GeoSES: A socioeconomic index for health and social research in Brazil.

The individual's socioeconomic conditions are the most relevant to predict the quality of someone's health. However, such information is not usually found in medical records, making studies in the area difficult. Therefore, it is common to use composite indices that characterize a region socioeconomically, such as the Human Development Index (HDI). The main advantage of the HDI is its understanding and adoption on a global scale. However, its applicability is limited for health studies since its longevity dimension presents mathematical redundancy in regression models. Here we introduce the GeoSES, a composite index that summarizes the main dimensions of the Brazilian socioeconomic context for research purposes. We created the index from the 2010 Brazilian Census, whose variables selection was guided by theoretical references for health studies. The proposed index incorporates seven socioeconomic dimensions: education, mobility, poverty, wealth, income, segregation, and deprivation of resources and services. We developed the GeoSES using Principal Component Analysis and evaluated its construct, content, and applicability. GeoSES is defined at three scales: national (GeoSES-BR), Federative Unit (GeoSES-FU), and intra-municipal (GeoSES-IM). GeoSES-BR dimensions showed a good association with HDI-M (correlation above 0.85). The model with the poverty dimension best explained the relative risk of avoidable cause mortality in Brazil. In the intra-municipal scale, the model with GeoSES-IM was the one that best explained the relative risk of mortality from circulatory system diseases. By applying spatial regressions, we demonstrated that GeoSES shows significant explanatory potential in the studied scales, being a compelling complement for future researches in public health.

Introduction

The ZIP code paradigm says that the place where a person lives is a more critical health predictor than their genetic code [1]. In fact, at the individual level, the relationship between the socioeconomic status (SES) and the prevalence of chronic diseases presents an evident inverse linear gradient [2]. In other words, as SES improves, prevalence diminishes correspondingly. This gradient is reliable and consistent in the relationship found with cardiovascular diseases, type 2 diabetes, metabolic syndrome, arthritis, chronic respiratory tuberculosis, and adverse birth outcomes, as well as violent and accidental deaths [2]. However, individual conditions are not enough to fully explain spatial variation in disease rates and the relationship between social inequalities and health. Area-based studies show that the socioeconomic conditions of places also affect people's health [3-5]. Thus, understanding which characteristics of the socioeconomic environment most explain health conditions is a pressing issue. Such understanding can contribute to the implementation of intersectoral public policies that would be more efficient to improve the health of the population and to reduce inequalities. As individual measures of socioeconomic indicators are rarely available in medical records [6], it is common to use a single geographical variable that summarizes living conditions (e.g., income, education, per capita Gross Domestic Product). Although this approach helps to understand how an aspect of the socioeconomic context is related to health, the interpretation of the findings is limited, as the socioeconomic context is multidimensional, involving aspects such as employment, income, education, housing, segregation, mobility, among others [7].

Furthermore, by including more than one socioeconomic variable in a regression model—the most used statistical analysis in ecological design studies—we can violate the underlying assumptions of this analysis due to the effects of collinearity [8]. The use of composite indexes aims to overcome such problems, adding explanatory power to the socioeconomic context of the places. Indexes can be especially useful if they allow us to evaluate how a particular dimension can influence health [9].

In Brazil, studies on health with an ecological approach often use a single variable as a proxy for the socioeconomic context—generally monthly household income or other variables from public statistics. The Human Development Index calculated by the municipality level (HDI-M) [10], is the most often used on the national scale. In addition to presenting construct validity and reliability, it allows for international comparability. However, this index expresses how much the development process guaranteed access to education and culture, conditions of enjoying a long and healthy life, and having an adequate standard of living for the population [11]. Although in practice it has helped to identify development inequalities among Brazilian municipalities, there is mathematical redundancy when it is applied to explain health outcomes by regression models. The HDI longevity component measures the life expectancy at birth, comprising health conditions and risks to morbidity and mortality. Therefore, there is a lack of a synthetic index of socioeconomic conditions prepared from theoretical references for health studies in Brazil.

Considering this gap, here we introduce a tool intended to estimate the burden of the problems attributable to the different social dimensions in health and social research. GeoSES (Geographic Index of the Socioeconomic Context for Health and Social Studies) synthesizes the most relevant socioeconomic dimensions to contextualize health for research purposes, to evaluate and monitor inequalities, and to develop resource and service allocation strategies. We developed the new index for use at three aggregation scales: national (GeoSES-BR), Federative Unit (GeoSES-FU) and intra-municipal (GeoSES-IM, for the 140 municipalities with three or more census sample areas). Without loss of generality, here we present the application on national and intra-municipal scales.

Methods

Geographic units

The enumeration area is the smallest geographic entity for which the Brazilian Demographic Census tabulates decennial data, including all household units. It is similar to the Census Block Group in the US Census. Enumeration areas are grouped to form a valid sample area, for which statistical procedures guarantee representation of the whole population. The questionnaires applied to the sample households include the universal basic questionnaire, in addition to others of a more detailed investigation about the characteristics of the household and its residents [12]. Thus, we created the synthetic index by selecting the variables contained in the questionnaire applied to the sample during the 2010 Population Census, comprising about 11% (6,400,000 units) of the Brazilian households.

Socioeconomic variables and dimensions of context

We based the choice of the variables for the index construction on theoretical studies on health [7,13], keeping seven dimensions of the socioeconomic context. The dimensions (and the number of initial variables in each of them) are education [7], poverty [5], wealth [3], income [1], segregation [5], mobility [6] and, deprivation to resources and services [14]. We list all variables and their meaning on S1 Appendix.

The dimension income may influence the etiology of several health outcomes, in part, through mechanisms that involve the acquisition of material resources. Education can reflect non-economic features as general and health-related knowledge, the capacity of problem-solving, prestige, influence, social network and access to technological innovation [15] that can bring advantages to the individual’s health [9]. Poverty refers to absolute poverty, directly linked to the minimum capacity of survival and access to material resources. Wealth, on its turn, is different from income, since it is a proxy for all long-life economic resources [9]. Our definition of material deprivation and access to public services bases on Townsend’s concept of material deprivation [16] that refers to disadvantages concerning other people in the same society to which one belongs. We intend to measure how much material resources and conveniences that are part of modern life (such as adequate housing, car ownership, refrigerator, computer, among others) a person has, also evaluating their access to services, including sanitation, electricity, and internet. Mobility can affect a person's health in many ways. One of them concerns the time spent commuting from home to work, which can cause stress on many levels and compromise the time available for study or leisure. In addition, longer commuting time may expose people to higher doses of air pollution in large cities [17]. Finally, residential segregation is a broad concept that refers to housing separated from different population groups in different parts of a city [18]. Segregation affects health by intensifying psychosocial effects involving insecurity, anxiety, social isolation, socially dangerous environments, bullying, and depression [14,19,20]. In our analysis, we considered two aspects of segregation: education and income, including levels of income stratified by ethnic groups, which better describe socioeconomic differences in Brazil. We used the Index of Concentration at the Extremes (ICE) to measure residential segregation [14]. Consider the income segregation as an example: the formula uses the number of people who earns more than the 80% percentile, minus the number who earns less than the 20% percentile, divided by the total number of people who have income. The ICE varies from -1 (most deprived) to 1 (most privileged). A negative ICE means that the area presents more people in the condition of deprivation than in the higher extreme; and a positive value, the opposite. A value of zero indicates that the area is not dominated by extreme concentrations of either of the two groups. The calculations of the other segregation types follow the same formula.

Data collection and processing

The data used to generate the index comes from the 2010 Census, made available by the Brazilian Institute of Geography and Statistics (IBGE), organized by Federative Unit (FU), including questionnaires about "People" (information at the individual level, e.g., income, level of education, time spent commuting to work, etc.) and their "Households" (e.g., the existence of material goods, access to resources, etc.). The first step is to gather the original data according to theoretical references [7,13] and data availability related to the interest of the study. Original data contains quantitative information on the variables of interest, for example, “the number of people with higher education in a municipality”.

