Using geographical random forest models to explore spatial patterns in the neighborhood determinants of hypertension prevalence across chicago,illinois,USA

Data

We analyzed the population’s hypertension (“Hypertension prevalence” dependent variable) based on ten socioeconomic variables for the reference year 2018 for all 793 census tracts in Chicago. The hypertension data are provided by the Centers for Disease Control and Prevention’s PLACES Project and are based on responses to the Behavioral Risk Factor Surveillance System survey (U.S. CDC, 2021). Hypertension is defined as “Respondents aged ≥18 years who report having been told by a doctor, nurse, or another health professional that they have hypertension.”

Socioeconomic data were obtained from various sources. Severe rent (“Severe rent” variable) is defined as the percentage of the population spending more than 50% of income on housing rent; Poor Households with no food assistance percentage (“No food assistance” variable) is quantified based on the percentage of low-income households who did not receive food stamps; Eviction percentage (“Eviction rate” variable) is defined as the percentage of renter-occupied units that experience an eviction filing; and percentage of vacant housing (“Vacant housing” variable) per census tract were derived from the Chicago Health Atlas (CHA, 2021). “No food assistance” variable explains government attempts to establish the Supplemental Nutrition Assistance Program (SNAP) to promote healthy eating habits, discourage unhealthy eating habits, and penalize unhealthy nutritional practices. The percentage of Racial/Ethnic diversity in the neighborhoods (“Racial/Ethnic diversity” variable) was obtained from City Health Dashboard (CHD, 2021). We also quantified the mobility density ratio (“Mobility ratio” variable) measured as the ratio between the number of all types of trips (biking, walking, public transit, and private vehicle users) to and from census tracts to the corresponding population provided by the Multiscale Dynamic Human Mobility Flow Dataset in the U.S. (Kang et al., 2020).

Lastly, we integrated CDC’s Social Vulnerability Index (SVI) (Centers for Disease Control and Prevention (CDC), 2018), which quantifies social vulnerability to hazards like natural disasters or disease epidemics. The SVI comprises four themes: (1) Socioeconomic Status percentile calculated based on a low income, no high school diploma, living below the poverty line, and unemployment indicators (“Socioeconomic status” variable), (2) Household Composition & Disability percentile measured based on aged 65 and older, below age 17, single parent, and people with disability indicators (“Household composition” variable), (3) Minority status and Language percentile quantified based on minority and limited English proficiency (“Minority & Language” variable), and (4) Housing/Transportation percentile calculated on multi-unit structures, mobile homes, crowded houses, and people without access to the private car (“Housing type & Transportation” variable) per census tract. We obtained census tract polygon geometries as TIGER/Line Shapefiles from the United States Census Bureau (U.S. ACS, 2019) to conduct spatial analysis and mapping using geographic information systems (GIS). The census tract-level variables were linked to the geometries via their 11-digit FIPS codes.

Methods

To model the relationships of hypertension prevalence with the above-presented socioeconomic variables, we applied two local spatial regression models (GRF and GWR) and two global models (Random Forest and OLS). Models were compared based on their performance. We also calculated the partial dependence plots to identify if the relationships of the dependent variable (hypertension prevalence) with the independent variables are linear or not. For the random forest and GRF models, we also calculated the importance ranking of each variable by calculating the increase in IncMSE.

Random forest and OLS (global models)

Random Forest (RF) was introduced by Breiman (Breiman, 2001) and is a global non-parametric machine learning method. A random forest is an ensemble of decision trees trained and tested for classification or regression analysis. Each decision tree is created from a given training dataset. First, a subset is created by randomly selecting samples with replacements from the original training set (usually 2/3 of the training set is selected). The remaining data (usually the other 1/3) comprise the out-of-bag (OOB) set used for evaluation. In addition, a subset of variables is also selected per decision tree. The same process is repeated for hundreds or thousands of trees, and thus a forest of random trees is created. For each tree, the prediction or classification error is calculated. Then the most common class for classification, or the average value for predicting all trees, is used as the final output.

The OOB set is also used to assess the importance of each variable. A typical method to estimate importance is by calculating the change in the IncMSE (Georganos et al., 2021). The values of each variable in the OOB set are randomly permuted in turn, and the OOB error is calculated. If the OOB error increases, then the variable is important, and the higher the change, the more important the variable is to the estimation of the dependent variable (Grekousis et al., 2022a).

A strong point of a RF is that it can assess the relative importance of each independent variable. In other words, it quantifies which variable has a greater effect on the dependent variable. Ranking the variables according to their importance makes research outputs easily communicated to non-specialists and decision-makers. OLS lacks this ability unless the standardized (beta) coefficients are calculated. However, standardized coefficients are not easily interpretable and are not so commonly used.

