Abstract
Recent advances in geographic information systems software and multilevel methodology provide opportunities for more extensive characterization of “at-risk” populations in epidemiologic studies. The authors used age-restricted, geocoded data from the all-African-American Jackson Heart Study (JHS), 2000–2004, to demonstrate a novel use of the Lorenz curve and Gini coefficient to determine the representativeness of the JHS cohort to the African-American population in a geographic setting. The authors also used a spatial binomial model to assess the geographic variability in participant recruitment across the Jackson, Mississippi, Metropolitan Statistical Area. The overall Gini coefficient, an equality measure that ranges from 0 (perfect equality) to 1 (perfect inequality), was 0.37 (95% confidence interval (CI): 0.30, 0.45), indicating moderate representation. The population of sampled women (Gini coefficient = 0.34, 95% CI: 0.30, 0.39) tended to be more representative of the underlying population than did the population of sampled men (Gini coefficient = 0.49, 95% CI: 0.35, 0.61). Representative recruitment of JHS participants was observed in predominantly African-American and mixed-race census tracts and in the center of the study area, the area nearest the examination clinic. This is of critical importance as the authors continue to explore novel approaches to investigate the geographic variation in disease etiology.
Keywords: African Americans; Bayesian model; binomial model; epidemiologic methods; Gini coefficient; Lorenz curve; representation; topography, medical
Appropriately characterizing “at-risk” populations in epidemiologic studies is critically important to facilitate investigations of the underlying mechanisms and occurrences of disease in a population over time. Recent advances in geographic information systems software and multilevel methodology allow for more extensive characterization of cohort representativeness than heretofore reported because of their ability to link data from multiple sources. Adequately describing the variation in epidemiologic study samples in comparison with the at-risk population ensures the accuracy, validity, and generalizability of study findings. Still needed are quantitative methods that fully characterize study samples and provide empirical evidence regarding the generalizability of results, error estimation when studying a sample rather than the population, and causal inferences concerning disease etiology.
Theoretical and analytical methods in spatial epidemiology are often adapted from traditional statistics and allow for investigation of disease with regard to spatial location in relation to explanatory factors that may modify or exacerbate risk (1–3). In largely separate research, the Lorenz curve and the Gini coefficient have been used by economists (4–6), sociologists (7–9), demographers (10), political scientists (11), infectious disease epidemiologists (12, 13), and health-care practitioners (14–16) to assess the distribution of some commodity—income, mortality, and medical care providers—across a geographic region. We propose a novel use of the Lorenz curve and Gini coefficient to assess the representativeness of a geographically referenced, population-based cohort when compared with the underlying at-risk population.
Our work is motivated by the Jackson Heart Study (JHS), a large, single-site, population-based, longitudinal cardiovascular health study, which recruited participants from 3 adjacent geographic areas by using a variety of sampling algorithms (17). A number of questions, however, arise regarding the implementation of these different sampling algorithms, namely: 1) How representative is the sampled population of the true, underlying a t-risk population?; 2) Does the lack of randomness in the purposive sample (i.e., JHS Family Study) limit the use of probability theory and inferences within this cohort?; 3) To what extent are results externally generalizable?; and 4) Is there enough variability at both the individual and neighborhood levels to utilize multilevel methodology to examine contextual effects on health and health behavior?
The JHS provides an excellent opportunity to explore the utility of the Lorenz curve and Gini coefficient to fully characterize the comparability of the cohort to the at-risk population in a geographic setting. In this paper, we demonstrate the utility of using (in)equality measures to assess the representativeness of the JHS cohort with respect to the African-American population in the Jackson, Mississippi, Metropolitan Statistical Area, the most densely populated area in Mississippi, and we describe the geographic variation in recruitment.