The second step is to process the original data generating the variables of interest of the methodology, which means translating the original information into percentage values. In our example, when quantifying people in a municipality who have completed higher education, the processing result is a value that represents the percentage (from 0 to 100) of that population that has completed higher education. Exceptions apply to variables of direct significance, such as income, in which the average values were considered. During the second step our calculations always considered the weight of the sample area, since the questionnaires represent samples from the regions from which they were collected.

The third step refers to grouping the generated variables into single CSV files considering the scope of the index to be generated, that is, for a municipal scope the information was made available by sample areas; for a statewide coverage, information was made available on a consolidated basis for each municipality of that FU.

At the end of this process, we have the information in the expected format for index calculation, separated by FU and type (sample area or municipality). Also, each file type (sample area or municipality) contains the generated variables for “People” and “Household”, consolidating the desired information in a single source.

GeoSES definition

We developed the index by successively applying the principal component analysis (PCA) technique [21], based on the methodology of Lalloué et al. [22], with a modification in Step 1, considering the correlation matrix of the original variables. The principal components are uncorrelated linear combinations of the original variables and are constructed so that the first component has the maximum variance, the second has maximum variance and is uncorrelated with the first one and so on. The maximum number of components is equal to the number of variables in the study, but in general, it is possible to explain practically all the variability of the data with a smaller number of components. We used the data described above, selected according to the area of interest under analysis, which can be: national (the whole country, using consolidated data from all municipalities), FU (an indicator of each state, using data from its municipalities) or intra-municipal (for a specific municipality using sample area data). The steps for index generation are the same regardless of the area of interest. A project in the municipality of São Paulo was initially developed [23] with the later application on a national scale.

Alternatively, a method of factor analysis could also be used. However, we would have to assume an a priori model. Furthermore, it is well known that in the Principal Components Solution of the Factor Model, which does not suppose any multivariate distribution for the data, the factor loadings are the scaled coefficients of the principal components. Thus, the results obtained by PCA and factor analysis would be, in this case, equivalents.

Preprocessing

The calculation of the index starts by reading the data described in the previous section. Then, we add a constant equal to 10 to all read values. The purpose of this sum is to avoid the instability of the method during matrix inversion. The choice of value 10 is random, but any constant number would have the same effect, without interfering in the final result. That is, since we added the same value to all data, its relative differences remain the same.

Steps

1) The objective in this first step was to generate aggregate indices within each of the dimensions, and a PCA was performed in each of them. The number of components selected was such that the percentage of total variance explained was greater than or equal to 75%. For ease of interpretation, we considered the variables with the highest coefficient in each component.

2) Considering the variables selected in step 1, we applied another PCA, and we considered its first principal component. The objective here was to bring all dimensions together into an overall component.

3) To eliminate variables that have little contribution to the index obtained in step 2, only those whose absolute coefficient values were below the average of the coefficients were eliminated, and we applied the PCA method to the remaining variables. The resulting first component defines the GeoSES (Socioeconomic Index of Geographic Context for Health and Social Studies).

4) The GeoSES values (scores) were then calculated.

5) The scores were standardized for the interval -1 to 1.

Fig 1 compares the development processes of HDI and GeoSES.

Fig 1

The development processes of HDI and GeoSES.

The figure shows the dimensions each index employs and how the variables are combined to produce a single measure. Dimensions with the same color are present in both HDI and GeoSES. Image is best seen in color.

The index obtained in Step 2 could have been considered the final one. However, for its calculation, we would need to know the values of variables that do not have an important contribution. In Step 3, these variables were eliminated, and the coefficients of the remainder were calculated again, following the procedure presented in Lalloué et al. [22].

Interpretation

Extreme GeoSES values mean the worst (-1) and the best (1) socioeconomic contexts in the analyzed scale. In other words, to have a GeoSES of 1 at the national level, the municipality must have the best relative socioeconomic context of the country. So, if in 2010 a municipality had a GeoSES index of 0.2 and in the next Census the index is 0.3, there would have been a relative improvement in the socioeconomic context because even with possible changes in the most discriminating variables, this municipality is closest to the best municipality than it was in 2010.

Just as we can decompose the HDI into Longevity, Income, and Education, we developed an approach of expressing the contribution of each GeoSES dimension to better interpretability of the results. We consider that the most significant variable in each dimension expresses its contribution to the index. So, if in the FU analysis of São Paulo, the most relevant variable in the Education dimension is the "percentage of people without education", we use the values of such variable to quantify the development of Education. Thus, considering that for the municipality of São Paulo this value is 45.78, the municipal manager can compare this value with that of other municipalities in the state.

If there is more than one variable in the same dimension, we present only the one most correlated with GeoSES. We understand that by selecting only the most correlated variable, we are using the most representative measure of that dimension. Such a procedure avoids complex processing; also, considering more than one variable per dimension could eventually lead to uninterpretable results.

It is substantial to note, however, that the interpretation of GeoSES as well as of each dimension must consider comparisons with one municipality to another. For example, the single value of a GeoSES = 0.2 does not have a meaning per se, but the relative differences between the GeoSES of distinct municipalities do, in terms of socioeconomic development.

To facilitate the use and dissemination of results, all indexes and their associated information are available on interactive maps in HTML format. Each municipality or state has a file with its name in which it is possible to observe the geographical distribution of the data interactively. There is a layer on the map for each dimension used in the analysis, plus the prime layer that illustrates the spatial distribution of the index itself. We present an example in Fig 2.

Fig 2

The GeoSES-SP interactive map.

The figure shows the geographical distribution of GeoSES values, considering the state of São Paulo. In highlight, the city of São Paulo/SP presents its index and the values of its dimensions. In this analysis, we note that the dimension “mobility” is not activated; that is, it is not significant to characterize the socioeconomic differences of the state. Besides the prime layer (the index), we can also plot all other significant dimensions of the analysis.

The interactive maps and CSV files, with tabulated values by region of interest, will be made available by the Brazilian Ministry of Health in a place to be defined until the time of publication of this article.

GeoSES extensive creation

Once defined the methodology described above and validated for the municipality of São Paulo, using statistical software, the process was completely automated via computer systems. We developed a computer system based on Python language, allowing the scalability of the index generation for the entire national territory, ensuring agility and consistency of results.

For computational development, we adopted a modularized approach for dimensions’ parameterization. We facilitate the adaptability of the computer program to data from other Censuses (both past and future), by generalizing how the dimensions and their variables are defined and used.

Results

The GeoSES evaluation comprised its content, its construct, and its applicability to health studies. Content validation verifies the relevance and representativeness of the dimensions that make up GeoSES to describe the measured phenomenon [24]. Due to the PCA mechanism, the selected variables are naturally representative of the dimensions to which they belong, and the dimensions that make up GeoSES are relevant to contextualize the socioeconomic phenomena due to the theoretical frameworks. Besides, we calculated Cronbach's alpha coefficient for the generated indices, obtaining the values of 0.93, 0.89, and 0.97 for GeoSES-BR, GeoSES-FU, and GeoSES-IM, respectively. Remember that the closer to 1, the more homogeneous are the index variables.

GeoSES construct evaluation

The construct validation verifies, from the theoretical point of view, whether the new index is associated with the supposed measured concept. We evaluated GeoSES by comparing it with the HDI-M–a widely accepted and applied indicator for the same level of aggregation (in this case, for municipalities). We verified the association between GeoSES and HDI-M qualitatively and quantitatively.

In qualitative terms, the average of GeoSES-BR among the municipalities of Brazil was -0.40. Melgaço, in the FU of Pará, received the worst rating (-1) and Santana de Parnaíba, in the FU of São Paulo, the best (+1). According to the HDI-M, the average HDI of the Brazilian municipalities is 0.659. Melgaço (0.418) also occupies the worst position, but São Caetano do Sul, in the FU of São Paulo, the best (0.862). Such comparison reinforces the similarity between the indices, but highlights that differences may arise, which potentially better explain the socioeconomic conditions of the Brazilian regions.