RF does not make any assumption about the statistical distribution of the data. As such, it better handles variables that have non-linear relationships. On the contrary, OLS builds a probabilistic model based on various assumptions, for example, that the relationships between the dependent variable and the independent variables should be linear (Grekousis, 2020). In reality, though, non-linearity is quite common, and OLS models perform poorly. In addition, both RF and OLS are global models. Global models provide statistics and assessments that summarize the entire study area. Consequently, they do not take into account any spatial variation of the data. Therefore, global models are of lower performance in the geographical analysis as they fail to account for spatial dependence or heterogeneity.

Geographical random forest and geographically weighted regression (local models)

Local geographical regression models take into account spatial non-stationarity by estimating a set of local parameters that reveal how relationships vary in space. To do so, a spatial weight matrix that reflects the conceptualization of spatial relationships is created (Grekousis, 2020). In this research, we applied both GRF and GWR models.

GRF uses a spatial weights matrix and is calibrated locally using only nearby observations through a spatial kernel. This study used the adaptive spatial kernel to estimate the optimal number of nearest neighbors (for both GRF and GWR) as it is the most widely used and more appropriate if spatial data autocorrelation exists (Grekousis, 2020). Thus, GRF would require a separate RF hyper-parameter optimization for every single spatial unit. This approach faces three major challenges. First, it would increase the processing time dramatically. Second, applying different hyper-parameters per spatial unit would make further analysis and evaluation of the optimal hyper-parameters and the subsequent predicting accuracies extremely complex. Third, such an approach has not been applied yet, and has to be developed in future research (something beyond the scopes of our study). Following the example of others (Grekousis et al., 2022a; Quinones et al., 2021), we optimized the hyper-parameters of GRF (“number of variables randomly sampled,” and “number of trees”) using Random Grid Search (RGS) on the RF model (using CARET library in R). We then kept these hyper-parameters fixed on GRF and applied the 10-fold cross-validation method to select the best values for the bandwidth (from a set of possible bandwidth values) and selected the one with the highest OOB R².

The optimal bandwidth for GWR (number of nearest neighbors to be used in the local regression models) was measured by minimizing the Akaike Information Criterion (AICc) (Fotheringham et al., 2015). GWR fits OLS to the data of the neighboring spatial units. In this sense, GWR follows the same assumptions as of the OLS model, for example, linearity, which is a severe deficiency when data are not linearly related.

The GWR model produces the local R², the local residual, and the set of local coefficients for each spatial unity. This allows for analyzing the spatial variation of relationships between dependent and independent variables. On the other hand, GRF yields the local feature importance for each predictor in each local random forest model, the local residuals, and the local goodness of fit (training and OOB) (Kalogirou and Georganos, 2022). Here we mapped local importance, which allows for a thorough inspection of how the effect of each independent variable on the dependent (hypertension prevalence) varies geographically, something important when it comes to decision making.

We trained the GRF with the following values (estimated—except for bandwidth—using the random grid search at the global model): bandwidth (“bw”) = 30 (estimated through the adaptive spatial kernel), number of variables randomly sampled (“mtry”) = 6, and number of trees (“ntree”) = 1000. Both the global and local RF models were trained with data to explore variation in feature importance due to the data distribution. Like RF, we ranked the variables’ importance based on the percent change in the MSE (Georganos et al., 2021).

To test the predictive performance of local models, we used ten randomly chosen splits of the data with 90% retained for training the models and 10% of the data held back for testing the models. We also assessed the model’s predictive performance using 80%, 70% trained data and 20%, 30% test data, respectively, and found that prediction accuracy with a 90:10 split was only marginally higher. Previous research (e.g., Helbich and Griffith, 2016) confirms that the predictive performance varies insignificantly between the train/test splitting ratios of 90:10 and 80:20. As there is no precise train/test split ratio in the spatial statistics literature, we decided to keep the 90–10 split of the data. In addition, optimizing the bandwidth for each train/test split could also be applied. However, as our main objective is to use mainly GRF as an exploratory tool, we anticipate that this would not affect the overall variable importance ranking.

