We used the cross-sectional data from the third wave of the European Health Interview Survey (EHIS) conducted in Spain in 2019 and 2020 to identify intersectional groups. The sample size of the survey was 22,072 respondents, corresponding to 59% of the invited participants (N = 22,072; 59% response rate). The survey, legally binding from the second wave onwards, is conducted every 5 years (every 6 years since 2019) and targets the population over 15 years old living in private households. Its main objective is to gather data on the population’s health status, the utilization of health services, and determinants of health in a harmonized and comparable manner at the European level (b). The survey is framed within the European Commission’s (EC) Regulation 1338/2008, and the current legally binding EC Regulation describing the survey’s definitions is EC 2018/255 of 19 February 2018 (26, 27).

No ethical approval is required for this study as it is a secondary analysis of de-identified publicly available data.

The primary outcome of this study was self-reported breast cancer screening attendance at some point during their lifetime via mammography for women aged 45–69 in 7 out of 19 Autonomous Communities (Castilla-La Mancha, Castile and León, Valencian Community, La Rioja, Navarre, Ceuta, and Melilla) and for women aged 50–69 in the rest of Autonomous Communities. Possible answers to these questions were: yes, no, unknown, or unanswered. Answers were dichotomized, removing those few who responded unknown or unanswered to avoid incorporating uncertainty on whether the respondent reported never attending BCS (no = 0, yes = 1).

The explanatory variables used in this research are based on the PROGRESS-Plus framework (28). Their use to disentangle social inequalities has been extensively discussed (29) and used (30). For this study, we categorized existing indicators of the survey into the PROGRESS-Plus categories and used them as potential predictors of non-attendance at BCS.

Place of Residence was determined through two different variables: the size of the municipality and the specific Autonomous Community. The first variable was composed of the following seven categories: less than 10,000 inhabitants, 10,000–20,000 inhabitants, 20,000–50,000 inhabitants, 50,000–100,000 inhabitants, more than 100,000 inhabitants, capital of the province, or more than 500,000 inhabitants. As mentioned above, the specific Autonomous Community also serves as a proxy for the time period of the implementation of BCS programs and the density of health professionals in the region.

Race, ethnicity, culture, and language were measured by the respondents’ country of origin. The information provided by this variable in the EHIS was whether the participants were born in Spain or another country. Thus, the variable was employed as a binary variable (Spain = 1 and other = 2).

Occupation was operationalized through the respondents’ current working situation. The derived categorical variable had the following categories: paid employment, unemployed, retired, unable to work, (unpaid) household work, and others. The “others” category is a merged category that includes EHIS classification such as unable to work, studying, and others, as the two first categories had very few participants, 17 and 1, respectively.

Sex was not included as an explanatory variable but rather as a requirement needed for including participants in the analysis: to be a female. Gender and religion dimensions were not included in the present research, as the EHIS did not comprise any questions covering gender identification or religious preferences.

Education was measured following the CNED14 classification, the Spanish adaptation of ISCED-2011 (31). The variables employed had the following categories: illiterate, uncompleted primary education, completed primary education, first-stage high school, finished high school, intermediate vocational training, superior vocational training, and university degree.

Socioeconomic status was operationalized by the type of occupation. The variable’s classification was obtained based on the Spanish Society of Epidemiology classification developed in 1995 and revised in 2012. This grouping comprises 6 groups, with 1 being the highest social class and 6 being the lowest (32).

Social capital was not explicitly included in the dataset; however, we used two proxy variables: marital status (single, married, legally separated/divorced, or widowed; indicating the availability of spousal support) and type of household (alone, with a partner, with a partner and children, alone with children, or others; indicating the availability of family support).