In quantitative terms, Table 1 shows the correlations between “GeoSES vs. HDI-M” and its “Dimensions vs. Components”. GeoSES dimensions showed a good correlation with the HDI-M, above 0.85, except for wealth and segregation. Observe that in the national analysis, "education" and "poverty" appear negatively correlated to GeoSES because education is measured in terms of the population without instruction. That is, in the national context, the number of people without instruction is more relevant than people with instruction for describing socioeconomical differences.

Table 1

Correlation matrix between the indices and their dimensions in the national scale.

	GeoSES	education	poverty	deprivation	wealth	income	segregation	HDIM	HDI-educ	HDI-long	HDI-inc
GeoSES	1
education	-0.86	1
poverty	-0.96	0.81	1
deprivation	0.93	-0.74	-0.90	1
wealth	0.57	-0.61	-0.43	0.41	1
income	0.93	-0.82	-0.88	0.83	0.60	1
segregation	0.82	-0.54	-0.77	0.80	0.27	0.67	1
HDIM	0.94	-0.93	-0.93	0.86	0.53	0.89	0.70	1
HDIM_educ	0.85	-0.95	-0.82	0.76	0.51	0.78	0.60	0.95	1
HDIM_long	0.82	-0.71	-0.83	0.78	0.41	0.76	0.64	0.85	0.70	1
HDIM_inc	0.95	-0.84	-0.96	0.87	0.53	0.94	0.73	0.95	0.82	0.83	1

GeoSES applicability assessment in health

As an additional evaluation, we validated GeoSES’ explanatory potential for health outcomes at two aggregation scales: national (GeoSES-BR), and intra-municipal (GeoSES-IM). The national evaluation considers the calculation of the relative risk of avoidable causes of deaths (from 5 to 74 years old) due to interventions at the Brazilian Health System [25], between 2013 and 2017. This health outcome was chosen since it is a very sensitive indicator of differences in populations, enabling the identification of higher-risk groups for the implementation of special health and development programs [26].

The intra-municipal evaluation considers the calculation of the relative risk of mortality from circulatory system diseases of residents of the municipality of São Paulo, in the FU of São Paulo, by sample area, between 2006 and 2009. Death data by municipality and population by gender and age groups are publicly available by the DATASUS “Vital Statistics” and “Mortality Information System” (SIM). We obtained the São Paulo data aggregated by sample area from the “São Paulo State System for Data Analysis Foundation” (SEADE), with no access to individual information.

The motivation for choosing such outcomes and periods results from two significant theoretical concerns. The first refers to the quality of death data on the national scale. To avoid the impact of sub-notification by cause of death in the North and Northeastern regions of the country, using causes grouped in the avoidable deaths reduces uncertainty in the calculated relative risks by municipality. In this sense, using the most recent data, from 2013 to 2017, helps to reduce uncertainty since data quality has been improving year by year in Brazil. The second point concerns the intra-municipal scale. At this scale, for which death data are of high quality in the municipality of São Paulo, we chose to study deaths related to circulatory system diseases (ICD-10: I00-I99), since this is an outcome admittedly known to be associated with socioeconomic conditions. Deaths occurred from 2006 to 2009, very close to the 2010 Demographic Census. Data were indirectly standardized by gender and detailed age range in the two scales using the software SaTScan [27].

We used simple linear regression models to validate the explanatory power of GeoSES on health. We compared the regression of outcomes with GeoSES (and its dimensions), against the regression of outcomes with HDI-M (and its components). See S1 and S2 Datasets.

It started with the verification of the assumptions for the Ordinary Least Squares regression between the outcomes and the studied indices and the spatial dependence analysis on the residues [28]. We used the geographic coordinates of the municipal headquarters in the analyzes for Brazil and the displaced coordinates of the sample areas for the intra-municipal analyzes of São Paulo. In this case, the displacement was made due to the heterogeneity of the population distribution in the peripheral sample areas, where there are dams and environmental protection sparsely populated areas. Due to the occurrence of spatial dependence on residues at both aggregation scales, we applied geographically weighted regression (GWR) models calculated in the ArcGIS 10.1 program (“Adaptive” Kernel analysis; Bandwidth Parameter method, with 53 neighbors on the national scale, and 30 in the intra-municipal). GWR is a regression that allows exploring spatial heterogeneity on data, which exists when the process being modeled varies across the study area. We evaluated the models via resulting AIC (Akaike Information Criterion) values, according to which lower values indicate a better fit of the model [29]. A spatial model with good fit should yield no spatial autocorrelation on its residues meaning that the most important variables explaining spatial variability were addressed. To verify spatial dependence on the residues, we calculated the Moran’s I coefficients for the standardized residuals and their p values in the GeoDa program. Moran’s I coefficient measures the likelihood that an apparent spatial pattern was produced merely by chance or if there is an effect of distance on the distribution of a variable. The coefficient ranges from -1 to 1 and is equal to zero when there is no effect of the distance. We used a “Queen” neighborhood matrix, a contiguity-based relation due to the presence of irregular polygons with varying shape and surface (municipalities and sample areas). First-order Queen contiguity defines a neighbor when they have at least a point in common on their border. A significant spatial pattern was defined when p <0.05.

The results show that, on a national scale, the model with GeoSES presented a better fit (AIC: -4,583.44), when compared to the one considering the HDI-M (AIC: -524.22), although both had presented spatial dependence on its residues (Table 2). Models with the dimensions of poverty, deprivation, income, and segregation best explained the relative risk of avoidable mortality from 5 to 74 years in Brazil, without spatial dependence on their residues. Among the dimensions of this index, the model that most explains the spatial variability of risk is with the poverty dimension (Table 2). The map in Fig 3 shows the observed risks and the risks explained by GeoSES-BR/poverty. The mobility dimension was not a deterministic criterion to characterize socioeconomic differences on the national scale and did not contribute to GeoSES-BR. Almost 44% of the spatial variability is explained by the model with the poverty dimension, which can be realized by the visual similarity among the observed and explained maps. The most striking differences among them occur in the Northern portion of the country where observed risks (map A) are higher than expected (map B) due to the socioeconomic context. This difference may be due to health assistance or another factor not addressed in the model that should be further investigated.

Table 2

Results of simple geographically weighted regression models (GWR) between standardized relative risk of avoidable mortality from 5 to 74 years and indices (HDI-M and GeoSES-BR) and their dimensions–adjusted global R2 values, Akaike Criterion Information (AIC), Moran’s I Coefficients and p-value for spatial dependence on residues.

Indicator	Adjusted global R2	AIC	Moran’s I Coefficient	p-value
HDI-M	0.504	-524.22	0.016	0.014^
HDI/education	0.406	-3,817.45	0.017	0.008^
HDI/longevity	~	~	~	~
HDI/income	0.529	-1,017.92	0.017	0.010^
GeoSES-BR	0.422	-4,583.44	0.015	0.029^
GeoSES/income	0.428	-4,636.58	0.009	0.107
GeoSES/education	0.434	-3,290.28	0.015	0.013^
GeoSES/wealth	0.398	-4,344.18	0.022	0.002^
GeoSES/deprivation	0.428	-4,648.99	0.000	0.465
GeoSES/segregation	0.380	-4,073.14	0.011	0.066
GeoSES/poverty	0.436	-4,702.75*	0.012	0.067

* best fit

^spatial dependency on residues

~local multicollinearity does not allow modeling

Fig 3

Relative risks of mortality from avoidable causes of deaths (from 5 to 74 years old) due to interventions at the Brazilian health system in Brazil (2013 to 2017).

3A) Observed relative risk. 1B) Estimated relative risk explained by the model with GeoSES-BR/poverty. Data sources: Brazilian Institute of Geography and Statistics and, Department of the Unified Health System (DATASUS). Geographic Coordinate Systems SIRGAS 2000.

