Ecuador is a middle-income country with a current per capita GNP of US$ 6.400 [37] located in the northwest of South America. With a total population of 16.9 million inhabitants recorded in the 2022 census [38], it is the second-smallest country in the Andean region. The country is divided into four natural regions (Sierra, Coast, Amazon, and Galapagos), 24 provinces, and 221 municipalities. Ecuador is mainly populated (72%) by Mestizos (mixed ethnic groups), followed by some minority groups: Afro-Ecuadorian/black (7%), Montuvio (7%), Indigenous (7%) and White (4%) [39].

The 2010 census was chosen since it was last available at the time this project started. The census collected information on 72 questions throughout the country in four main sections: housing conditions, household characteristics, migration, and population. The later section covered topics related to demographics, education, employment, social security, fertility, and mortality. The data are summarized in Table 1.

A total of 40.628 census sectors were included in the analysis at the national level, with a mean population size of 354 inhabitants (SD of 164.9) (Figure 2). Exclusion criteria were applied to the data set to include only houses with people present and people with habitual residence within the country and excluded 12 census sectors without individual and household information. In total, approximately 0.74% (103,369 inhabitants) of the total population registered in the original published census database were excluded.

Townsend, Carstairs, and a broader scope index using census data (the Ecuadorian Deprivation Index, or EDI) were calculated using the Ecuadorian 2010 Census and the census sector as a geographic area. All variables were aggregated from individual data at the census sector level and transformed into percentages.

For the selection of the deprivation indicators, overcrowding and unemployment (original variables) were kept for the Townsend and Carstairs indices, while ’not owned housing’ and a proxy of ’low social class’ were used as originally proposed by Townsend and Carstairs, respectively. A variable ’no car ownership’ was replaced by the no qualifications/education indicator, as proposed by Allik et al. [40] in the revised version of the Carstairs index for Scotland. The use of car ownership to measure deprivation has been criticised for not accurately representing the need for cars (instead of measuring wealth) in rural areas. Since this variable was not available from the census and is not social expectation in Ecuador, it was replaced by a variable related to education.

For the broader scope index (EDI index), a principal component analysis was performed on a total of 30 previously selected variables (40 variables selected from first screening and 10 discarded in the second screening) from the census questionnaire that were related to previous developments of deprivation indices. In particular, the scoping review by Zelenina et al. [13] (Table S2), who collected the indicators used in the development of 60 previous deprivation measures and the scoping review by Ichihara et al. [7] who described area deprivation measures used in Brazil were used as references to select the indicators for this study. Furthermore, the indicators used in previous studies related to Ecuador [14, 16, 17] (see Appendix 1) were also used as critical references to identify the indicators for this study. The first screening reviewed all variables of the census questionnaire (148 in total) and selected 40 that were related to the Townsend deprivation framework. In the second screening, 10 variables that were redundant because they showed the same phenomenon (i.e., the percentage of houses with damaged roofs and the percentage of houses with roofs in bad condition) were discarded. A number of 25 additional variables to the 5 used in the construction of the Townsend and Carstairs indices were identified, depicting education, socioeconomic characteristics, housing, and living conditions. The description of the indicators used in the principal component analysis (PCA) is presented in Supplementary Appendix 2. Principal component analysis was used to reduce the number of variables from these 30 to those variables that are highly correlated with the latent construct of deprivation. PCA can be used as a data reduction technique by identifying the principal components as linear combinations of the input variables that maximise the total variance [41, 42]. Therefore, PCA identified the variables that explain the highest proportion of the variability in the data and therefore those variables that have the highest correlation with the underlying deprivation construct are retained and those that are not are excluded.

A statistical test was performed to assess the suitability of the data before applying PCA. The overall Kasier-Meyer-Olkin sampling adequacy measure (KMO test) was 0.95, showing that the correlation patterns are compact (values close to 1). The KMO values for each of the 30 items (indicators) were found to be greater than 0.50. The Bartlett sphericity test is significant:ξ²(435) = 915061, (p < .001) supporting a correlation matrix statistically different from an identity matrix and a component analysis approach for investigating the data.