MATERIALS AND METHODS
Recruitment
Between 2000 and 2004, a total of 5,301 noninstitutionalized African Americans residing in Hinds County, Madison County, and Rankin County, Mississippi, were recruited by using 4 population-based sampling frames: participants from the Jackson, Mississippi, site of the Atherosclerosis Risk in Communities (ARIC) Study; Jackson, Mississippi, Metropolitan Statistical Area residents selected at random; volunteers constrained by US Census characteristics; and first-degree relatives of enrolled participants. Details of the recruitment protocol and sample characteristics have been described previously (17). Briefly, living participants of the ARIC Study cohort, originally recruited from within the boundaries of the City of Jackson (Hinds County) by using the driver's license registry (18), comprised approximately 31% of the JHS cohort. The community sample included a random (17%) selection of adults aged between 35 and 84 years who resided in households within US Census tracts with a 30%–79% African-American population. Volunteers (30%) from each county who met census-derived age, sex, and socioeconomic eligibility criteria supplemented the random sample. On the basis of the criterion of at least 2 siblings and 4 first-degree relatives of ARIC Study and community sample participants, first-degree relatives (22%), including those aged <35 and >84 years, were enumerated and recruited as part of the JHS Family Study (19). The analysis in this study was restricted to participants between the ages of 35 and 84 years to reflect the original target cohort and because of the small number of participants outside this age range.
Geographically, the Jackson Metropolitan Statistical Area has an estimated land area of 2,361 square miles (611,496.19 hectare), larger than Rhode Island and Delaware combined, and contains 104 census tracts: 63 (60.6%) in Hinds County; 20 (19.2%) in Madison County; and 21 (20.2%) in Rankin County (20). African Americans comprised 45.9% (440,801 persons) of the estimated total population. The JHS-eligible African-American population (35–84 years) in the tri-county area was 76,366 persons, with 33,415 (43.8%) men and 42,951 (56.2%) women, and varied by county: 57,804 (75.7%) in Hinds County; 10,411 (13.6%) in Madison County; and 8,151 (10.7%) in Rankin County.
Trained African-American interviewers administered standard questionnaires to obtain age, sex, and contact information, including primary mailing address. Address information was abstracted and used to geocode each JHS participant to a specific latitude-longitude coordinate (21). A total of 5,236 participants were successfully geocoded and georeferenced to 102 (98.1%) census tracts in the Jackson, Mississippi, Metropolitan Statistical Area. Of these, 4,977 (95.1%) met the 35- to 84-year age restriction, which represented 6.5% of the corresponding African-American population.
Statistical analysis
Lorenz curve.
The Lorenz curve is a graphical comparative representation of the cumulative distribution functions of 2 quantities of interest and is formed by plotting the cumulative distribution of 1 entity (e.g., JHS participants within each census tract) against the cumulative probability distribution of the other entity (e.g., African-American population within each census tract) (4, 12). In this analysis, the Lorenz curves were formed by plotting the cumulative percentage of JHS participants on the vertical axis against the cumulative percentage of the corresponding age-eligible African-American population on the horizontal axis. The tracts were ranked in ascending order (i = 1, …, 104) according to the increasing proportion of JHS participants within a given tract referent to the total number of age-eligible JHS participants. If no JHS participant was georeferenced to a particular census tract, the relative percentage for this census tract was assigned a value of 0 and ranked accordingly. By definition of the Lorenz curve, if the proportion of JHS participants was equal across tracts, then the plot would be a diagonal line (i.e., 45-degree “line of equality”); an unequal proportion would yield a curve, and the distance away from the diagonal line would represent the amount of inequality (Figure 1A).
Figure 1.
Lorenz curves and corresponding Gini coefficients assessing the representation of the Jackson Heart Study cohort to the census-derived African-American population in the Jackson, Mississippi, Metropolitan Statistical Area, 2000–2004. A, a hypothetical Lorenz curve and Gini coefficient; B, the Lorenz curve and Gini coefficient for the entire cohort and stratified by sex; C, the Lorenz curve and Gini coefficient for each county (Hinds, Rankin, Madison); D, the Lorenz curve and Gini coefficient stratified by racial composition type of the census tract. AA, African American; JHS, Jackson Heart Study.
Gini coefficient.
