkansas and was determined to meet exemption 4 for “research involving the collection or study of existing data or specimens if publicly available or information recorded such that subjects cannot be identified.” The University of Arkansas Institutional Review Board protocol number is 14-07-026. This study followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guideline. The childhood obesity rate in Arkansas ranks among the highest in the United States, and Arkansas became the first US state to institute a BMI screening program for public school children. All schoolchildren were measured annually from the 2003-2004 academic year through the 2006-2007 academic year. Afterward, children were measured biennially in even-numbered grades (kindergarten and grades 2, 4, 6, 8, and 10). Standard protocols and equipment are used to measure BMI in schools across the state. Data from this program are maintained by the Arkansas Center for Health Improvement (ACHI), and the ACHI compiles annual reports of the screening program by academic year. The ACHI facilitated development of the data set for this research. Participants and Measures We examined obesity rates over a 12-year period (academic year 2003-2004 through academic year 2014-2015) across 2 levels of spatial aggregation: census tracts and census block groups. The census tracts are the larger of the 2 units and, according to the US Census Bureau, are designed to optimally contain approximately 4000 people. Census block groups are subdivisions of tracts and are the smallest unit at which we can feasibly characterize geography in this study. In the 2010 census geography, there are 686 tracts and 2147 block groups in Arkansas. The 2010 census geography was used for all 12 years of our sample. We calculated the proportion of obese schoolchildren in each census block group and in each tract in Arkansas for each academic year. The obesity rate was defined as the proportion of children in the tract or block group with a BMI z score above the 95th percentile using the standard reference growth curves from the Centers for Disease Control and Prevention. We also computed the mean age in years of children by tract or block group along with proportions of children by race/ethnicity and school meal status. The school meal status measures reflect the proportion of low-income children in the tract or block group. Children from households with an income less than 130% of the poverty level qualify for free meals, and children from households with an income less than 185% of the poverty level qualify for reduced-price school meals. After these aggregations, we had two 12-year panel data sets: one for census tracts and another for census block groups. The methods described below require nonmissing values for each tract or block group. Depending on the year, between 1 and 3 of the 686 tracts and between 6 and 9 of the 2147 block groups had missing proportions. To avoid artificially inducing special dependence into these data, the missing values for these few block groups or tracts were replaced with the state averages. Statistical Analysis 24,25 The study used spatial autoregressive moving average (SARMA) models. Details of this model are provided in the eAppendix in the Supplement. The SARMA models may have an advantage because they are able to separate spatial dependency caused by social contagion from that caused by the contextual environment. This is done through the construction of weight matrices that place higher 24-26 weights on neighboring geographic units. There are 2 considerations in the estimation of a SARMA model. First, a study area needs to be divided into nonoverlapping geographic units. A modifiable areal unit problem occurs when studies that use aggregate data do not distinguish between spatial associations created artificially by the aggregation and real associations presented by the individuals within the geographic units. Given JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 3/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity this problem, the estimate of spatial effects could be sensitive to the manner of aggregation. Second, McMillen cautioned that autocorrelation is often produced spuriously by model misspecification, such as omitted variables, and he argued that the high degree of parameterization of spatial lag and spatial error models could induce an incorrect structure for the covariance. A common remedy for the omitted variable issue raised by McMillen is the inclusion of spatial 28 28 fixed effects. According to Anselin