The Plus dimension of the PROGRESS-Plus framework was proposed to extend the social determinants of health that could potentially be discriminating features. Among these contextually dependent factors, characteristics that attract discrimination, features of relationships, and time-dependent relationships have been highlighted (33). In this study, we assessed characteristics that attract discrimination through the Global Activity Limitations Indicator (GALI) and age (34). The GALI self-reported measure is conceived by assessing the degree of limitation experienced in the last 6 months, with the possible answers being severely limited, mildly limited, or not limited. Age is a categorical variable comprising women aged 45–69 in quintiles (45–49 years old, 50–54 years old, 55–59 years old, 60–54 years old, and 65–69 years old). While one would anticipate a proportional relationship between age and BCS attendance (i.e., older women being invited to BCS more times in their lives than younger women), this variable was included to assess its potential interactions with other PROGRESS-Plus variables. Specifically, it aimed to examine whether distinct social determinants of health intersect in different age groups.

As a final point, none of the categories of the explanatory variables were collapsed (e.g., illiterate and uncompleted primary education); Instead, they were included in the model individually with all categories. This approach was chosen because decision tree algorithms permit a high level of granularity and the ability to capture interactions and potential intersections among the various categories (35).

Descriptive analytics, frequencies, and percentages were calculated for all variables. The statistical significance between participants who attended BCS and those who did not was tested using a chi-squared test for all variables.

For this study, a complete case analysis was conducted when missing data were present. The total sample size was restricted to women aged 45–69 in 7 out of 19 Autonomous Communities (Castilla-La Mancha, Castile and León, Valencian Community, La Rioja, Navarre, Ceuta, and Melilla) and to 50–69 years in the rest of Autonomous Communities (n = 4,180). Among these women, those who did not provide information on whether they ever underwent mammography (n = 8) were excluded, and those who did not provide their marital status (n = 21) were excluded. Hence, the final total sample size of the study was 4,151 participants.

We used decision trees to identify the groups of women most at risk of not attending BCS. There is scarce literature that suggests which decision trees better operate on diverse health outcomes. CART bases its splitting decision on the lowest Gini impurity (or entropy) coefficient of every possible split (21). It is often criticized for not providing statistical significance measures and being biased toward variables with many categories. CIT was developed to overcome some of CART’s limitations. CIT employs a formal statistical hypothesis for building the decision trees and avoids variable selection bias by dividing the selection process into two steps (36). CHAID was the first decision tree developed based on statistical significance tests, in which all covariates are tested against the outcome, and the one with the highest association is selected as the splitting variable. The limitation of CHAID is that it computes only categorical variables and is based on the chi-squared test (37). C5.0 is a non-parametric method that uses the entropy of the imputed variables to generate splits. Therefore, nodes are generated based on the data split that produces a higher information gain (i.e., the entropy of the data split is the lowest, meaning the homogeneity among the included cases is the highest) and therefore appears to be more advantageous for classification (38). After C5.0 generates a vast tree, it applies the binomial confidence limit method to every subtree for pruning through a high predicted error rate. Moreover, C5.0 uses adaptive boosting (39) and winnowing in the growing process (40, 41).

In the present study, the four most commonly used decision trees were implemented using R packages “caret” (42) for exploratively hypertuning the models and “rpart” (CART) (43), “chaid” (CHAID) (44), “partykit” (CIT) (20), and “C50” (C5.0) (40) for outputting the final model in R version 4.2.3.

Decision trees that use classification algorithms employ several metrics derived from a confusion matrix to evaluate their performance. In the case of a binary outcome, the confusion matrix is a 2 × 2 table that illustrates the total number of true positives (TP – hit), true negatives (TN – correct rejection), false negatives (FN – type II error), and false positives (FP – type I error) when comparing the predicted positive (PP) and predicted negative (PN) cases to the actual positive (P) and actual negative (N) cases. Measures such as balanced accuracy, recall, precision, and F1 score (Table 1) can then be calculated and used for model performance evaluation (45).