At the intra-municipal scale, the model with GeoSES-IM explains about 67% of the outcome variability (AIC: -357.86). In this case, the synthesis of dimensions made a definite contribution, since no single dimension outperformed GeoSES-IM (Table 3). Fig 4 allows the comparison between observed and explained values. Full regression model results are available as S1 and S2 Tables. In the municipality of São Paulo, the model with GeoSES-IM overestimated the relative risks in the outskirts of the study area. This means that given the socioeconomic context of the areas, the observed relative risk should have been higher. Those areas correspond to parks of natural vegetation with very small populations. Thus, differences may be attributed to the effect of small population size because rates based on a few deaths are highly variable.

Table 3

Results of simple linear geographically weighted regression models (GWR) between relative risks of mortality from circulatory system diseases in the municipality of São Paulo and GeoSES-IM index and its dimensions–values of adjusted global R2, Akaike Information Criterion (AIC), Moran’s I coefficient and p-value for spatial dependency on residues.

Indicator	Adjusted global R2	AIC	Moran’s I Coefficient	p-value
GeoSES-IM	0.673	-357.86*	-0.032	0.196
GeoSES/income	0.644	-333.42	-0.020	0.331
GeoSES/education	0.649	-338.72	-0.029	0.213
GeoSES/wealth	0.618	-313.86	-0.012	0.436
GeoSES/deprivation	0.594	-297.72	-0.037	0.146
GeoSES/segregation	0.651	-338.15	-0.023	0.298
GeoSES/poverty	0.628	-313.28	-0.041	0.117
GeoSES/mobility	0.574	-276.01	-0.026	0.261

* best fit

Fig 4

Relative risks of mortality from circulatory system diseases (2006 to 2009) in São Paulo (SP).

4A) Observed relative risk. 4B) Estimated relative risk explained by the model with GeoSES-IM. Data sources: Brazilian Institute of Geography and Statistics and, Department of the Unified Health System (DATASUS). Geographic Coordinate Systems SIRGAS 2000, UTM Projection, Fuse 23 South.

Therefore, GeoSES showed significant explanatory potential in both studied scales. Because health has multiple causes, including biological, behavioral, and contextual features, GeoSES is not expected to clarify all spatial variability of an outcome. Even in the area-based level, other aspects contribute to the understanding of phenomena, such as conditions of the natural and built environment, access and quality of health services, and political and macroeconomic issues.

Discussion

Regarding the relationship between socioeconomic conditions and health, despite being a theme of the origin of Social Epidemiology, there are still disagreements as to the definition of its indicators and the contribution they exert [30-32].

The current consensus reaffirms the complexity of the theme by noting that there is no universal indicator that can explain all outcomes [9]. Thus, it is common to choose a one-dimensional variable to represent it, resulting in simplifications that do not contribute to the understanding of the studied problem. It is also trivial to use indices not designed for that purpose and that do not allow pointing the most urgent actions that should be taken by the decision-makers.

In this study, we presented an index capable of synthesizing seven dimensions that make up the socioeconomic context, allowing a global assessment of the context and its particularities from different aspects. The GeoSES does not intend to explain all the determinants of health but allows us to identify if the socioeconomic context is related to the studied outcome, how much and which aspects stand out. Residential segregation in Brazil–although conceptually very relevant–has been poorly evaluated in health studies [32]. Primarily on an intra-municipal scale, residential segregation is reflected in many outcomes. Highlighting it can encourage affirmative social inclusion policies. If poverty best explains the relative risk of avoidable mortality from 5 to 74 years due to interventions at the Brazilian Health System in Brazil on the national scale, it means that the focus still should be on ensuring minimum income for a part of the population.

Since we implemented GeoSES in a programming language, one can easily update it for each edition of the Demographic Census. It can also be adapted to the previous Census. Besides, other versions of GeoSES can be developed, allowing for their enhancement by including dimensions not covered in this first version.

It is noteworthy, however, that there is a significant correlation of the new index with the HDI-M because the data set used to compose them is similar. Though, there is an advantage since it is possible to break the new index down to seven dimensions, unlike the HDI-M, which uses only three. Furthermore, the intra-urban index generation allows health managers to make decisions at the municipal level by observing similarities/differences among regions of the same city.

The elaboration of GeoSES starts from theoretical references according to data availability but allows the most explanatory variables to be chosen mathematically by statistical analysis. In this sense, the most explanatory variable is not arbitrary, but the most discriminating, and may differ according to the region under analysis (national, state, and municipal). It brings an innovative and insightful perspective for understanding what is most relevant in the socioeconomic context of each Brazilian region. For example, the most significant dimension at the national level is poverty; for São Paulo state, it is the residential segregation of the educational context; for the state of Rio Grande do Norte, income is the most critical dimension. Taking the sample area as an example, when comparing the principal variable in the education dimension, in the municipality of São Paulo, the percentage of people with superior level is the variable for discrimination among areas while in the municipality of Salvador (Bahia) is the percentage of people in the low educational level. Segregation seems to be central in the intra-municipal settings of the metropolitan areas, while mobility may be more relevant in other-sized municipalities. Thus, GeoSES is a robust tool for carrying studies on health and in other areas of knowledge, such as geography, sociology, and economics.

The potential contribution of a tool must be assessed given the limitations involved in its design and application. Some are inherent to the option for constructing a composite indicator. In this regard, we tried to minimize the main points when possible. One of the main objections is the selection of indicators. Here, we performed a literature search to identify the most used socioeconomic indicators on health research to include the corresponding dimensions in the composite indicator.

Another point concerns the interpretation of the index. As we defined a scale of negative and positive values, the composite index is intuitive by itself. If further information is needed to understand the variables which lead to a low GeoSES it is possible to identify the variables that compose the index in each dimension. Comparing the variables in their original units among the geographic units is a way to allow better interpretation. For instance, in the dimension “poverty” (variable P_POBREZA), it is possible to go from the best value in Brazil (2.1% in Carlos Barbosa) to the worst (91.5% in Marajá do Sena). Poverty was the most important dimension in the principal component. Policymakers should continue to focus on cash transfer programs associated with other ways to reduce it in the country.

The subject judgment also raises as a potential constraint in composite indicators. In this sense, the PCA minimizes the subjectivity since it drives the choice of the most discriminant variables, defining their weights.

Concerning the limitations in the index application, as the Brazilian demographic censuses provide data at one point in time every 10 years, the effectiveness of using Census data depends on the health outcome studied. Associations between distal social determinants and population health depend on the time lags between exposure to these risk factors and their effects on different types of health outcomes [33]. Thus, lags are widely variable. For instance, for acute or infant mortality, it makes sense to have proximity between both health and socioeconomic population data. For chronic diseases, on the other hand, lags of 20 years are expected to be more plausible [34]. Although this lag time imprecision, Census data allow a comparative spatial evaluation between the rates and risk factors and identify associations due to social-spatial inequalities occurring at the same point in time.

Other sensitive points regarding Census data are changes in the questionnaires from one Census to other and trends to cut or severely hamper Census and public health information that has occurred internationally [35]. Thus, when one chooses several variables whose meaning expresses the intended “dimension” and lets the principal component analysis point out which is the most important to explain it, the "dimension" in the two or more censuses can be compared. Actually, this is an advantage of the index, since the theoretical background of the dimensions is preserved even if there are changes in the variables among censuses. Regarding cuts in the next Census, the experimental questionnaires last available (June 2019) show a significant reduction in questions about household features and its surroundings. Due to the coronavirus pandemics in course, the Brazilian government has just decided to postpone the 2020 Demographic Census to 2021 (experimental questionnaires in the 2021 Census are available at https://www.ibge.gov.br/media/com_mediaibge/arquivos/19361f45cc3e3b003f0a552ecde1c45f.pdf and https://www.ibge.gov.br/media/com_mediaibge/arquivos/ee88a6181125873a8acd7b8c7ab9ad3c.pdf, in Portuguese). Comparing to the variables used in GeoSES 2010, the only affected dimension will be the material deprivation, since the ownership of various items will not be included in the basic or sample questionnaires. Based on the preliminary questionnaires, the following items will not be present in 2021: access to electric energy, ownership of television, refrigerator, cell phone, computer, motorcycle and, automobile. Nevertheless, among those that will remain, PCA will help to define the most discriminant that will help to measure material deprivation and access to public services.