A statistical measure of (in)equality, the Gini coefficient represents the ratio of the area between the Lorenz curve and the diagonal line of equality divided by the total area below the line of equality (Figure 1A). We estimate this area via the unbiased Gini coefficient (22, 23), which can be written as
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where xi is the relative percentage of participants within a given tract, i is the rank of the tract according to the relative percentage of JHS participants within the tract, and n is the total number of tracts. The Gini coefficient ranges between 0 and 1. A value close to 0 indicates near equality in the distribution of JHS participants compared with that of the at-risk population across the study area, and a value close to 1 indicates little similarity in the 2 distributions. Conceptually, a higher Gini coefficient suggests that a greater concentration of JHS participants was drawn from a fewer number of census tracts than from the overall census-defined population at risk. A confidence interval of the Gini coefficient was estimated by using a bootstrapping approach developed by Efron and Tibshirami (24). A 95% confidence interval was estimated as the values for the 2.5th and 97.5th percentiles of Gini coefficient estimates generated from a bootstrap sample of 10,000 replications.
Hierarchical Bayesian models.
In addition to global summaries of distributional similarity such as the Lorenz curve and the Gini index, local variations in representativeness are also of interest. Toward this end, we used hierarchical spatial Bayesian methods to compute smoothed estimates of the probability of inclusion in the JHS cohort and mapped these estimates to assess the geographic variability of recruitment across the Jackson, Mississippi, Metropolitan Statistical Area. Importantly, hierarchical Bayesian models “borrow strength” from the available data to stabilize local estimates based on small local sample sizes. Methodological details have been described in detail elsewhere (25, 26) and are briefly outlined below.
The first-stage model assumes the following:
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where pi denotes the probability of recruitment in tract i, and ni is the population size in tract i. In the context of generalized linear mixed models, this model can be written as
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where X represents the design matrix of observed covariate values, β is the corresponding vector of unknown model parameters, and θi are the tract-specific random effects. A tract with an African-American population ≥70% was defined as predominantly African American, whereas a tract with an African-American population <70%, but ≥30% was defined as mixed, and a tract with an African-American population <30% was defined as predominantly white.
The vector of model parameters, ß, is given a uniform prior distribution. This assumes that the covariate effects are constant across the study area and that any residual geographic correlation is modeled in the random effects, θi. We assign θi a conditional autoregressive Gaussian prior structure (27–29) commonly denoted as
![]() |
where wij denotes a set of weights indicating the spatial adjacency of neighboring tracts, and ψ denotes a variance hyperparameter. If 2 tracts share a common border, wij = 1; otherwise, by convention, wij = 0. This prior structure takes into account the local contextual similarities and induces a spatial dependency among tracts. In comparison, we fit an exchangeable Gaussian prior, which smoothes local estimates toward the overall mean rather than the mean of neighboring regions. This prior structure can be denoted as
![]() |
The hyperparameters, ψ and φ, capture the sampling variability of the random effects (25). The Gamma distribution provides a commonly used conjugate prior and can be written as
![]() |
where we set α = δ = 0.001. The chosen parametric model serves as a relatively uninformative prior (29).
We fit the hierarchical spatial binomial models with 2 independent chains of a Markov chain Monte Carlo sampler for 10,000 iterations, following an initial “burn-in” period of 1,000 iterations, using each of the prior specifications (i.e., conditional autoregressive and exchangeable priors) for the random effects. The Deviance Information Criterion (30) assessed model fit.
A posterior probability distribution of JHS participant recruitment was determined for each tract from the hierarchical linear spatial binomial model. A recruitment ratio was then calculated by dividing the median posterior recruitment probability estimate by the ratio of the JHS cohort sample size to the age-restricted African-American population (6.5%). A recruitment ratio greater than 1 indicated an increased level of recruitment, and a value less than 1 indicated a lower level of recruitment. Local recruitment ratio probabilities were computed to identify tracts where the likelihood of over- or underrecruiting JHS participants may have occurred. Several thresholds for overrecruitment (1.1, 1.2, and 1.3) and underrecruitment (0.9, 0.8, and 0.7) were considered in this analysis. These thresholds represent an increasing risk (10%, 20%, and 30%, respectively) that the recruitment ratio deviated from 1. A recruitment ratio probability >0.70 indicated that the recruitment ratio deviated from 1, suggesting over- or underrecruitment, respectively.