Despite decision trees being reliable tools for intersectional subgroup identification, they are unstable given their dependence on the data used to train them and, thus, posing the risk of overfitting. Small changes in the training data could lead to differences in decision tree construction; hence, the implementation of ensemble algorithms is recommended (46). There are several ensemble algorithms that employ different procedures, such as bagging (Random Forest), boosting (AdaBoost), and bagging and boosting (extreme gradient boosting). Following the results of previous research (47–49), we decided to use extreme gradient boosting (XGBoost) to increase the internal validation and robustness of the decision trees. The algorithm was implemented using the package “xgboost” (49) in R version 4.2.3.

A summary of the descriptive statistics of the sample can be found in Table 2. Association chi-squared tests suggest marginal associations between each independent variable and the outcome, except for municipality size. The total sample size is 4,151. Of those, 3,886 attended BCS during the last 2 years, while 285 did not. As expected, the youngest group, women aged 45–49 years, attended less in their lifetime (18.34% – never attended) than older women (χ² = 76.93, df = 4, p < 0.001). Women not born in Spain (14.78%) attended less BCS compared to those born in Spain (χ² = 35.54, df = 1, p < 0.001). Illiterate women (43.75%) (χ² = 74.94, df = 7, p < 0.001) and women in the lowest social class (10.51%) (χ² = 38.00, df = 6, p < 0.001) had the smallest number of attendances at BCS. Regarding the place of residence, women living in municipalities with 10,000–20,000 inhabitants (8.82%) (χ² = 16.95, df = 6, p < 0.151) and women living in Melilla (37.14%) (χ² = 157.26, df = 18, p < 0.001) had the lowest attendance at BCS. Finally, legally separated women (13.39%) (χ² = 68.11, df = 4, p < 0.001), women living alone with children (8.21%) (χ² = 27.8, df = 4, p < 0.001), women in a working situation labeled as other (10.90%) (χ² = 26.92, df = 4, p < 0.001), and severely limited women (12.44%) (χ² = 13.15, df = 2, p < 0.0106) participated in BCS the least among their PROGRESS-Plus dimension.

Several pre-processing steps were taken to prepare the data to be analyzed. First, a complete case analysis was conducted, as only 29 cases had missing data on any variable. Second, to improve external validity, data were randomly split into a training subset (N = 3,321, 80% of the entire dataset) and a testing subset (N = 830, 20% of the entire dataset), with stratification of the outcome (i.e., to respect the distribution of classes in both subsets). Furthermore, balance sampling methods were applied to the training data given the imbalanced nature of the dependent variable (93.13% ever attended BCS, 6.87% never attended). Several studies have demonstrated that model performance improves when resampling the training data in highly imbalanced datasets (50–52). Four balanced sampling techniques that minimize the majority class (undersampling), maximize the minority class (oversampling), or minimize the majority class and maximize the minority class (SMOTE and ROSE) were tested (Table 3). Oversampling outperformed the other sampling techniques, estimated through the area under the curve (AUC) of logistic regression (LR).

We tested several decision trees, CART, CIT, CHAID, and C5.0, to the oversampled training data. C5.0 outperformed the others with a balanced accuracy of 81.1%, recall of 80.7%, precision of 24.3%, and F1 score of 0.374. See Supplementary material 1 for more details and Figure 1; Table 4 for the final C5.0 decision tree.