Specifically, the data set (n = 793) was randomly split into 713 training data objects used to train the random forest models and 80 test data objects used for evaluating the model performance. We then computed performance metrics such as the MSE, root-mean-square error (RMSE), and coefficient of determination (R²). Lastly, we reported the average value of these metrics over the 10 iterations. All our statistical analyses were conducted on the “SpatialML” package (Kalogirou and Georganos, 2022) and the “GWModel” package (Gollini et al., 2013) in R Statistical Computing Environment (R Core Team, 2020), and for cartography, the ArcGIS 10.8.1 was used. For a thorough presentation of the GRF regarding formulas, overfitting issues, and confounding variables, see Grekousis et al. (2022a), and Georganos and Kalogirou (2022).

Geographical random forest (GRF)

In the out-of-sample predictions (OOB set), the GRF model had lower MSE values and a higher local R² than the global RF model (Table 1). According to the percent change in the MSE, the household composition is the most important variable in the RF model, followed by eviction rate, minority and language, and racial/ethnic diversity. Similarly, the household composition is the most important variable in the GRF, followed by the minority and language, socioeconomic status, and racial/ethnic diversity. As shown in Table 1 with averaged positive IncMSE of the GRF model, most tracts with local relevance to hypertension prevalence have a positive local importance variation. Higher values imply increased importance. Determinants’ importance ordering of the GRF model varies from the global RF model. Eviction rate, for example, is placed second in the RF model (more IncMSE) but fifth in the GRF model (less IncMSE) (Table 1).

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Table 1.

Summary results of random forest (RF) and geographical random forest regression (GRF) models.

RF			GRF
		Global feature importance (IncMSE)		Local feature importance (IncMSE)			Std
Ranks	Variables		Variables	Min	Max	Mean
1	Household composition	80.001	Household composition	−12.996	48.438	14.127	11.920
2	Eviction rate	57.384	Minority & language	−11.492	39.820	8.151	9.330
3	Minority & language	52.795	Socioeconomic status	−9.930	34.294	7.7089	8.813
4	Racial/Ethnic diversity	38.649	Racial/Ethnic diversity	−9.474	32.314	6.509	7.258
5	Vacant housing	22.304	Eviction rate	−15.040	36.003	4.709	7.775
6	Socioeconomic status	21.237	Vacant housing	−13.402	31.916	3.631	6.665
7	Severe rent	19.747	No food assistance	−12.268	28.632	3.268	6.005
8	Mobility ratio	15.309	Severe rent	−11.053	26.913	1.791	5.082
9	Housing type & transportation	10.544	Mobility ratio	−16.020	21.151	1.171	4.796
10	No food assistance	7.192	Housing type & transportation	−15.282	19.106	0.927	5.282
	R2 OOB	0.898		0.912
	MSE (OOB)	11.877		10.273

Partial Dependence Plots (PDPs) for socioeconomic determinants were developed to characterize the non-linear relationship between the variables and hypertension prevalence (Figure 2). By presenting the expected target response as a function of the input features of interest, PDPs can reveal whether the relationship between the target and a feature is linear, monotonic, curvilinear, or of another type (Friedman, 2001). The findings show that the majority of factors (such as mobility ratio (Figure 2(b)), vacant housing (Figure 2(c)), and no food assistance (Figure 2(e)) are not linearly related to hypertension prevalence.OPEN IN VIEWER

Some variables may exhibit linear relationships but only within specific ranges. For instance, there is a nearly positive linear link between “No food assistance” and hypertension prevalence in the 1%–15% range, but the effect is minimal after that (Figure 2(e)). Generally, when all variables are linearly related to the output, traditional statistics may perform similarly or even better than machine learning. However, limiting our dataset to only these variables oversimplifies the analysis and, more importantly, excludes variables that are statistically significant determinants for hypertension, diminishing thus the spatial epidemiological importance of the study. Overall, the findings reveal that nearly all relationships are non-linear, emphasizing the importance of using non-linear regression models compared to classic linear ones. We used the GRF to deal with non-linearity.

We also mapped the determinants to understand better the spatial distribution of the local variable importance (IncMSE) (Figure 3). While the socio-economic condition of tracts in the mid-north and southwest is important concerning the hypertension epidemic (Figure 3(a)), the household composition has the greatest influence on hypertension along Lake Michigan’s north shore (Figure 3(b)). The tracts in the southeast and west have the highest importance in terms of minority & language proficiency of the population in the hypertension epidemic (Figure 3(c)). On the contrary, household type & transportation has minor importance in creating the hypertensive environment across Chicago tracts (Figure 3(d)). Some tracts on the west of downtown and north have high importance in the hypertension epidemic. However, a poor household with no food stamp assistance is vulnerable to the risk of hypertension, notably on tracts at northwest and south of downtown, along lake Michigan (Figure 3(f)). Vacant housing has the highest importance in the hypertension epidemic, predominantly in the southwest (Figure 3(g)). However, severe rent identifies with minor importance across tracts (Figure 3(h)). Eviction rate has the strongest importance in west tracts and some tracts in the south and north (Figure 3(i)), whereas for racial/ethnic diversity, tracts with the highest importance are on the south side and some in the north (Figure 3(j)). The results of the aforementioned analysis are explored in greater detail in the discussion section.OPEN IN VIEWER