These analyses were stratified by sex and, as a result, JHS participants georeferenced to a census tract differed by sex: 98 (94.2%) tracts for men and 101 (97.1%) tracts for women. R, version 2.9.1 (31), was used to create the Lorenz curve and to estimate the Gini coefficients. WinBUGS (32) was used to fit the spatial binomial model. All maps were created in ArcGIS, version 9.2 (Environmental Systems Research Institute (ESRI), Redlands, California).
RESULTS
Most JHS participants resided in Hinds County (n = 4,295, 86.3%), followed by Madison County (n = 452, 9.1%) and Rankin County (n = 230, 4.6%). Nearly 64% of the participants included in this analysis were women. Similar rates of women participants were observed across counties (Hinds County: 64.5%, Madison County: 57.7%, and Rankin County: 59.1%) and racial composition of census tracts (predominantly African American: 64.5%, mixed: 61.6%, and predominantly white: 59.2%).
Figure 1, B–D, displays the Lorenz curve and the corresponding Gini coefficient for the overall cohort and by sex, county, and census tract racial composition, respectively. The Lorenz curve shows that roughly 60% of the JHS participants reside in census tracts that account for 80% of the age-eligible African-American population (Figure 1B). The overall Gini coefficient was 0.37 (95% confidence interval (CI): 0.30, 0.45), indicating moderate representation of the JHS cohort representation with respect to the age-restricted African-American population. Women (Gini coefficient = 0.34, 95% CI: 0.30, 0.39) were more equitably distributed than men (Gini coefficient = 0.49, 95% CI: 0.35, 0.61). The Lorenz curve for men bends further away from the axis of equality than the curve for women, suggesting that men were more concentrated in a smaller number of tracts than were women (Figure 1B). The Gini coefficient for Hinds County was 0.32 (95% CI: 0.26, 0.36) and for Rankin County was 0.33 (95% CI: 0.23, 0.39), indicating better representation of the JHS cohort in these counties than in Madison County, where the Gini coefficient was 0.56 (95% CI: 0.23, 0.69) (Figure 1C). The Gini coefficient, as well as the Lorenz curve in Figure 1D, also suggests better representation of the JHS cohort in mixed (Gini coefficient = 0.27, 95% CI: 0.17, 0.37) and predominantly African-American (Gini coefficient = 0.29, 95% CI: 0.23, 0.34) tracts than in predominantly white tracts (Gini coefficient = 0.44, 95% CI: 0.29, 0.57).
The Deviance Information Criterion suggests that the model with the conditional autoregressive prior (700.83) fit the data slightly better than did the model with the exchangeable prior (705.12), although the estimates are quite similar between the 2 models. We present the results below using the conditional autoregressive prior. In addition, we present the results using the 1.3 threshold heretofore, because this increased recruitment risk allowed us to better identify tracts where over- or underrecruitment occurred. Figure 2 illustrates the spatial pattern in the recruitment of the JHS cohort across the Jackson Metropolitan Statistical Area. Equal population-representative recruitment of JHS participants was observed in 54.0% of the census tracts in Hinds County. The proportion of tracts with equal recruitment was observed to be slightly higher in Rankin County (47.6%) than in Madison County (40.0%). Underrecruitment and overrecruitment were observed to occur less frequently (30.0% and 16.0%, respectively) in Hinds County. A lower rate of underrecruitment was observed in Madison County (40.0%) than in Rankin County (52.4%); however, overrecruitment was observed to be lower in Rankin County (0.0%) than in Madison County (20.0%).
Figure 2.
Geographic variation in the recruitment of Jackson Heart Study participants by census tracts in the Jackson, Mississippi, Metropolitan Statistical Area, 2000–2004. “Underrecruitment” is defined as the probability that the recruitment ratio probability (RRP) <0.70 exceeded 0.70; “overrecruitment” is defined as the probability that the RRP >1.30 exceeded 0.70; “equal recruitment” is defined as a probability that neither the RRP <0.70 nor the RRP >1.30 exceeded 0.70. JHS, Jackson Heart Study.
Overrecruitment occurred primarily in the northeastern area of Hinds County. Conversely, underrecruitment occurred throughout the study area, but more so along the southern and eastern peripheries and in a small cluster of tracts in the northeastern region (Figure 2).