The provided results–interactive maps and tabulated values by region of interest–may contribute to relevant future actions. In the scientific field, the index can support studies of the specific aspects of health inequalities and the mechanisms that lead to them. In practical terms, the index may guide the elaboration of intersectoral public policies or in state and municipal administrations.

Abstract in portuguese.

(PDF)

Click here for additional data file.

List of input variables for creating GeoSES.

(DOCX)

Click here for additional data file.

Dataset including the variables used in the geographically weighted regressions for Brazil.

(XLS)

Click here for additional data file.

Dataset including the variables used in the geographically weighted regressions for São Paulo.

(XLS)

Click here for additional data file.

Geographically weighted regression results of models for the relative risk of causes of deaths (from 5 to 74 years old) in Brazil due to interventions at the Brazilian health system in Brazil (2013 to 2017).

(DOCX)

Click here for additional data file.

Geographically weighted regression results of models for the relative risk of mortality from circulatory system diseases in the municipality of São Paulo (2006 to 2009).

(DOCX)

Click here for additional data file.

10 Feb 2020

PONE-D-19-35982

GeoSES: a socioeconomic index for health and social research in Brazil

PLOS ONE

Dear Prof Barrozo,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

This is a very interesting paper and an important contribution. Based on the reviewers´ comments and my own reading I still believe the paper needs some revision. The reviewers comments are detailed below. Please, considered the very careful suggestions they made:

revised the organization and presentation of the material

review the paper to present a clear and transparent as regards the explanation and justification of the methodological choices

improve the discussion of limitations of your approach

improve discussion (theoretical and methodological) of variables choice.

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Reviewer #1: This paper aims to introduce the GeoSES, a composite index that summarizes the main dimensions of the Brazilian socioeconomic context for health research purposes, to evaluate and monitor inequalities, and to develop resource and service allocation strategies.

I would first congratulate the Authors of this manuscript of their extensive work. However, there are some important issues, listed below, that should obligatory be discussed / corrected / improved.

1 - In my opinion, the main contribution of the paper is methodological and the authors should highlight and discuss this. If the authors don’t agree with my opinion, then it would be good for them to advance a little bit.

2 –Intra-municipal index (lines 102-103). I suggest that the authors bring (and discuss, if necessary) how many municipalities, among 5,565, fit this criterion. (“GeoSES-IM, for municipalities with three or more Census sample areas”).

3 - How effective is the index for health research taking into account that the data is ~10 years ago? The authors could discuss this in the discussion section, conclusion section or in a section about the limitations of the work.

4 – Lines 417-420. The authors state that the index "can easily update it for each edition of the Demographic Census." There is an important discussion in Brazil about what the 2020 Census will look like and what issues will remain in the questionnaire, since the government has already signaled for the budget cut, which will affect the size of the questionnaire and so on. Therefore, it can be imagined that some variables used in this study will no longer be there as of the next Census. How do the authors see this and what could be proposed? Furthermore, and assuming that some variables will not be in the next Census, or were not in previous censuses, how can the index be compared in time and space? I would appreciate a discussion about it in the paper.

Reviewer #2: This is a potentially interesting paper describing a new composite index of socio-economic well-being (the so-called GeoSES) for the more than 5500 municipalities in Brazil around 2010. Such index, which is constructed on the basis of the 2010 Census data, could be potentially used both by researchers and policy-makers. Yet, there are many aspects of the paper that should be improved.

1. In general, the paper is not very clearly written, and in some sections, it is confusing. While readers acquainted with the literature on the construction of composite indices might have an intuition of what the authors are talking about, this might not be the case for the general reader. In addition, some references look arbitrary or strange. The literature on epidemiology and health inequalities is huge, and the authors have chosen a curious selection for their reference list. Last but not least, the paper needs a thorough English revision.

2. The paper needs to be much more clear and transparent as regards the explanation and justification of the methodological choices. This applies to the entire “Methods” section (i.e. from page 5 to page 11). For instance:

- What is the meaning of the segregation component? From its definition, I understand it can take negative values. How is that interpreted?

- The authors are mixing all kinds of variables, very often going in opposite directions, so to say. For instance, higher values of the income variable are normatively desirable, whereas higher values of the poverty variable are normatively undesirable. If all the data crunching exercise has to have some meaning, it is crucial that all the variables point to the same direction (e.g. the higher the values, the better/the more desirable). It is unclear to me if this basic recoding exercise has been carried out by the authors.

- The subsection of “Data collection and processing” is particularly obscure.

- In the “Preprocessing” subsection the authors say they have added a value of 10 to their indicators to avoid problems with the zeroes, arguing that this does not affect the correlation structure of the data. This looks like an extremely arbitrary decision. Why not adding 1, or 100? What would happen to the results for these alternative choices? If the results are overly sensitive to the values of such constant, perhaps the use of PCA techniques is not the best one.

- When explaining the steps followed to construct the GeoSES index, it is unclear to me why do the authors need to perform PCA up to three times. I understand the first one (to generate aggregate indices within each of the six/seven dimensions) and the second one (to bring all dimensions together into an overall component). Why then a third round of PCA? More explanations and justifications should be provided.

- It would be helpful if the authors explained what do the extreme GeoSES values of -1 and 1 truly mean. That is: what would need to happen in a municipality to get a score of 1?

- Again, the subsections of “Interpretation” (page 10) and “GeoSES extensive creation” are unclear.

Very often, the authors take many things for granted and do not explain them (or even show a reference). Examples: Explaining what Moran’s I coefficient is and what it means, the same for the Geographically Weighted Regression models (GWR), the “Queen” neighborhood criterion to choose neighbors, and so on and so forth. Again, even if these are well-known methods for the specialist, they might be unknown to the general reader.

3. In the empirical section of the paper where the authors “prove” the validity of their measure by predicting certain health outcomes, the text lacks order and clarity. The authors add decorative maps (e.g. Figures 3 and 4) that are barely mentioned in the text, but nothing substantive comes out of them.

4. The authors try to sell the relevance of their approach by highlighting the limitations of currently existing approaches (e.g. like the municipal level HDI, or HDI-M). Yet, they should also point out the several limitations of their own approach. There is no such thing as “a perfect measure”, and all approaches have their advantages and disadvantages. For instance: (i) Composite indices have the advantage of simplifying complex information, at the cost of hiding important patterns that might exist in the data. (ii) In this line, composite indices are sometimes difficult to interpret, as they are made up by averaging all sorts of variables (e.g. a GeoSES score of, say, 0.1, might be obtained from high levels of poverty and low levels of segregation, or from very low education levels and high incomes, and so on). Thus, when policy makers have to make decisions on the basis of the GeoSES index, it is crucially important to know the values of the underlying variables. (iii) The use of PCA techniques might complicate comparisons over time. If the GeoSES index wants to be replicated with the new (2020?) Census or with previous censuses, the different components of the index will get different weights. Thus if the GeoSES index equals 0.2 in year 2010 and 0.3 in year 2020, we do not know if there has been a real improvement in the underlying variables or simply a variable reweighting through the PCA algorithm (or both of them simultaneously). (iv) PCA is one among several other dimensional-reduction techniques. Why not using, say, Factor Analysis?

5. In several parts of the paper, the authors state that the choice of variables included in the GeoSES index was driven by theoretical considerations. Looking at the list of selected variables and the standard questionnaires included in Censuses, I would rather say that the choice was driven by data availability issues.