Predictive performance of global and local models

Our validation approach found that the GRF model performed better than the GWR model (Table 2). In cross-validation testing, the R² in GRF was 0.90, explaining 90% of the variability in hypertension prevalence. When shifting from OLS to RF global models, the results indicate consistent increases in accounting for hypertension variability (R²) and RMSE, which subsequently improve even more when comparing the GRF to the GWR. The GRF model accounts for slightly greater variability in hypertension prevalence (R² = 0.90) than the GWR model (R² = 0.85) and has a lower RMSE value (3.40 vs 4.1). GRF OOB also shows that GRF outperforms in terms of hypertension variability and RMSE and MAE reduction (R² = 0.91, RMSE = 3.25, MAE = 2.31).

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Table 2.

Evaluation of the predictive performance of models based on the test dataset.

	OLS	GWR	RF	GRF	OOB
R 2	0.80	0.85	0.88	0.90	0.91
RMSE	4.89	4.18	3.70	3.40	3.25
MAE	3.81	3.09	2.53	2.42	2.31

GRF performs better (OOB MSE = 10.273) than RF (OOB MSE = 11.877) (Table 1). As with every local metric, GRF uses a subset (neighborhood defined by the bandwidth) of the entire one by creating non-linear regression for each census tract. Although the subset is relatively small, the overall OOB MSE is lower than the global model, indicating that when many local geographically defined RF are created and jointly analyzed, they can achieve improved predictions compared to the global RF. The local form of GRF allows to map the importance of each variable at each spatial unit (see Figure 3). Seemingly, there is a minor improvement in OOB MSE of GRF over RF. However, this improvement is significant in terms of prediction accuracy and gaining insight into the socio-economic drivers of hypertension at the local level, something that in global RF is completely lost (RF does not explain spatial variation). In this sense, it is essential to focus on how the importance of each variable varies spatially rather than only cross-compare the variables' importance rank for the summarized GRF model (Table 1). We further discuss how the importance of each variable varies spatially in the Results and Discussion sections. We also observe that GRF outperforms all models (Table 2), including spatial regression model GWR, indicating that it can better handle non-linearity, a major deficiency of linear regression methods.

It is worth noting that the local GWR Variance Inflation Factors (VIFs) for each independent variable show minor collinearity (predominately less than 3) (see Supplementary Figure S1). The local collinearity concerns the GW regression model if VIFs are more than ten (Lu et al., 2014).

We also depict the standardized residuals’ spatial distribution to understand better how GRF dealt with spatial heterogeneity (Figure S2(a)). In addition, we use local Moran’s I to assess spatial autocorrelation and track potential clustering in the residuals for all models (Figure S2(b)-(e)). Results show the local spatial autocorrelation of residuals is evident in most parts of the case study area for the GWR, OLS, and RF models. On the contrary, GRF results reveal no geographical clustering of residuals in most locations exhibiting spatial randomness.

Household composition

The proportion of older, younger, disabled, and single parents (the household composition variable) is highest in census tracts associated with the hypertension epidemic on the north side of Lake Michigan, where mixed-income residents of Streetsville, Lincoln Park, and low-income European migrants of Uptown and Edgewater live (Figure 3(b)). Besides that, as illustrated in Figure 1, the highest importance of household composition in hypertension is associated with increased urban mobility (Figure 3(b)), consistent with other studies (Münzel et al., 2014; Li and Xie, 2021). They identified association links between traffic-related noise and air pollution and the development of hypertension.

With the aging population and urbanization, the environment in which individuals grow old is likely to impact their health, lifespan, and well-being (Cagney and Cornwell, 2010). Hypertension is a prominent cause of death in poor and wealthy places, and its prevalence rises with age (Del Pinto and Ferri, 2019; Menec et al., 2010). Adolescent hypertension is also a concern when children grow up in an obesogenic environment, predisposing them to hypertension in adolescence and adulthood (Ewald and Haldeman, 2016).

Overall, low-income adolescents, the elderly, and people with disabilities face numerous barriers to leading an active lifestyle that helps control hypertension risks, such as a lack of gyms, access to healthy foods, and recreational facilities in their schools and neighborhoods, as well as a lack of support from their parents and families, especially single parents (Lee and Laffrey, 2006). To offer areas with accessible and affordable facilities and programs, neighborhood organizers, government agencies, schools, and public health specialists must collaborate and use the outputs of analyses focusing on the local level, like the one presented here.