DISCUSSION
This study examines the representativeness of the JHS cohort with respect to the African-American population in the Jackson, Mississippi, Metropolitan Statistical Area by using both global and local summaries. To our knowledge, no longitudinal cardiovascular epidemiologic study has examined the representation of its study participants to the underlying at-risk population by using measures of (in)equality, such as the Lorenz curve and the Gini coefficient. This study demonstrates the utility of using these measures to characterize the representation of epidemiologic samples, particularly in study populations recruited through a variety of different sampling algorithms. Failure to understand and to describe sample representation could result in erroneous contextual inferences and limit external validity. Further, this enables us to generalize disease distribution and to infer the impact of built environment effects on health in African Americans in the Jackson, Mississippi, Metropolitan Statistical Area using JHS data in future studies.
We documented relatively high representativeness of the JHS cohort at the census tract level across the study area. The moderate deflection of the Lorenz curve from the axis of equality and low corresponding Gini coefficient suggests, for the most part, a fairly uniform distribution of JHS participants to the corresponding African-American population. Similar Gini coefficient estimates have been reported in previous studies that assessed the equality of the distribution of some commodity over a geographic area (5–7, 9, 13–15). The distribution of JHS women participants tends to be more representative than the distribution of JHS men participants, indicating potentially better representation of African-American women in the Jackson, Mississippi, Metropolitan Statistical Area than African-American men in the JHS. As expected, participants residing in mixed and predominantly African-American tracts were more representative of the underlying population than residents in predominantly white tracts. Also, JHS participants were more representative of the underlying population in Hinds County and Rankin County than in Madison County. Three spatial patterns in the recruitment of JHS participants emerged. First, equal recruitment was observed more often in Hinds County than in other areas dispersed in Madison County and Rankin County. Second, overrecruitment was observed in the northeastern area of Hinds County (the City of Jackson, the capital of Mississippi). Third, underrecruitment occurred more often in the southern (Hinds County), eastern (Rankin County), and northeastern (Madison County) peripheries.
The observed differing level of representation and spatial variation in the recruitment of JHS participants could be attributed to a number of factors. First and foremost, oversampling in the northeastern Hinds County reflects the location of the ARIC Study subsample of the JHS. Although the ARIC Study relied on probability sampling from the driver's license registry, the city limits of Jackson formed the geographic boundary for sample selection. In addition, we recruited approximately 20% of our cohort from US Census tracts with 30%–79% African-American population using a commercial list of households with individuals aged between 35 and less than 85 years residing in census tracts with a 30%–79% African-American population (17). This may have led to better representation in mixed and predominantly African-American tracts and more proportional recruitment in Hinds County, a region with a high African-American population. None of the tracts in Rankin County, however, met this recruitment criterion, thus limiting recruitment in this area using the community random sample recruitment protocol and potentially contributing to the low recruitment in this county. This was not unexpected as the initial recruitment activities (e.g., recruits received a brochure and heard about the study on the radio) yielded low recruitment from a number of rural areas in Rankin County. We are not led to believe that the slightly lower number of JHS participants residing in Rankin County (4.7%) from the target age-eligible population (10.7%) would markedly alter the results in current and future studies, although we note this potential limitation. The travel distances from the outer peripheries to the single examination site located in the center of the study area also may have contributed to the low recruitment rates in these areas. On average, the travel distance from these areas was 25 miles (40.23 km), an approximate 30-minute travel time travelling 55 miles (88.51 km) per hour. Moreover, these tracts contained small African-American population sizes. Finally, issues of mistrust among African Americans toward public health and medical research are well established (33). The JHS used a culturally specific, community-driven model of recruitment (34) to address these issues. Women are more likely to participate in medical and public health research studies than are African-American men, which may have led to the better representation among women in the JHS.