**********

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Reviewer #2: Yes: Iñaki Permanyer

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23 Mar 2020

Dear Academic Editor and Reviewers,

We appreciate the editors' and reviewers' work on our article. In the revised version we addressed all the reviewers' concerns, with a significant rewriting of the main sections to present our contributions, better explaining the theoretical and methodological foundations, and also improving discussions towards the limitations of our approach as well as the choice of the variables.

In this letter, we have addressed point by point the issues raised by the reviewers. In the manuscript itself, we have highlighted the text changes in blue, except for minor changes, to lessen clutter.

Summary of changes

We start with a summary of the main changes:

- Introduction: improved description of the main result and contributions;

- Methods:

o better explaining the segregation component;

o including justifications for theoretical and methodological choices;

o clarifying the algorithm steps and their objectives;

o pointing out how to interpret the results;

- Results: explanations of the statistical methods used for GeoSES validation;

- Discussion: extension of the applicability and limitations of our work, and the availability of the used data.

Next, we comment the Journal Requirements and address in detail the reviewers' comments.

Journal Requirements

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at http://www.plosone.org/attachments/PLOSOne_formatting_sample_main_body.pdf and http://www.plosone.org/attachments/PLOSOne_formatting_sample_title_authors_affiliations.pdf

We checked the style requirements according to the provided links. We are confident that the final manuscript fulfills the requirements.

2. Please include a copy of Table 3 which you refer to in your text on page 17.

Thank you for the observation. Tables 3 and 4 are the same: we have numbered the tables incorrectly. Now, we corrected the number of the table in the text and in the material support files.

3. We note you have included a table to which you do not refer to the text of your manuscript. Please ensure that you refer to Table 4 in your text; if accepted, production will need this reference to link the reader to the Table.

As mentioned above, it was a numbering error: there are only three tables in this paper. Table 4 in the text and Table 3 refer to the same information.

Answers to Reviewer #1

Reviewer #1: This paper aims to introduce the GeoSES, a composite index that summarizes the main dimensions of the Brazilian socioeconomic context for health research purposes, to evaluate and monitor inequalities, and to develop resource and service allocation strategies.

I would first congratulate the Authors of this manuscript of their extensive work. However, there are some important issues, listed below, that should obligatory be discussed / corrected / improved.

We appreciate the reviewer's positive reception of our work and their comments that allow us to improve our article.

1 - In my opinion, the main contribution of the paper is methodological and the authors should highlight and discuss this. If the authors don’t agree with my opinion, then it would be good for them to advance a little bit.

We thank the reviewer for this observation, but we kindly disagree. The primarily intended contribution is to provide a tool - the index - to enhance health and social research, which need to understand/estimate the burden of the problems attributable to the different social dimensions. The contribution of the article is more in the application domain than in the methodological domain. Although the methodological aspect is crucial to the acceptance and broader utilization of the index, this approach does not represent an innovation per se, since it relies on traditional statistical analysis (mainly, Principal Component Analysis). In the application perspective, however, the use of techniques in the scales studied and in the territorial scope is unprecedented. We showed the validity of the index, and it has already been successfully used in Takano et al. (2019) and Santos et al. (2020). We highlighted our contribution in the Introduction of the final manuscript.

2 –Intra-municipal index (lines 102-103). I suggest that the authors bring (and discuss, if necessary) how many municipalities, among 5,565, fit this criterion. (“GeoSES-IM, for municipalities with three or more Census sample areas”).

It is a good observation. The Brazilian population is spatially dispersed. In 2010, from 5,565 Brazilian municipalities, 4,967 (89,3%) had less than 50,000 inhabitants. Because of this, only 140 municipalities present three or more sample areas (that is, had more than 190,000 inhabitants, the minimum required population to define sample areas by the Census).

However, GeoSES covers the entire Brazilian population due to the BR and UF levels. We can assess almost 45% of the population at an even more detailed level, through the IM level, which is a novelty. Although there are few municipalities with 190k inhabitants, we are talking about the most significant areas in terms of population density.

3 - How effective is the index for health research taking into account that the data is ~10 years ago? The authors could discuss this in the discussion section, conclusion section or in a section about the limitations of the work.

Associations between distal social determinants and population health depend on the time lags between exposure to these risk factors and their effects on different types of health outcomes (LYNCH et al., 2005). Thus, lags are widely variable. For instance, for acute or infant mortality, it makes sense to have proximity between both health and population data. For chronic diseases related to the consumption of alcohol and tobacco, on the other hand, lags of 20 years are expected to be more plausible (JIANG et al., 2018). In the literature, most studies try to keep health data close to the Census to have a better denominator of the population for the calculated rates. Few studies have discussed this critical issue. Kim (2019) used average lag periods between 3 to 17 years, according to the different social determinants analyzed to study firearm-related homicides. Studying life expectancy, OECD (2017) used explanatory factors lagged by five years to account for the delayed effects on health. The association between Social Determinants of Health indices and premature mortality (defined as death before age 75 years) in Chicago was measured by years of potential life lost and aggregated to a 5-year mean (2009-2013) and calculated as an age-adjusted rate at the census tract level. All variables derive from the 2014 American Community Survey 5-year mean (KOLAK et al., 2020). Thus, the length of the lag is not precise in the literature yet. Although this lag time imprecision, Census data allow a comparative spatial evaluation between the rates and risk factors and to identify associations due to social-spatial inequalities occurring at the same point in time. We introduced such a discussion and references to the final manuscript.

4 – Lines 417-420. The authors state that the index "can easily update it for each edition of the Demographic Census." There is an important discussion in Brazil about what the 2020 Census will look like and what issues will remain in the questionnaire, since the government has already signaled for the budget cut, which will affect the size of the questionnaire and so on. Therefore, it can be imagined that some variables used in this study will no longer be there as of the next Census. How do the authors see this and what could be proposed? Furthermore, and assuming that some variables will not be in the next Census, or were not in previous censuses, how can the index be compared in time and space? I would appreciate a discussion about it in the paper.

We appreciate the reviewer for bringing this point to the light. It surely deserves a more in-depth discussion. We start it quoting Wilson et al., (2017), stating that “over the past few years, trends to cut or severely hamper census and public health information have occurred internationally”. Such a statement relates to Canada, the United Kingdom, the United States of America, and the European Union.

Brazil follows the same lack of cost-benefit analysis of the Census related to public policies and public health interventions. Due to the coronavirus pandemics in course, the Brazilian government has just decided to postpone the 2020 Demographic Census to 2021. Regarding cuts in the next Brazilian Demographic Census, the experimental questionnaires last available (June 2019) show a significant reduction in questions about household features and its surroundings (experimental questionnaires in the 2020 Census are available at https://www.ibge.gov.br/media/com_mediaibge/arquivos/19361f45cc3e3b003f0a552ecde1c45f.pdf and https://www.ibge.gov.br/media/com_mediaibge/arquivos/ee88a6181125873a8acd7b8c7ab9ad3c.pdf, in Portuguese).

Brazilian censuses always have suffered changes from one decade to others, for other reasons beyond budget cuts. For instance, when we intend to express the material deprivation dimension measuring how many material resources and conveniences that are part of modern life a person has (such as adequate housing, car ownership, refrigerator, computer, among others) the questionnaire must include goods that are available for a significant part of the population. In 2000, the cell phone was not a good widely afforded for Brazilians and did not enter in the questionnaire. However, in 2010 cell phone was added to the questionnaire, and other items as video cassette recorder and microwave oven were no longer inventoried as they had been in 2000. Thus, when one chooses several variables whose meaning expresses the intended “dimension” and lets the principal component analysis (PCA) point out which one best explains the variability of the data, the "dimension" in the two or more censuses can be compared.That is an advantage of the index since the theoretical background of the dimensions is preserved even if there are changes in the variables among censuses.