and Arribas-Bel, a spatial fixed effects specification is appropriate when individual observations are organized into well-delineated groups and some characteristics of the group are unobserved. For example, when physical education classes vary by school district but no data are available to measure the performance of the schools, a spatial fixed- effects variable can capture how this variation is reflected in the prevalence of obesity. Geographic fixed effects will reduce spatial autocorrelation resulting from inadequate specification of contextual factors. However, Anselin and Arribas-Bel stated that spatial fixed effects could address only a form of spatial heterogeneity and not true spatial dependence. They argued that, if true spatial dependence is present, spatial fixed effects would not remove this dependence, with the only exception being that the spatial autocorrelation takes on a group-wise structure that is the same as the spatial unit. In terms of our study, the implication is that true spatial dependence, such as that associated with social contagion, should still be detectible even if fixed effects successfully account for dependency arising from contextual and correlated effects as described by Manski. As Manski notes, endogenous peer effects, contextual effects, and unobserved correlated effects can all contribute to similar behaviors and are inherently difficult to separate with linear-in- mean models. The panel SARMA model allows for such separation because the endogenous effect is calculated as the association of the weighted average obesity rate of neighboring units (block group or tract) with the obesity rate of the focal unit. Assuming the unobserved effect also follows a spatial pattern, the correlated effect is addressed in part by the geographic fixed effect and in part by applying the spatial weight matrix to the error term. Given these considerations, we estimated SARMA models using both the tract and block group panels described above. If spatial autocorrelation is associated with social contagion, it should be more pronounced across the smaller census block groups. This is because neighborhood-based friendship networks are more likely to extend across block group boundaries than across tract boundaries. Moreover, children in neighboring block groups are more likely to be in the same public school catchment areas and therefore more likely to be in the same school-based social networks than children in neighboring tracts. Using similar reasoning, compared with tract effects, block group effects would better capture characteristics of the microenvironment that could explain geographic differences in obesity rates because children in the same block group are more likely to attend the same schools, have similar school nutrition and physical activity programs, and be homogeneous with respect to access to parks and safe places for vigorous play. Thus, the strongest evidence of social contagion would be indicated by spatial autocorrelation in the block group panel after inclusion of block group effects. The SARMA models were estimated using the spml package in R, version 3.4.3 (R Foundation). The feature of primary interest is the spatial autoregressive term (ρ) obtained from the different model specifications. The models also included a spatial error term (λ), which accounts for unobserved correlated effects not captured in the geographic fixed effects or in other model covariates. A standard z score (normal distribution) was used to calculate P values, and 2-sided distribution was used. P < .05 was considered to be statistically significant. Data were analyzed from August 2017 to February 2018. Results Participants The census tract and block group aggregations used in this study were based on 935 800 children (51% male) with a mean (SD) age of 132 (39) months. At least 1 valid weight status indicator was JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 4/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity available for 689 809 of these children. Sixty-five percent of the children were white, 21% were black, 10% were Hispanic, 2% were Asian, and the remainder (2%) were of other or unidentified race or ethnicity. Descriptive Statistics Summary statistics for the tract and block group aggregate data sets used in the SARMA models are presented in Table 1. The mean values were similar across the 2 samples. There were higher SDs in the block group panel because block groups are smaller geographic units and reflect less aggregation. Primary Analysis Estimates from