PCA was applied to the 30 previously selected variables to identify the variables that would be correlated with the first component. The results of this exploratory technique are presented in Figure 3, the scree plot identified a principal component, which explained 43.5% of the variance, the next component accounts only with 8.3% of the variance and the third 6.3% showing that the first component captures most of the information before the scree line considerably changes its angle. On the auxiliary PCA with only the selected fifteen variables the first component accounts for the 68% of the variability in the data. The variables for the EDI were selected based on the analysis of the correlation matrix and the results of the PCA analysis. Thirteen variables were selected from those that had loads greater than 0.7, common variance greater than 0.5 and contribution greater than average (1/30 = 3.3%). Additionally, two variables (low employment categories and overcrowding) were selected, given their proximity to previous cutoff points and their theoretical importance to the concept of deprivation. In total 15 indicators from 5 domains (see Table 2 for the descriptors of the variables used in the construction of Townsend, Carstairs, and EDI deprivation measures) were selected for the construction of the Ecuadorian deprivation index.

Figure 4 presents a biplot of the census sectors stratified by urban-rural classification (as used in Ecuadorian official statistics) and the indicators selected by the PCA. It can be observed that the 15 selected variables represent the latent concept of deprivation on the horizontal axis of the plot, and the rural sectors (green) are found to be plotted mostly on the right-hand side, meaning higher deprivation levels than urban census sectors for the same 15 indicators.

The variables were standardised, and the resulting Z-values were added together to obtain the measures for each index. This method of adding the resulting Z-values was followed by Townsend and Carstairs, meaning that each variable contributes an equal weight to the index.

The means of the standardised indicators for each of the five domains were calculated and added with equal weights to obtain the Ecuadorian deprivation index. Each domain was assigned the same weights, assuming that each is equally important to measure deprivation. Without previous evidence of the weights of the five identified domains the equal weight approach was chosen. To compare the resulting indices, they were classified in population-weighted quantiles (quintiles and deciles) and crosstabulations with the most important axis of inequality (area, sex, ethnicity, and age groups, urban-rural classification and geographical regions) were performed.

To summarise the index into higher geographical areas corresponding to the political and administrative division of Ecuador, two methods used in the IMD for England case were adopted [43]. Both the population weighted average score, and rank are calculated for parishes, cantons, and provinces. The former has the characteristic of not average out in high-deprived areas to the same degree as when using ranks.

To have information for all 40,628 census sectors (completeness), a data recovery procedure was established before summarising the index at higher levels (EDI index) and for mapping all census sectors in the GIS system (all three indices). Missing information for each indicator was imputed by averaging the nearest higher hierarchical area. Only 37 (.1%), 37 (.1%) and, 73 (.2%) census sectors were subject to this procedure for Townsend, Carstairs and EDI indices, respectively. Sensitivity analysis showed an ignorable effect of the imputation on index descriptors. EDI visualisation has been conducted using ArcGIS Pro 3.2.2 a Geographic Information System (GIS) software.

The validation of the proposed index was carried out using the three criteria proposed by Pampalon et al. [44] and Carr-Hill et al. [34]: validity, reliability, and responsiveness. Validity is tested using the following three approaches: content validity, criterion validity, and construct validity. Content validity refers to the agreement between the broad concept of deprivation and its indicators and dimensions. Content validity will be tested using Spearman’s correlations between the obtained index and its dimensions. A high level of correlation between the index and the identified dimensions is expected. The second approach, criterion validity understood as the ability of an index to correlate highly with other measures of deprivation, will be tested by comparing the three indices using correlation analysis.

The third approach, construct validity, investigates how consistent the relationships are between the deprivation measure and other health or social outcomes. Pampalon et al. [44] propose that this validity approach could be better understood in terms of convergence and predictive validity. Predictive validity refers to testing the performance of the deprivation index in explaining associations with health outcomes. These can be chosen from the mortality and morbidity outcomes and used to test a specific deprivation index. Convergence validity refers to comparing the index with external measures that reflect deprivation not only with measures from census data.