Comparing to the variables used in GeoSES 2010, the only affected dimension will be the material deprivation, since the ownership of various items will not be included in the basic or sample questionnaires. The following items will not be present in 2020: access to electric energy, ownership of television, refrigerator, cell phone, computer, motorcycle and, automobile. Nevertheless, among those that will remain, PCA will help to select the variable that best explains the material deprivation and access to public services.

We incorporated such a discussion in the final manuscript.

Answers to Reviewer #2

Reviewer #2: This is a potentially interesting paper describing a new composite index of socio-economic well-being (the so-called GeoSES) for the more than 5500 municipalities in Brazil around 2010. Such index, which is constructed on the basis of the 2010 Census data, could be potentially used both by researchers and policy-makers. Yet, there are many aspects of the paper that should be improved.

We thank the reviewer for recognizing the academic and government potential of our work.

1. In general, the paper is not very clearly written, and in some sections, it is confusing. While readers acquainted with the literature on the construction of composite indices might have an intuition of what the authors are talking about, this might not be the case for the general reader. In addition, some references look arbitrary or strange. The literature on epidemiology and health inequalities is huge, and the authors have chosen a curious selection for their reference list. Last but not least, the paper needs a thorough English revision.

We acknowledge that some used terms are specific-area related. We respond to this suggestion by broadening the understanding of terms for general readers. We also made another English revision to enhance the writing.

Regarding literature choice, we honestly and kindly disagree with the reviewer. We cited papers that addressed some issues related to the individual x area-level socioeconomic indicators, the choice of socioeconomic indicators for ecologic studies, methods to define a socioeconomic index, or related to the social determinants of health. Some important specific issues are sometimes described as not the main topic of the cited papers and published in journals not dedicated to Epidemiology, which leads to the impression that the references are curious. Nevertheless, all of them support the ideas where we cited them in the text. Michel Marmot, Nancy Krieger, and Anne V. Diez-Roux, for instance, are relevant authors from the Epidemiology and Social Epidemiology literature.

2. The paper needs to be much more clear and transparent as regards the explanation and justification of the methodological choices. This applies to the entire “Methods” section (i.e. from page 5 to page 11). For instance:

- What is the meaning of the segregation component? From its definition, I understand it can take negative values. How is that interpreted?

We better explained the segregation component, indicating that it varies from -1 (most deprived) to 1 (most privileged). A negative ICE means that the area presents more people in the condition of deprivation than in the higher extreme; a positive value, the opposite. A value of zero indicates that extreme concentrations of either of the two groups do not dominate the area.

- The authors are mixing all kinds of variables, very often going in opposite directions, so to say. For instance, higher values of the income variable are normatively desirable, whereas higher values of the poverty variable are normatively undesirable. If all the data crunching exercise has to have some meaning, it is crucial that all the variables point to the same direction (e.g. the higher the values, the better/the more desirable). It is unclear to me if this basic recoding exercise has been carried out by the authors.

It is not crucial that all the variables point to the same direction. The principal components analysis is concerned with explaining the variance-covariance structure through few linear combinations of the original variables (JOHNSON; WICHERN, 2007, Chapter 8). Variables that point to opposite directions have negative covariance and correlation, and their coefficients in the linear combinations (principal components) will have opposite signs. Examples can be found in Johnson and Whichern (2007) and Lalloué et al. (2013).

- The subsection of “Data collection and processing” is particularly obscure.

This section has two main objectives: a) to show how IBGE organize and made available the original data, and b) to describe how we treat such data to express its information in terms of percentage coverage of the population. For example, if there was initially a count of people without instruction in a municipality, we are now interested in knowing what percentage of the municipality's population this count represents.

We believe that objective b) is clear and justified in this and other parts of the text. However, objective a) may not be visible to readers who are not familiar with how IBGE makes Census data available. We thank the reviewer for calling our attention to this point, so we edited the text to characterize both objectives of the section better.

- In the “Preprocessing” subsection the authors say they have added a value of 10 to their indicators to avoid problems with the zeroes, arguing that this does not affect the correlation structure of the data. This looks like an extremely arbitrary decision. Why not adding 1, or 100? What would happen to the results for these alternative choices? If the results are overly sensitive to the values of such constant, perhaps the use of PCA techniques is not the best one.

The PCA is sensitive to data when identifying correlations between variables. However, the constant value was added to all data in the sample, causing its statistical distribution to remain the same. The purpose of this sum is to avoid the instability of the method during matrix inversion. Indeed, the choice of value 10 is random, but any constant value would have the same effect.

- When explaining the steps followed to construct the GeoSES index, it is unclear to me why do the authors need to perform PCA up to three times. I understand the first one (to generate aggregate indices within each of the six/seven dimensions) and the second one (to bring all dimensions together into an overall component). Why then a third round of PCA? More explanations and justifications should be provided.

We thank the reviewer for calling our attention to this topic. In the final manuscript, we better explained the purpose of each step:

1) The objective in this first step was to generate aggregate indices within each of the dimensions, and a PCA was performed in each of them. The number of components selected was such that the percentage of total variance explained was greater than or equal to 75%. For ease of interpretation, we considered the variables with the highest coefficient in each component.

2) Considering the variables selected in step 1, we applied another PCA, and we considered its first principal component. The objective here was to bring all dimensions together into an overall component.

3) In order to eliminate variables that have little contribution to the index obtained in step 2, only those whose absolute coefficient values were below the average of the coefficients were eliminated, and we applied the PCA method to the remaining variables. The resulting first component defines the GeoSES (Socioeconomic Index of Geographic Context for Health and Social Studies).

Also, we added the justification for applying the third PCA step: “In fact, the index obtained in step 2 could have been considered the final one. However, for its calculation, we would need to know the values of variables that do not have an important contribution. In Step 3, these variables were eliminated, and the coefficients of the remainder were calculated again, following the procedure presented in Lalloué (2013).”

- It would be helpful if the authors explained what do the extreme GeoSES values of -1 and 1 truly mean. That is: what would need to happen in a municipality to get a score of 1?

Extreme GeoSES values mean the worst and the best socioeconomic contexts in Brazil (for the national scale), in the Federation Unit (in the state) and, in the municipality (in the intramunicipal setting). In other words, to have a GeoSES of +1 at the national level, the municipality must have the best relative socioeconomic context of the country in the most discriminating variable.

We included the text below into the “Interpretation” section to clarify this point:

“Extreme GeoSES values mean the worst (-1) and the best (1) socioeconomic contexts in the analyzed scale. In other words, to have a GeoSES of 1 at the national level, the municipality must have the best relative socioeconomic context of the country in the most discriminating variable. So, if in 2010 a municipality had a GeoSES index of 0.2 and in 2021 the index is 0.3, there would be a relative improvement in the socioeconomic context because even with possible changes in the most discriminating variables, this municipality is closest to the best municipality than it was in 2010.”

- Again, the subsections of “Interpretation” (page 10) and “GeoSES extensive creation” are unclear.

In the section "Interpretation" we show how GeoSES can also be analyzed in terms of the dimensions that compose it, in addition to the final value itself. We can decompose GeoSES into multiple dimensions, so we use data from the most significant variable for each activated dimension to illustrate how they contribute to the final score. For example, in terms of Education, a municipality may have that dimension represented by the percentage of people with complete higher education. The perception of the "advance" or "backwardness" of this municipality in this dimension must also be carried out in comparison with other municipalities.

The section "GeoSES extensive creation" tells how the methodology developed and evaluated for the municipality of São Paulo was implemented in programming language for the generation of GeoSES throughout the national territory, at its three levels: BR, UF, and IM. The section ends by describing computational aspects of the resulting source code.

We have edited both sections to make reading and understanding easier for the general reader.

Very often, the authors take many things for granted and do not explain them (or even show a reference). Examples: Explaining what Moran’s I coefficient is and what it means, the same for the Geographically Weighted Regression models (GWR), the “Queen” neighborhood criterion to choose neighbors, and so on and so forth. Again, even if these are well-known methods for the specialist, they might be unknown to the general reader.