the tract-level and block group–level spatial models are reported in Table 2. Table 2 presents estimates from a non–spatial panel model as a reference point along with SARMA models estimated with year fixed effects only and with both geographic fixed effects and year fixed effects. Using a conditional Lagrange multiplier (LM) test, we rejected the null hypothesis of a non–spatial panel model in favor of the SARMA model for both the tract and block group data sets. For the tract- level panel, the test statistic was LM = 6.189 (P < .001). For the block group–level panel, the test statistic was LM = 7.920 (P < .001). As discussed above, our focal interest was spatial autocorrelation across the tracts or census block groups. This is captured by the estimate for the spatial autoregressive parameter (ρ). A comparison of ρ across the 2 SARMA models at the tract level revealed positive and significant spatial autocorrelation. The inclusion of tract fixed effects caused the estimate of spatial autocorrelation to decrease by nearly one-half, from ρ = 0.511 (95% CI, 0.469-0.553; P < .001) to ρ = 0.271 (95% CI, 0.147-0.396; P < .001). In contrast, a comparison of ρ across the 2 SARMA models at the block group level showed that there was no longer significant spatial autocorrelation after inclusion of block group effects. The inclusion of block group effects caused the estimate of spatial autocorrelation to decrease from ρ = 0.569 (95% CI, 0.543 to 0.595; P < .001) to ρ = −0.075 (95% CI, −0.264 to 0.114; P = .44). Additional insight is provided by the spatial error term (λ). As noted above, λ accounts for spatial dependence in the model errors. The λ continued to be significant in the tract-level panel even after including fixed tract effects (λ = −0.252; 95% CI, −0.404 to −0.100; P = .001) (Table 2). By contrast, λ was no longer significant in the corresponding model with block group fixed effects (λ = 0.124; 95% CI, −0.052 to 0.3; P = .17). This indicates that the smaller, block group effects better captured unobserved contextual features that influenced obesity rates. Covariate estimates in Table 2 provided additional insights into the importance of the tract and block group fixed effects in the model. A comparison of estimates from the non–spatial models with those from the SARMA models with tract and block group effects revealed similar point estimates. This was expected because the point estimates are unbiased regardless of spatial dependency in the Table 1. Model Variables for Census Tract-Level and Block Group–Level Panels Census Tract-Level Panel Census Block Group–Level Panel Variable (n = 8232) (n = 25 746) Obesity prevalence 0.22 (0.06) 0.22 (0.08) Unless otherwise specified, data are mean (SD) Race/ethnicity proportion of students within the census tract or Black 0.24 (0.29) 0.24 (0.31) census block group. Asian 0.02 (0.03) 0.02 (0.04) Eligibility for free and reduced-price school meals Hispanic 0.07 (0.11) 0.07 (0.12) represents the proportion of children from lower- Other 0.01 (0.02) 0.01 (0.02) income families in the census tract or block group. Female sex 0.49 (0.03) 0.49 (0.05) Children from families with incomes less than 130% of the poverty level are eligible for free meals. Eligible for free school meals 0.50 (0.21) 0.51 (0.23) b Children from families with incomes between 130% Eligible for reduced-price meals 0.10 (0.05) 0.10 (0.07) and 185% of the poverty level are eligible for Mean age, y 11.04 (0.35) 11.03 (0.48) reduced-price meals. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 5/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity model errors. Point estimates from the models without tract or block group fixed effects were similar in sign, but the point estimates diverged, suggesting that the geographic fixed effects were accounting for contextual and correlated factors that were not directly observed. Although these findings were not the central focus of this study, estimates in Table 2 suggested that neighborhoods with a higher proportion of Hispanic children were associated with higher rates of obesity, and neighborhoods with a higher proportion of children qualifying for free school meals were also associated with higher rates of obesity. The finding of a negative association with obesity for neighborhoods with higher proportions of black children was unexpected, but this finding could be explained by regional differences across the state. Statewide, 222 of 2147 block groups and 64 of 686 census tracts were predominantly composed of black children (>80% of the