Reliability or internal consistency refers to the ability of a certain index to produce the same result under the same circumstances and is usually tested by analysing the degree of correlation between the indicators that make up the index using Cronbach’s Alpha. Finally, responsiveness is related to the ability of a deprivation index to detect differences or changes depending on time, location, and individual characteristics.

To test predictive validity, a health outcome was chosen from the same census data at the sector level, and both correlation and health inequality analysis were carried out. Teenage pregnancy, for this analysis, is defined as the percentage of females experiencing first pregnancy between 12-18 years of age. The univariate statistics of this health outcome are presented in Table 3, the national average percentage of teenage pregnancy reaches 23.81%, with higher percentages found in the Amazon region (33.29%), the Coast (28.41%) and the rural area (26,21%). The Spearman and Pearson correlations between the indices and teenage pregnancy are calculated. The gradient of inequalities is shown by tabulations between the rates of teenage pregnancy and the quintiles of deprivation of each index. Furthermore, the absolute gap or difference (D), the relative gap or ratio (R), the Slope index of inequality (SII) and the Relative index of inequality (RII) are calculated to assess and compare the performance of the deprivation indices in identifying health inequalities [45].

Internal consistency was tested by calculating the Cronbach’s Alpha for individual indicators that were selected after the PCA analysis for the EDI index. The convergence validity and responsiveness were tested using index summaries in higher geographical areas, the ranks of the proposed index were compared with a previously published deprivation index for Ecuador. Peralta et al. [14] developed a deprivation index at the municipal level (canton) using information from the 2010 census and the 2013-2014 national Living Conditions Survey. Both, Spearman and Kendall’s Tau-b rank correlations were calculated.

The final step in creating deprivation indices is dealing with uncertainty. Every measure of deprivation is an estimate of a ’true’ value that cannot be observed directly. Therefore, a common way researchers face this issue is by using categorical measures of deprivation (i.e., quintiles or deciles) obtained from the continuous index measure. Transforming the index scores into categorical measures reduce uncertainty by splitting the areas into groups; hence, small variations in the score generally have no impact on the assigned quantile [32]. Another way to deal with uncertainty is by calculating cross-tabulations among available indices or measures of deprivation [32, 33, 46]. Most areas are expected to fall on the diagonal of the cross-tabulated table, showing that the uncertainty about the deprivation measure is small [40]. For this analysis, the three indices are cross-tabulated and compared using population-weighted deciles.

Table 4 presents the distribution characteristics of the three deprivation indices obtained in this study at census sector level.

The histograms of the three indices, segmented by urban or rural areas, are presented in the Supplementary Appendix 3. The bimodal distribution of the EDI index is explained by the left component being described by urban deprivation and the right component (higher) by rural deprivation. Carstairs and Townsend indices do not differentiate between urban and rural distributions.

The results obtained from the cross tabulation between quantiles (population weighted) by population count and by region and urban-rural areas are presented in the Supplementary Appendix 4 (Q1 = Less deprived to Q5 = Most deprived) (Table 5).

Analysing cross-tabulations of the deprivation quintiles by axis of inequalities, the three indices presented similar results in sex and age, but sensible differences by ethnic auto-identification. In the case of sex, no differences or inequalities were found by either index at the aggregate level. In the case of age groups, the Townsend, Carstairs, and EDI indices presented similar results, with a similar proportion (46%) of young (0-14 years) in Q4 and Q5. The proposed index has a slightly higher proportion of people 65 years or older in Q4 and Q5 (Supplementary Appendix 5). In the case of ethnic autoidentification, the Mestizo and Montuvio groups have similar distributions in the quintiles of the three indices, while the Indigenous and Afro-ecuadorian groups present the highest differences. The Ecuadorian Deprivation Index categorises a higher proportion of indigenous people in the two highest quintiles and a lower proportion of Afro-Ecuadorians relative to Townsend and Carstairs (Supplementary Appendix 6).