Indeed, the text needs clarity on these points to be more accessible to a broader public. We explained these particularities, as follows. The blue text is the new one.

FROM: Due to the occurrence of spatial dependence on residues at both aggregation scales, we applied geographically weighted regression models calculated in the ArcGIS 10.1 program (“Adaptive” Kernel analysis; Bandwidth Parameter method, with 53 neighbors on the national scale, and 30 in the intra-municipal). We evaluated the models via resulting AIC (Akaike Information Criterion) values, according to which lower values indicate a better fit of the model [29]. To verify spatial dependence on the residues, we calculated the Moran’s I coefficients for the standardized residuals and their p values in the GeoDa program.

TO: Due to the occurrence of spatial dependence on residues at both aggregation scales, we applied geographically weighted regression (GWR) models calculated in the ArcGIS 10.1 program (“Adaptive” Kernel analysis; Bandwidth Parameter method, with 53 neighbors on the national scale, and 30 in the intra-municipal). GWR is a regression that allows exploring spatial heterogeneity on data, which exists when the process being modeled varies across the study area. We evaluated the models via resulting AIC (Akaike Information Criterion) values, according to which lower values indicate a better fit of the model [29]. A spatial model with good fit should yield no spatial autocorrelation on its residues meaning that the most important variables explaining spatial variability were addressed. To verify spatial dependence on the residues, we calculated the Moran’s I coefficients for the standardized residuals and their p values in the GeoDa program. Moran’s I coefficient measures the likelihood that an apparent spatial pattern was produced merely by chance or if there is an effect of distance on the distribution of a variable. The coefficient ranges from -1 to 1 and is equal to zero when there is no effect of the distance. We used a “Queen” neighborhood matrix, a contiguity-based relation due to the presence of irregular polygons with varying shape and surface (municipalities and sample areas). First-order Queen contiguity defines a neighbor when they have at least a point in common on their border. A significant spatial pattern was defined when p <0.05.

3. In the empirical section of the paper where the authors “prove” the validity of their measure by predicting certain health outcomes, the text lacks order and clarity. The authors add decorative maps (e.g. Figures 3 and 4) that are barely mentioned in the text, but nothing substantive comes out of them.

We enhanced the descriptions of Figures 3 and 4, describing how the observed results confirm the correlations of socioeconomical development with the phenomena under study. For the sake of completeness, we reproduce here the further introduced explanations:

For Figure 3: “Almost 44% of the spatial variability is explained by the model with the poverty dimension, which can be realized by the visual similarity among the observed and explained maps (Fig 3). The most striking differences among them occur in the Northern portion of the country where observed risks (map A) are higher than expected (map B) due to the socioeconomic context. This difference may be due to health assistance or another factor not addressed in the model that should be further investigated.”

For Figure 4: “In the municipality of São Paulo, GeoSES-IM overestimated the relative risks in the outskirts of the study area. This means that given the socioeconomic context of the areas, the observed relative risk should have been higher. Those areas correspond to parks of natural vegetation with very small populations. Thus, differences may be attributed to the effect of small population size because rates based on a few deaths are highly variable and may be unreliable.”

4. The authors try to sell the relevance of their approach by highlighting the limitations of currently existing approaches (e.g. like the municipal level HDI, or HDI-M). Yet, they should also point out the several limitations of their own approach. There is no such thing as “a perfect measure”, and all approaches have their advantages and disadvantages. For instance:

(i) Composite indices have the advantage of simplifying complex information, at the cost of hiding important patterns that might exist in the data.

Indeed, this is one of the critiques of the composite index. Because of this constraint, we believe that keeping the different dimensions with few variables in each avoid hiding the patterns. This approach allows an in-depth analysis of the social context. We addressed this point, adding the following text into the Discussion section of the final manuscript:

“The potential contribution of a tool must be assessed in view of the limitations involved in its design and application. Some are inherent to the option for constructing a composite indicator. In this regard, we tried to minimize the main points when possible. One of the main objections is the selection of indicators. Here, we performed a literature search to identify the most used socioeconomic indicators on health research to include the corresponding dimensions in the composite indicator.

Another point concerns the interpretation of the index. As we defined a scale of negative and positive values, the composite index is intuitive by itself. If further information is needed to understand the variables which lead to a low GeoSES it is possible to identify the variables that compose the index in each dimension. Comparing the variables in their original units among the geographic areas is a way to allow better interpretation. For instance, in the dimension “poverty” (variable P_POBREZA), it is possible to go from the best value in Brazil (2.1% in Carlos Barbosa) to the worst (91.5% in Marajá do Sena). Poverty was the most important dimension in the principal component. Policymakers should focus on cash transfer programs or other ways to reduce it in the country.

The subject judgment also raises as a potential constraint in composite indicators. In this sense, the PCA minimizes the subjectivity since it drives the choice of the most important variables, defining their weights.”

(ii) In this line, composite indices are sometimes difficult to interpret, as they are made up by averaging all sorts of variables (e.g. a GeoSES score of, say, 0.1, might be obtained from high levels of poverty and low levels of segregation, or from very low education levels and high incomes, and so on). Thus, when policy makers have to make decisions on the basis of the GeoSES index, it is crucially important to know the values of the underlying variables.

We agree with the reviewer that "when policy makers have to make decisions on the basis of the GeoSES index, it is crucially important to know the values of the underlying variables". Multiple combinations of dimensions and variables can explain the final GeoSES score. We emphasize here, again, that GeoSES must be interpreted in a comparative way between regions (municipalities or weighted areas) of the same analysis (BR, UF, or IM). The score alone does not have an isolated semantic value, as we have pointed out in other responses and highlighted in the text of the revised manuscript. That is why we introduced in section "Interpretation" how values must be understood.

(iii) The use of PCA techniques might complicate comparisons over time. If the GeoSES index wants to be replicated with the new (2020?) Census or with previous censuses, the different components of the index will get different weights. Thus if the GeoSES index equals 0.2 in year 2010 and 0.3 in year 2020, we do not know if there has been a real improvement in the underlying variables or simply a variable reweighting through the PCA algorithm (or both of them simultaneously).

We addressed this point in a previous question. The primary purpose of the index is to allow to discriminate the differences among the socioeconomic contexts and spatial comparison among the geographic units in the considered level of aggregation. The best socioeconomic context (+1) drives a ranking among the following decreasing values. So, if in 2010 a municipality has a GeoSES index of 0.2 and in 2020 the index is 0.3, there was a relative improvement in the socioeconomic context because even with possible changes in the most discriminating variables, this municipality is closest to the municipality with the best social context (+1) than it was in 2010.

(iv) PCA is one among several other dimensional-reduction techniques. Why not using, say, Factor Analysis?

Indeed, we could have used a method of factor analysis. However, we would have to assume an a priori model. Furthermore, it is well known that in the Principal Components Solution of the Factor Model, which does not suppose any multivariate distribution for the data, the factor loadings are the scaled coefficients of the principal components. Thus, the results obtained by PCA and factor analysis will be, in this case, equivalents.

5. In several parts of the paper, the authors state that the choice of variables included in the GeoSES index was driven by theoretical considerations. Looking at the list of selected variables and the standard questionnaires included in Censuses, I would rather say that the choice was driven by data availability issues.

The comment is very pertinent. Besides theoretical considerations, data availability also drove the choice of the variables. What we meant is that it was not a choice based on our assumptions but that we chose the variables based on the literature from the available variables in the Brazilian Census.

Nevertheless, for the sake of completeness, we include mentions of data availability along with the text of the final manuscript.

References

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8 Apr 2020

GeoSES: a socioeconomic index for health and social research in Brazil

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17 Apr 2020

PONE-D-19-35982R1

GeoSES: a socioeconomic index for health and social research in Brazil

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