children in these block groups and tracts were black), and these block groups and tracts tended to be concentrated in urban areas, such as Little Rock. There were differences across the tract and block models for estimated associations between the obesity rate and the proportion of Asian children and girls. This reflected the higher variation across block groups compared with tracts. Table 2. Coefficient Estimates for Census Tract-Level and Block Group–Level Models Non–Spatial Panel Data Model With Time and Geographic SARMA Model Without SARMA Model With Time and Variable Fixed Effects Geographic Fixed Effects Geographic Fixed Effects Census tract-level models (n = 8232) Spatial error term, λ NA −0.251 (−0.321 to −0.181) −0.252 (−0.404 to −0.100) Spatial NA 0.511 (0.469 to 0.553) 0.271 (0.147 to 0.396) autoregressive term, ρ Race/ethnicity Black −0.060 (−0.086 to −0.034) −0.011 (−0.015 to −0.007) −0.058 (−0.081 to −0.034) Hispanic 0.096 (0.058 to 0.134) 0.051 (0.043 to 0.06) 0.088 (0.055 to 0.122) Asian −0.074 (−0.162 to 0.013) −0.214 (−0.253 to −0.175) −0.062 (−0.141 to 0.018) Other −0.458 (−0.522 to −0.395) −0.36 (−0.409 to −0.311) −0.447 (−0.506 to −0.388) Female sex 0.006 (−0.023 to 0.035) −0.011 (−0.037 to 0.016) 0.004 (−0.023 to 0.031) Eligible for free 0.027 (0.012 to 0.043) 0.089 (0.082 to 0.096) 0.024 (0.011 to 0.038) school meals Eligible for 0.006 (−0.014 to 0.026) 0.096 (0.08 to 0.113) 0.003 (−0.013 to 0.020) reduced-price school meals Mean age, y 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.005) Year effects Yes Yes Yes Tract effects Yes No Yes Census block group–level models (n = 25 764) Spatial error term, λ NA −0.456 (−0.5 to −0.412) 0.124 (−0.052 to 0.3) Spatial lag term, ρ NA 0.569 (0.543 to 0.595) −0.075 (−0.264 to 0.114) Race/ethnicity Abbreviations: NA, not applicable; SARMA, spatial autoregressive moving average. Black −0.003 (−0.022 to 0.015) −0.007 (−0.009 to −0.004) −0.002 (−0.019 to 0.016) Unless otherwise specified, data are estimated Hispanic 0.087 (0.062 to 0.111) 0.032 (0.026 to 0.038) 0.087 (0.063 to 0.11) proportion of students within the census tract or Asian 0.137 (0.097 to 0.177) −0.06 (−0.081 to −0.039) 0.137 (0.098 to 0.176) census block group (95% CI). The dependent Other −0.208 (−0.271 to −0.145) −0.307 (−0.349 to −0.265) −0.204 (−0.264 to −0.143) variable is proportion of children with obesity in the Female sex −0.062 (−0.079 to −0.044) −0.052 (−0.067 to −0.038) −0.062 (−0.078 to −0.046) census tract or census block group. Eligible for free 0.024 (0.012 to 0.035) 0.074 (0.07 to 0.079) 0.024 (0.012 to 0.035) b Eligibility for free and reduced-price school meals school meals represents the proportion of children from lower- Eligible for 0.008 (−0.007 to 0.023) 0.074 (0.063 to 0.085) 0.009 (−0.007 to 0.024) income families in the census tract or census block reduced-price school meals group. Children from families with incomes less than 130% of the poverty level are eligible for free meals. Mean age, y 0.009 (0.007 to 0.011) 0.006 (0.005 to 0.008) 0.009 (0.008 to 0.011) Children from families with incomes between 130% Year effects Yes Yes Yes and 185% of the poverty level are eligible for Block group effects Yes No Yes reduced-price meals. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 6/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Secondary Analyses The choice of the weight matrix and the resulting specification of distance decay could lead to different spatial effects. In this study, the weight matrix captured the empirical path through which social contagion was associated with obesity rate. The weight matrix used in the models reported in Table 2 was based on queen contiguity, wherein census tracts or block groups sharing a border, even a single point, were assigned nonnegative values in the weight matrix. As alternative specifications, we considered models with weight matrices constructed with the 4 or 8 nearest census tracts or block groups. Estimates from these models are presented in eTables 1 and 2 in the Supplement. Similar to findings reported in Table 2, estimates from models with the alternative weight matrices showed high levels of spatial autocorrelation when census tract or block group fixed effects were not included. Spatial autocorrelation continued to exist in tract-level models after the census tract fixed effects were included, but as in Table 2, there was no evidence of positive spatial autocorrelation in the census block group–level models after including census block group effects. Given the growth in social