Minority & language

Minority status and English language proficiency of adults per census tract are most important in some neighborhoods associated with the hypertension epidemic, such as the mid-north, west, southwest, and southeast (Figure 3(c)). According to our findings, minorities and people with limited language ability have greater importance on hypertension in west side tracts with high urban mobility (Figure 1). Similarly, minorities on the west side live in regions with a large percentage of vacant houses, which creates an unpleasant outside experience that limits their active lifestyle (Figure 1). Additionally, minorities with limited language abilities are housed in overcrowded multi-unit complexes in the mid-north (Figure 1), where they get less sleep and are more likely to acquire stress, hypertension, and obesity (Chambers et al., 2016). Minorities in ethnically diverse districts of the mid-north are also at risk of hypertension due to low income (Figures 1 and 3(c)). The urban services provided in mixed-income and ethnic enclaves should be affordable to all groups, with no cultural clashes among users.

The results of our analysis are consistent with other works. Kim et al. (2017) found a link between English language proficiency and high blood pressure. Limited English proficiency (LEP) is a major risk factor for lack of access to medical care, poor health, and adverse outcomes (Wilson et al., 2005). Patients may not grasp the significance of their conditions, the importance of medication adherence, or prognosis if a practitioner and a patient speak different languages and no translator is present. People with LEP were also more likely to be socioeconomically disadvantaged than people with acceptable English proficiency; they were more likely to have poor income, no insurance coverage, and a low educational level (David and Rhee, 1998). For example, Chinese Americans who solely speak Chinese or have little English are three times more likely than those who do not speak English to have bad pharmaceutical habits (Wu et al., 2010).

Socioeconomic status

Evidence suggests that socioeconomic status (SES), as defined by education, occupation, or income, influences significant health characteristics such as environmental exposure, health behavior, chronic stress, and health care (Leng et al., 2015). SES is strongly associated with hypertension in the mid-north and south of downtown along Lake Michigan (Figure 3(a)). Most minorities live in the mid-north with poor households without food assistance (Figure 1). Little is known about SES at the neighborhood level (Dubowitz et al., 2012) or how community and individual SES may influence hypertension risk (Xu et al., 2022). Low-income, jobless, and uneducated persons are more susceptible to hypertension, exacerbated by a lack of nutritious foods, and limited exposure to green spaces (Grazuleviciene et al., 2020). Hypertension has been identified as an environment-related disease, with social environment components potentially controllable through lifestyle changes, and well-designed neighborhoods can affect individuals’ healthy behaviors.

Racial/ethnic diversity

In recent decades, racial and ethnic diversity in the United States has gradually increased based on daily mobility among neighborhoods (Phillips et al., 2021). In our study, racially/ethnically diverse neighborhoods in southern tracts with most Black residents played a significant role in the hypertension rate (Figure 3(j)). While most people believe that urban diversity is a positive development that promotes inclusion and tolerance (Ashley et al., 2022), others believe that ethnic diversity may have unintended negative consequences, such as increased crime fear (Hooghe and De Vroome, 2016; Hipp, 2011).

Per the Kim and Wo (2022), more diverse neighborhoods had fewer violent and property crimes, particularly in more diverse neighborhoods. Having enough opportunities for frequent interpersonal contact with other groups can aid in the elimination of group bias. More importantly, interpersonal connections should occur on a small scale with a high probability of social engagement with others (Kim and Wo, 2022). Neighborhood diversity may act as a motivator for healthy behaviors by increasing people’s perceived self-efficacy and protecting them from hypertension.

Eviction rate

Housing is widely recognized as an important social determinant of health, recognizing how insecure housing (Palacios et al., 2021) or poor-quality housing (Braubach et al., 2011) can harm health and well-being. While academics frequently study toxins in the home, overcrowding, and safety issues (WHO, 2018), tenants’ security sentiments (Evans, 2021), and health repercussions, particularly hypertension, are poorly known (Rolfe et al., 2020). According to our findings, the eviction filing rate with the greatest importance on hypertension prevalence is on Chicago’s west side (Figure 3(i)), including a low-income population and unoccupied properties that create unsafe surroundings (Figure 1). Household instability and high-burdened household expenditures (i.e., severe rent) are linked to worse self-reported health, psychosocial distress, and a higher risk of deferring medical treatment due to financial constraints (Meltzer and Schwartz, 2016).