Design and data
We did a secondary analysis study based on the Chilean National Health Surveys (NHS) dataset. These datasets are held by the Subsecretaria de Salud Pública del Ministerio de Salud de Chile and are anonymized and freely available by request at
https://www.portaltransparencia.cl/. Consequently, this study did not require ethical approval, consent to participate, and other administrative permission. All methods were carried out in accordance Declaration of Helsinki and Chilean regulations.
Chile is geographically divided into three administrative levels: regions (15 regions until 2017), provinces (56 provinces), and communes (346). On the other hand, Chile conducted three National Health Surveys (NHS). The last two NHS (NHS-2009 and NHS-2016) were considered for our analysis because sampling designs are similar; nevertheless, there are some differences in measured health conditions or risk factors. NSH-2009 and NSH-2016 are probabilistic samples of the general population aged 15 and over, with national and regional representativeness. The NHS’s four-stage sampling design includes a random sampling of communes, census zones, households, and individuals stratified by gender and urban-rural areas.
NHS-2009 was carried out between October 2009 and September 2010 and covered thirteen health conditions and other selected risk factors (alcohol, tobacco, food and salt consumption, passive exposure to environmental tobacco smoke). The participation rate was 85%; 5412 subjects completed the questionnaires and had clinical examinations, including laboratory tests and anthropometric measurements. The NHS-2016, developed between August 2016 to March 2017, extended its measures to 60 health conditions, including risk factors and population health determinants. The participation rate was 90%, 6233 subjects completed the health questionnaires, and 5220 had clinical and laboratory tests and anthropometry. In both surveys, health questionnaires, clinical examinations, and measured height (in centimeters) and weight (in kilograms) data were completed by trained nurses and study staff visiting each selected household and following standardized procedures and validated instruments/equipment. The variables analyzed were weight, height, gender, age, education level, the region of residence, and the individual’s health care system, including the HS records explained later. Only complete data from both surveys were included in our analysis.
Definition of obesity and subnational geographic levels
We used the Word Health Organization’s criteria to define adult obesity: body mass index (BMI) over or equal to 30. We calculated BMI as weight in kilograms divided by the square of the height in meters.
Chilean NHS has national, regional, gender, and urban-rural areas representativeness but does not collect representative data at the country’s second and third geographic administrative divisions (provinces and commune). Each participant’s commune or province of residence is not wholly and reliably registered either. Instead, we constructed a smaller geographical area using ancillary data recorded on both NHS, indirectly related to the commune or province, and the HS. The health system in Chile is based on 29 sub-regional geographical HS, which aim to manage and develop a public healthcare network under a defined jurisdiction, being different between them in terms of geographical area extension, population density, educational levels, and family income. In this way, we analyzed obesity prevalences rates at three geographical levels: national, regional, and HS areas, being the HS the smallest unit of analysis available.
By the time of NHS (2016–2017), Chile was administratively divided into 15 regions from north to south. Regions are grouped only for the interpretative purpose by the following macro zones: North zone, Central zone, Central-south, South, and Austral zone.
Data processing
All analyses accounted for the complex sampling design to produce population-based weighted nationally representativeness according to Chilean NSH analytic guidelines.
At the national and regional levels, we calculated obesity prevalence rates (obesity rate from now on) with 95% confidence intervals (95% CI) using the sampling expansion factors (Chilean NSH guidelines); we named this the traditional approach (TA). To estimate the absolute (difference between obesity rate in NHS-2016 and NHS-2009) and relative increase rates (ratio between difference and obesity rate in NHS-2009) and their 95% CI, we fitted linear regression and log-linear models; both models consider the probabilities of inclusion of each survey. These rates were also calculated for the following subpopulation: gender (male, female), age groups (15-24y, 25-44y, 45-64y 65y or more), and education level as a socioeconomic status proxy variable (low, medium, high). Due to Chile already having elevated obesity rates (NSH-2016), we emphasize the relative increase indicator, rather than the absolute one, to identify target areas or subgroups for early prevention since this indicator depends on its baseline value.
For SAE at the HS level, we used Fay-Herriot (FH) models for the obesity rates estimations. We preferred FH to other emerging SAE models because it is a well-known lineal-mixed-model approach to fill the data gap over small geographic areas. It accounts for too small sample sizes and provides accurate direct estimates [
24]. Two types of models were fitted:
FH model:
\({\hat{\delta}}_d^{DIR}={\delta}_d+{e}_d,{e}_d\sim N\left(0,{\psi}_d\right),\mathrm{and}\ d=1,\dots, D.\)
\({\delta}_d={x}_d^T\beta +{u}_d,\mathrm{where}\ {u}_d\sim N\left(0,A\right),\mathrm{and}\ d=1,\dots, D\)
Where δd is the parameter to be estimated in the area d (d = 1, …, D). \({\hat{\delta}}_d^{DIR}\) is the unbiased directed estimator (DIR) obtained with the sample design. ψd is the sample variance of the direct estimator in each area. \({x}_d^T\) are the auxiliary linear predictors related to variables of interest, and A is a matrix D × D, where D is the geographic unit or area of analysis.
SFH model is the spatial Fay-Herriot model (SFH) to reduce estimation variance at under-sampled areas and spatial autocorrelation due to neighborhood distance, which assumes that
u = (
u1, …,
uD) related to the areas that follow a first-order autoregressive process SAR [
1]. That is:
$$u={\rho}_1 Wu+\epsilon, \mathrm{where}\ \epsilon \sim N\left({0}_D,{\sigma}_1^2{I}_D\right).$$
Where 0D is a vector of zeros, and ID the identity matrix. W is the proximity matrix D × D obtained by a row standardization of an initial matrix with zeros and ones, where the number 1 indicates if the areas are neighbors. ρ1 is a scalar parameter.
The area-level auxiliary data and covariates used for SAE were children’s obesity/overweight and mortality rates at the commune level, population size, and the number of medical establishments at the HS level. These data are public and accessible in Chile [
25].
Direct (DIR), FH, and SFH estimates with standard errors (SE) were reported. DIR is calculated using data exclusively from the NHS and is similar to the obesity rate with TA. We fitted log-linear models and the FH and SFH modes for the relative increase in HS areas, and later FH and SFH models were fitted.
Graphs and maps to show geographic variation were also constructed for results visualization. All the analyses were conducted in R version 4.1.1 [
26]. Figures and maps are produced using R packages
ggplot (version 3.3.5),
ggrepel (version 0.9.1 [
23],
rgdal (version 1.5–23),
rgeos (version 0.5–5), and
chilemapas (version 0.2). Obesity rates were calculated using the package
survey (version 4.1–1), and FH models were estimated using package
SAE version 1.3.