The best tree identified the variables Autonomous Communities, origin, marital status, age, education, socioeconomic class, origin, and type of household as relevant in explaining attendance and non-attendance to BCS. The first splitting point, the root node, is found in Autonomous Communities, where women living in Ceuta or Melilla form a subgroup (Node 1, 464 cases /71 no-cases), and the rest of Spain further split. The second split is found in marital status, where single or separated women create a subgroup (Node 2, 1,112/585), and married, divorced, and widowed women further split. The third node relates to the respondent’s origin country: women born outside Spain form a subgroup (Node 3, 280/163), and women born in Spain proceed to split. Women born in Spain, married, divorced, or widowed, and not residing in Ceuta or Melilla are additionally divided based on being 55 years of age or older. The youngest group is further split based on the level of education, forming two final leaves: less than high school education or professional education (Node 4, 496/334) and greater than high school education except for professional education (Node 5, 93/221). The oldest group is fragmented based on the socioeconomic class of the respondents, where those belonging to the highest two social classes form a subgroup (Node 6, 30/312), and the rest is additionally divided based on the place of residence. The sixth split divides the abovementioned group into those living in the Autonomous Communities of Navarre, Aragon, Canary Islands, or Catalonia (Node 7, 0/316), those living in Andalusia, Balearic Islands, or Castilla-La Mancha, and the rest of Spain. Women living in Andalusia, Balearic Islands, or Castilla-La Mancha are further separated based on the type of household they live in: alone, with a partner, or with a partner and children (Node 8, 307/243), and those living alone with children or other household constellations (Node 9, 7/48). Finally, women living in Asturias, Cantabria, Castile and León, Valencian Community, Extremadura, Galicia, Madrid, Murcia, Basque Country, or La Rioja, from middle and low social classes, aged 55 years or older, born in Spain, and married, divorced, or widowed, are lastly split based on their level of education: illiterate (Node 10, 42/2) and primary education or greater (Node 11, 270/792).

For more robust information and internal validation of the decision tree, extreme gradient boosting was performed. XGBoost sequentially trains multiple decision trees (bagging), where each tree endeavors to correct the classification errors of the precious one by assigning specific weights to each tree and its leaves (boosting) (49). The parameters used to build the ensemble algorithm were a learning rate of 0.1 (low learning rate to be more robust to overfitting), a maximum number of boosting iterations of 53, and a learning objective of logistic regression for binary classification. XGBoost assessed the importance of the variables when building the boosted trees through the information gain criteria. In essence, this algorithm informs which variables were more significant in constructing the decision trees and therefore has a higher predictive power in the model. With an AUC of 78.80%, the algorithm resolved that Autonomous Community followed by education, age, and marital status are the most important variables for predicting whether targeted women in Spain will attend BCS or not. Following with less than 50% relative importance are origin, social class, GALI, population density, working situation, and type of household (Figure 2).

Supervised machine learning techniques, specifically decision trees and the presented ensemble algorithm, allow for a non-parametric and non-linear explanation of the relationship between explanatory variables and the outcome. Thus, unlike the classic statistical analysis, where including many potential predictors could lead to overfitting the model, machine learning techniques allow for a more comprehensive inclusion of all available PROGRESS-Plus variables in the dataset. Multicollinearity deriving from potentially correlated predictors is not an issue in machine learning approaches since decision trees split based on an individual variable at each node, and ensemble algorithms further mitigate the risk by outputting the average importance of each variable. In this study, machine learning algorithms allowed an inductive exploration of intersecting social determinants of health in women. At last, no predictive value is tested; instead, variables are evaluated as potential predictors for building the classification models (35).

The study is not without limitations. No causal inference can be drawn due to the cross-sectional design of the survey. Moreover, response and common-method bias may occur due to the nature of the self-reported survey. In fact, the response rate of EHiS wave 3 was 59%, emphasizing the need for caution when drawing conclusions from studies using this dataset. Previous researchers have speculated that the EHiS suffers from underestimating inequalities in access to screening programs (58). Along these lines, the nature of the target population in the survey—people living in private households—could potentially reveal details about individuals living in less advantaged housing situations, such as public or institutional housing. Furthermore, although the presented decision tree outperformed others, it is relatively large and outputs both simple and highly dimensional intersectional positions. Therefore, the large dimensionality of some subgroups might challenge the usability of their content. Indeed, the present analysis ought to enhance the understanding of the intersectional importance of different variables and describe those most at risk of not attending the BCS. Finding the balance between algorithm performance and public health interpretability and usability is essential in health prevention.

Finally, secondary data intrinsically limit the included variables and their categorization. The dimension of race/ethnicity could only be estimated based on the respondent’s country of origin, which does not fully capture the experience of discrimination that women might experience. An extensive body of literature shows how race/ethnicity is often a proxy for convergence factors such as experiences of discrimination, social mobility, and a lack of financial opportunities (62).