The results of summarising the EDI index, as population weighted averages of index scores, to the administrative-political division of the country are presented in the supplementary appendices, parish (Supplementary Appendix 7), canton (Supplementary Appendix 8), and province (Supplementary Appendix 9).

The geographic maps of the deprivation indices presented in Figure 6 show the EDI index presents a higher proportion of census sectors on the darker colour scale, depicting higher deprivation in rural areas. Both the Townsend and Carstairs indices represent lower deprivation even in geographical areas with low population density and at considerable distances from towns and villages, such as in the eastern part of the Amazon Region, the central part of the Coast, and the southern part of the Sierra Region. A closer analysis of the maps shows how the main urban areas of the country have lower levels of deprivation and are surrounded by ‘deprived areas’. In this case, the three indices present similar results.

Content validity was tested by the Spearman correlations between each of the five domains and the proposed measure of deprivation (EDI index) (Figure 5). The domains of education and living environment had the highest correlation with 0.95 and 0.94, respectively, followed by the housing domain (0.93), employment (0.95) and the socioeconomic domain (0.88). It is important to note the high inter-domain correlation, as expected, and to explain the latent construct of deprivation.

Criterion validity was tested by comparing the correlation coefficients between the three indices (Table 6). Pearson’s correlation coefficients measure the linear correlation between the scores of the indices, while Spearman’s coefficients measure the correlation between the ranks of the indices. The Townsend and Carstairs indices had a very strong correlation (Pearson = 0.918, Spearman = 0.92), while the EDI index had a lower but still strong correlation with both the Townsend (Pearson = 0.793, Spearman = 0.816) and Carstairs indices (Pearson = 0.787, Spearman = 0.809). Despite the differences in their construction, these results show the common agreement about the underlying concept of deprivation between the indices.

Predictive validity was conducted using one health outcome available from the same census at the same area level. Table 6 presents the correlation matrix (Pearson and Spearman coefficients) between teenage pregnancy and the three deprivation indices. Teenage pregnancy presented Spearman correlations between 0.533 (EDI index) and 0.657 (Carstairs index). Teenage pregnancy is positively correlated with the three indices, which means that the percentage of women older than 12 years with their first pregnancy before 18 years is higher in the highest quintiles of deprivation (Figure 7).

Measures of inequality are presented in Table 7 for all the three indices and shows how the average teenage pregnancy percentages increase with deprivation (higher quintiles). The Carstairs index shows the highest absolute difference (D) and the highest ratio (R) between the most deprived quintile (Q5) and the least deprived quintile (Q1) with 21.72 percentage points and a ratio of 2.5. The EDI index presents the lowest absolute difference (18.37) and the second highest ratio (2.51) but very close to that of Townsend’s (2.50). The SII and the RII of all three indices show higher levels of inequality for the most deprived quintiles. Carstairs and Townsend index present a SII of 24.4 (21.57-27.23) and 26.74 (24.22-29.25) respectively. The EDI index presents the lower slope with 23.44 (15.6-31.28) and the lower relative index 3.03 (1.91-4.79).

The measure of internal consistency of Cronbach’s alpha applied to the 15 selected variables reached a value of α = 0.94, showing that the deprivation index subscale is reliable. Convergence validity and responsiveness of the proposed index were tested using a comparative analysis between the ranks of the proposed index (EDI) and the deprivation index developed by Peralta et al. [14] at the municipal level (canton) are presented in Table 8. Spearman’s correlations for the three regions published in the previous study showed strong positive monotonic correlations (above 0.90) between the indices. Furthermore, the Kendall tau-b correlation showed a high positive association in terms of the agreement of orders between the two indices (above 0.82).

The final step was to deal with uncertainty using cross-tabulations of population-weighted deciles for the different indices. Between the EDI and Carstairs and Townsend indices, the overall cross-tabulation (Supplementary Appendix 10) does not yield a tight diagonal showing differences in the way each index classifies census sectors in deciles. However, the cross-tabulations only for urban areas (Supplementary Appendix 11) show the expected tight diagonal; this shows again that the main difference among the indices is the classification of the rural areas as identified before.