media participation, it is possible that geographic-based social networks have become less important in recent years. Consequently, we performed alternative estimations after breaking the panels into 2 periods: one covered the 2003-2004 through 2009- 2010 academic years, and the other covered the 2010-2011 through 2014-2015 academic years. Findings (eTables 3 and 4 in the Supplement) from the census tract-level models were similar to those reported in Table 2. There was no evidence of positive spatial autocorrelation in the census block group–level models in either period among estimations that included census block group fixed effects. However, the census block group–level model for the latter 5-year period provided evidence of significant spatial dependency in the model errors (λ = 0.244; 95% CI, 0.219-0.279; P = .002) even after the inclusion of census block group fixed effects. This could be interpreted as evidence of increased heterogeneity that transcends neighborhood, to which social media may be a contributing factor. Discussion Although we did not have information on children’s actual social networks, the empirical findings reported above provide indirect evidence that social contagion is unlikely to be associated with high rates of childhood obesity in Arkansas. Of interest, there was no evidence of spatial autocorrelation in models with the smallest geographic units (ie, block groups) after geographic fixed effects were included to account for unobserved and time-invariant contextual factors. If social contagion was associated with high childhood obesity rates, we would have expected to see significant evidence of spatial autocorrelation even after inclusion of these fixed effects. The tract-level models did continue to show positive spatial autocorrelation after the inclusion of fixed effects, but these models also showed significant spatial dependence in the error structure, which could suggest that the larger tract effects may have been too aggregate to accurately reflect key neighborhood features that were associated with obesity. The estimates of spatial autocorrelation in the tract-level models were similar to some of those estimated by Chen and Wen, who examined adult obesity rates across townships in Taiwan, a spatial scale that would be more aggregate than the tracts in our study. Similarly, Christman et al also found evidence of significant autocorrelation at the census tract level in their study of adult BMI. Despite evidence of spatial autocorrelation at the tract level, that spatial correlation was not present at the block group level was the primary finding of this study. If social contagion were important, it would be expected in these block group–level models because geographic-based social networks are more likely to span block boundaries than tract boundaries. Thus, the findings of this study provide little evidence of an association of social contagion with the increase in childhood obesity rates in Arkansas. This is not inconsistent with a recent study by Asirvatham et al that used a natural experiment involving a court decision that resulted in the plausibly exogenous reassignment of some children in Arkansas to different schools. Although their findings provide JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 7/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity significant evidence of social contagion, the effects that they report were small, and the results presented here are consistent with their findings. The implication for policy is that neighborhood contextual environments matter, but geographic-based social networks may not need to be the central focus of interventions. Limitations There are several limitations of our study. Although geographic proximity likely plays a role in the formation of friendship networks, social networks are complex and not based solely on this, especially in the age of social media. To the extent that geographic proximity is less important to social networks, social contagion could play an important role in childhood obesity that would not be reflected in dependency across spatial units. Second, we examined autocorrelation across census- based geographic areas. Use of school-based geographic areas may be more reflective of social networks; however, school catchment areas change with time. Moreover, schools change as children progress through the public school system, with intermediate and high schools drawing children from larger geographic areas than elementary schools. Nevertheless, most children in the same block