This study is not without limitations. Our use of the Gini coefficient (and Lorenz curve) may have influenced our findings, although Kawachi and Kennedy (7) have shown previously that the choice of inequality measure did not affect study outcomes. The Gini coefficient used in this analysis is the unbiased estimator of the population Gini coefficient, thus strengthening the accuracy of our results. Furthermore, the Gini coefficient is insensitive to outliers. We chose this measure rather than the other existing quantitative (in)equality measures (i.e., Robin Hood Index; Atkinson Index; Theil's entropy measure) (35) a priori because of its transdisciplinary applicability and ease of use. Some of the other appealing features of the Gini coefficient are its ease of computation and interpretation, with theoretical values ranging from 0 (i.e., perfect equality) to 1.0 (i.e., perfect inequality) (4, 12, 35). Free statistical software packages, such as the R statistical package (31), contain add-on macros that easily and readily compute the Gini coefficient. The R code used to construct the Lorenz curve, to estimate the Gini coefficient, and to estimate the spatial binomial models is included in the Web Appendix posted on the Journal's Web site (http://aje.oupjournals.org/). Because of the sensitivity of and consent regarding geocoded information, we are unable to provide direct access to these data to the public. Interested persons should contact the corresponding author (D. A. H.) to utilize these data in future analyses.
Confirming specific features in the distribution of participants in a longitudinal epidemiologic study in relation to the at-risk populations can offer insight into the distribution of disease within the underlying populations. As the JHS continues, we will be able to investigate the geographic pattern and etiology of cardiovascular, renal, and pulmonary diseases within this high-risk African-American population over time. For example, the Gini coefficient can be used to monitor the distribution of disease over time and to determine areas where this (in)equality has increased or decreased. The public health impact in reducing health disparities within this population could be substantial. Information from the JHS will lend insight into the development of geographically targeted interventions and further investigation into areas where disparate populations experience a high burden of disease. Recent evidence of increasing geographic variation of mortality risk in the United States (36) suggests that if we can fully characterize at-risk populations in epidemiologic studies, then studying regional samples of people (37) may become more relevant over time and help to explain the excess geographic variation in disease. Studies such as the JHS are beginning to test many of these hypotheses, and future data may offer further insights into contributing factors that underscore variation in disease morbidity and mortality.
In this study, we found that participants in the JHS are fairly representative of the African-American population in the Jackson, Mississippi, Metropolitan Statistical Area but also documented some geographic variation in the level of representation. Better representation was observed among women and US Census tracts with high African-American populations. Importantly, we demonstrated the utility of the Lorenz curve and Gini coefficient in measuring representation and Bayesian methods in assessing geographic variation in the recruitment of participants in an epidemiologic study. This is of critical importance as we continue to explore novel approaches to investigate geographic variation in the etiology of disease.
Supplementary Material
Acknowledgments
Author affiliations: Jackson Heart Study, Jackson State University, Jackson, Mississippi (DeMarc A. Hickson, Donna Antoine-Lavigne, Daniel F. Sarpong); Department of Medicine, University of Mississippi Medical Center, Jackson, Mississippi (DeMarc A. Hickson); Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, Georgia (Lance A. Waller); Center for Integrative Approaches to Health Disparities, School of Public Health, University of Michigan, Ann Arbor, Michigan (Samson Y. Gebreab); School of Nursing, University of Mississippi Medical Center, Jackson, Mississippi (Sharon B. Wyatt); and School of Health Sciences, Jackson State University, Jackson, Mississippi (James Kelly).
This work was supported by National Institutes of Health contracts (N01-HC-95170, N01-HC-95171, and N01-HC-95172) provided by the National Heart, Lung, and Blood Institute and the National Center for Minority Health and Health Disparities (NCMHD). This work was also supported in part by a pilot grant to D. A. H. from the University of Michigan Center for Integrative Approaches to Health Disparities (P60MD002249), which is funded by the NCMHD.
The authors thank the Jackson Heart Study team for their long-term commitment and important contributions to understanding the epidemiology of cardiovascular and other chronic diseases. The authors also thank all of the Jackson Heart Study recruiters (listed alphabetically): Felix Anderson, Christopher Ellis, Clara Funches, Verna Gess, Willie Jacobs, Belinda Johnson, Retina Johnson, Keisha Jones, Makeaba Latiker, Venetra McKinney, Sababu Rashid, Laverne Thigpen, and Zebbie Williams-Johnson.
Conflict of interest: none declared.
Glossary
Abbreviations
- ARIC
Atherosclerosis Risk in Communities
- CI
confidence interval
- JHS
Jackson Heart Study
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