group attend the same schools, and thus we expect that the geographic controls are adequate. Conclusions Social contagion and environmental factors are inherently different mechanisms that could be associated with the increase in childhood obesity. We found little evidence that geographic-based social contagion is associated with obesity rates across neighborhoods in Arkansas. Contextual factors operating at a neighborhood level were of greater importance in explaining spatial differences in obesity rates. ARTICLE INFORMATION Accepted for Publication: May2,2018. Published: August 3, 2018. doi:10.1001/jamanetworkopen.2018.0954 Open Access: This is an open access article distributed under the terms of the CC-BY License.©2018FangDetal. JAMA Network Open. Corresponding Author: Di Fang, PhD, Department of Agricultural Economics and Agribusiness, University of Arkansas, Fayetteville, AR 72701 (difang@uark.edu). Author Affiliations: Department of Agricultural Economics and Agribusiness, University of Arkansas, Fayetteville (Fang, Thomsen, Nayga); Arkansas Center for Health Improvement, University of Arkansas for Medical Sciences, Little Rock (Goudie). Author Contributions: Dr Fang had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Concept and design: Fang, Thomsen, Nayga. Acquisition, analysis, or interpretation of data: All authors. Drafting of the manuscript: Fang, Thomsen, Nayga. Critical revision of the manuscript for important intellectual content: All authors. Statistical analysis: Fang, Thomsen, Goudie. Obtained funding: Thomsen, Nayga. Administrative, technical, or material support: Nayga, Goudie. Supervision: Nayga. Conflict of Interest Disclosures: Dr Thomsen reported receiving grants from the National Institute of General Medical Sciences of the National Institutes of Health during the conduct of the study and being a project leader on a project funded by the National Institutes of Health Centers of Biomedical Research Excellence Center. No other disclosures were reported. JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 8/10 JAMA Network Open | Nutrition, Obesity, and Exercise Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity Funding/Support: This work was supported in part by P20GM109096 from the National Institute of General Medical Sciences of the National Institutes of Health. Role of the Funder/Sponsor: The National Institutes of Health 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. Disclaimer: The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. REFERENCES 1. Ogden CL, Carroll MD, Lawman HG, et al. Trends in obesity prevalence among children and adolescents in the United States, 1988-1994 through 2013-2014. JAMA. 2016;315(21):2292-2299. doi:10.1001/jama.2016.6361 2. Christakis NA, Fowler JH. The spread of obesity in a large social network over 32 years. N Engl J Med. 2007;357 (4):370-379. doi:10.1056/NEJMsa066082 3. Christakis NA, Fowler JH. Social contagion theory: examining dynamic social networks and human behavior. Stat Med. 2013;32(4):556-577. doi:10.1002/sim.5408 4. 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Environ Plan A. 1984;16(1):17-31. doi:10. 1068/a160017 28. Anselin L, Arribas-Bel D. Spatial fixed effects and spatial dependence in a single cross-section. Pap Reg Sci. 2013;92(1):3-17. doi:10.1111/j.1435-5957.2012.00480.x 29. Millo G, Piras G. splm: spatial panel data models in R. J Stat Softw. 2012;47(1):1-38. doi:10.18637/jss.v047.i01 30. Asirvatham J, Thomsen M, Nayga RM Jr, Rouse H. Do peers affect childhood obesity outcomes? peer-effect analysis in public schools. CanJEcon. 2018;51:216-235. doi:10.1111/caje.12321 31. Ugander J, Backstrom L, Marlow C, Kleinberg J. Structural diversity in social contagion. Proc Natl Acad Sci U S A. 2012;109(16):5962-5966. doi:10.1073/pnas.1116502109 SUPPLEMENT. eAppendix. Details on the spatial autoregressive moving average (SARMA) model eTable 1. Census tract-level spatial panel models for alternative spatial weight matrices eTable 2. Census block group–level spatial panel models for alternative spatial weight matrices eTable 3. Census tract-level spatial panel models for alternative time periods eTable 4. Census block group–level spatial panel models for alternative time periods JAMA Network Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 August 3, 2018 10/10 Supplementary Online Content Fang D, Thomsen MR, Nayga RM, Goudie A. Association of Neighborhood Geographic Spatial Factors With Rates of Childhood Obesity. JAMA Netw Open. 2018;1(4):e180954. doi:10.1001/jamanetworkopen.2018.0954 Supplement. eAppendix. Details on the spatial autoregressive moving average (SARMA) model eTable 1. Census tract-level spatial panel models for alternative spatial weight matrices eTable 2. Census block group level spatial panel models for alternative spatial weight matrices eTable 3. Census tract-level spatial panel models for alternative time periods eTable 4. Census block group level spatial panel models for alternative time periods This supplementary material has been provided by the authors to give readers additional information about their work. © 2018 Fang D et al. JAMA Network Open. eAppendix Details on the spatial autoregressive moving average (SARMA) model In the equation below, ! denotes the percentage of obese children living in spatial unit i at time "# t, and $ is the matrix of k demographic variables of the school children across time. As shown %"# in Table 1 of the article, these variables include average age, proportion by gender, race or ethnicity, and school meal status. Social contagion across nearby block groups would be captured by &'! , where W is the spatial weight matrix. To exclude the endogenous self- "# influence, the diagonals of W are set to zero. W is also row-standardized to summarize a weighted-average obesity rates of all “neighbors”. Therefore, the spatial autoregressive parameter, &, is the parameter of interest. A positive & indicates spillover (social contagion) in obesity across geographic space. We also assume that obesity can be influenced by the contextual environment, which we capture with census tract or census block group fixed effects denoted by ( . We control for time effects with ) to capture changes in the environment through " # time. As discussed, spatial units are represented by the weight matrix ' at either the census tract level or the census block group level. ! = + + ) + ( + - . $ + &'! + 2 "# # " % %"# "# "# and 2 = 3'2 + 4 "# "# "# Because unobserved factors may not be independent of spatial locations, we assume that 2 "# follows a similar autoregressive pattern, represented by 3'2 . This way we take care of the "# unobserved correlated effects that can contribute to obesity. © 2018 Fang D et al. JAMA Network Open.! ! eTable 1. Census tract-level spatial panel models for alternative spatial weight matrices b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Census tract level models (n = 8,232) -0.077 (-0.142 to -0.012) -0.156 (-0.314 to 0.002) 0.156 (0.082 to 0.230) -0.197 (-0.403 to 0.008) Spatial error term (l) Spatial lag term (r) 0.357 (0.313 to 0.401) 0.203 (0.069 to 0.338) 0.296 (0.241 to 0.351) 0.246 (0.089 to 0.404) African American -0.012 (-0.017 to -0.008) -0.060 (-0.084 to -0.036) -0.011 (-0.016 to -0.006) -0.060 (-0.084 to -0.036) Hispanic 0.047 (0.037 to 0.057) 0.088 (0.053 to 0.123) 0.060 (0.049 to 0.071) 0.087 (0.053 to 0.122) Asian -0.269 (-0.311 to -0.227) -0.070 (-0.151 to 0.011) -0.277 (-0.323 to -0.232) -0.071 (-0.152 to 0.010) Other race -0.389 (-0.441 to -0.337) -0.451 (-0.511 to -0.392) -0.363 (-0.417 to -0.308) -0.452 (-0.511 to -0.392) Female -0.005 (-0.032 to 0.023) 0.005 (-0.022 to 0.032) 0.005 (-0.022 to 0.032) 0.004 (-0.023 to 0.032) Free school meals 0.104 (0.097 to 0.112) 0.026 (0.012 to 0.040) 0.113 (0.106 to 0.121) 0.026 (0.012 to 0.040) Reduced-price meals 0.107 (0.089 to 0.126) 0.004 (-0.013 to 0.021) 0.127 (0.106 to 0.147) 0.004 (-0.013 to 0.021) Average age (years) 0.005 (0.002 to 0.007) 0.003 (0.000 to 0.006) 0.005 (0.002 to 0.008) 0.003 (0.000 to 0.006) Year effects Yes Yes Yes Yes Census tract effects No Yes No Yes Weight Four nearest neighbors Eight nearest neighbors a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or census block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! ! eTable 2. Census block group–level spatial panel models for alternative spatial weight matrices b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Census block-group level models (n = 25,764) -0.327 (-0.367 to -0.286) 0.196 (0.107 to 0.284) -0.229 (-0.286 to -0.171) 0.009 (-0.247 to 0.265) Spatial error term (l) 0.459 (0.433 to 0.485) -0.166 (-0.267 to -0.065) 0.459 (0.427 to 0.492) 0.070 (-0.176 to 0.316) Spatial lag term (r) African American -0.007 (-0.010 to -0.004) 0.000 (-0.018 to 0.017) -0.008 (-0.011 to -0.005) -0.002 (-0.020 to 0.015) Hispanic 0.027 (0.020 to 0.033) 0.086 (0.062 to 0.11) 0.029 (0.022 to 0.036) 0.085 (0.061 to 0.109) Asian -0.070 (-0.092 to -0.047) 0.138 (0.099 to 0.176) -0.065 (-0.089 to -0.042) 0.137 (0.098 to 0.175) Other race -0.350 (-0.395 to -0.306) -0.206 (-0.267 to -0.146) -0.341 (-0.388 to -0.295) -0.205 (-0.266 to -0.145) Female -0.057 (-0.072 to -0.042) -0.060 (-0.076 to -0.044) -0.058 (-0.073 to -0.043) -0.062 (-0.078 to -0.045) Free school meals 0.086 (0.081 to 0.091) 0.024 (0.013 to 0.036) 0.091 (0.085 to 0.096) 0.023 (0.012 to 0.035) Reduced-price meals 0.080 (0.069 to 0.092) 0.009 (-0.007 to 0.025) 0.085 (0.073 to 0.097) 0.008 (-0.007 to 0.023) Average age (years) 0.007 (0.005 to 0.009) 0.009 (0.008 to 0.011) 0.008 (0.006 to 0.009) 0.009 (0.007 to 0.011) Year effects Yes Yes Yes Yes Census block-group effects No Yes No Yes Weight Four nearest neighbors Eight nearest neighbors a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or census block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! ! eTable 3. Census tract-level spatial panel models for alternative time periods b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Census tract level models 2003/2004 through 2009/2010 Census tract level models 2010/2011 through Academic Years (n = 4,802) 2014/2015 Academic Years (n = 4,802) -0.251 (-0.321 to -0.181) -0.252 (-0.404 to -0.100) -0.251 (-0.321 to -0.181) -0.252 (-0.404 to -0.100) Spatial error term (l) 0.511 (0.469 to 0.553) 0.271 (0.147 to 0.396) 0.511 (0.469 to 0.553) 0.271 (0.147 to 0.396) Spatial lag term (r) African American -0.011 (-0.015 to -0.007) -0.058 (-0.081 to -0.034) -0.011 (-0.015 to -0.007) -0.058 (-0.081 to -0.034) Hispanic 0.051 (0.043 to 0.060) 0.088 (0.055 to 0.122) 0.051 (0.043 to 0.060) 0.088 (0.055 to 0.122) Asian -0.214 (-0.253 to -0.175) -0.062 (-0.141 to 0.018) -0.214 (-0.253 to -0.175) -0.062 (-0.141 to 0.018) Other race -0.360 (-0.409 to -0.311) -0.447 (-0.506 to -0.388) -0.360 (-0.409 to -0.311) -0.447 (-0.506 to -0.388) Female -0.011 (-0.037 to 0.016) 0.004 (-0.023 to 0.031) -0.011 (-0.037 to 0.016) 0.004 (-0.023 to 0.031) Free school meals 0.089 (0.082 to 0.096) 0.024 (0.011 to 0.038) 0.089 (0.082 to 0.096) 0.024 (0.011 to 0.038) Reduced-price meals 0.096 (0.080 to 0.113) 0.003 (-0.013 to 0.020) 0.096 (0.080 to 0.113) 0.003 (-0.013 to 0.020) Average age (years) 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.005) 0.003 (0.000 to 0.006) 0.003 (0.000 to 0.005) Year effects Yes Yes Yes Yes Census tract effects No Yes No Yes a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.! ! eTable 4. Census block group–level spatial panel models for alternative time periods b c b c (1) (2) (3) (4) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Estimate (95% CI) Block-group level models 2003/2004 through Block-group level models 2010/2011 through 2009/2010 Academic Years (n = 15,029) 2014/2015 Academic Years (n = 15,029) -0.466 (-0.522 to -0.410) -0.084 (-0.297 to 0.128) -0.450 (-0.520 to -0.380) 0.244 (0.086 to 0.401) Spatial error term (l) 0.591 (0.559 to 0.623) 0.113 (-0.084 to 0.311) 0.538 (0.496 to 0.581) -0.208 (-0.393 to -0.022) Spatial lag term (r) African American -0.009 (-0.013 to -0.006) -0.004 (-0.028 to 0.02) 0.000 (-0.005 to 0.004) -0.014 (-0.049 to 0.021) Hispanic 0.026 (0.019 to 0.034) 0.097 (0.065 to 0.129) 0.040 (0.030 to 0.049) 0.043 (-0.005 to 0.091) Asian -0.012 (-0.038 to 0.014) 0.237 (0.19 to 0.284) -0.118 (-0.153 to -0.083) 0.013 (-0.072 to 0.097) Other race -0.352 (-0.408 to -0.295) -0.262 (-0.353 to -0.171) -0.258 (-0.321 to -0.195) 0.002 (-0.105 to 0.108) Female -0.075 (-0.093 to -0.057) -0.092 (-0.114 to -0.071) -0.024 (-0.047 to -0.001) -0.023 (-0.053 to 0.006) Free school meals 0.072 (0.066 to 0.078) 0.006 (-0.008 to 0.021) 0.077 (0.069 to 0.085) 0.027 (0.004 to 0.051) Reduced-price meals 0.055 (0.043 to 0.067) 0.01 (-0.005 to 0.024) 0.129 (0.106 to 0.152) 0.024 (-0.011 to 0.06) Average age (years) 0.005 (0.003 to 0.007) 0.009 (0.007 to 0.012) 0.008 (0.006 to 0.011) 0.011 (0.007 to 0.014) Year effects Yes Yes Yes Yes Census block-group effects No Yes No Yes a. Unless otherwise specified all variables are proportion of students within the census tract or census block group. b. Spatial autoregressive moving average (SARMA) model without geographic fixed effects. c. SARMA model with time and geographic fixed effects. d. Free and reduced-price school meals represent the proportion of lower-income children in the census tract or census block group. Children from families with incomes below 130 percent of the poverty level are eligible for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible for reduced-price meals. © 2018 Fang D et al. JAMA Network Open.!

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Published: Aug 3, 2018

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