• View in gallery
    Figure 1.

    Data collected in the Pith Moromo/Pii En Ngima pregnancy cohort, by study time point (n = 371).1 Individual food insecurity (IFIAS), 24-hour food frequency, use of iron supplements;2 HIV status, 24-hour gastrointestinal distress recall, pregnancy status;3 depression (Center for Epidemiologic Studies-Depression scale), stress (Perceived Stress Scale);4 age, ethnic group, religion, and clinic location.

  • View in gallery
    Figure 2.

    Progress of participants through the Pith Moromo/Pii En Ngima study. Three hundred seventy-one women enrolled into the parent study; 11.3% were lost to follow-up.

  • View in gallery
    Figure 3.

    Proportion of women engaging in geophagy in the prior 24 hours by reproductive status relative to index pregnancy and HIV status (bars; black = HIV positive, gray = HIV negative); mean hemoglobin concentration (g/dL) by reproductive status relative to index pregnancy and geophagy in the prior 24 hours (lines; black line with diamond = geophagous, gray line with circle = nongeophagous). Mean hemoglobin was significantly lower among geophagous women than nongeophagous women during pregnancy and postpartum (P < 0.001). *P < 0.05.

  • View in gallery
    Figure 4.

    Logarithmic probability of engaging in geophagy based on hemoglobin concentration (g/dL). Between-person variations in hemoglobin (solid line) are more strongly associated with geophagy than within-person changes (dashed lines).

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Geophagy among a Cohort of Kenyan Women with Mixed HIV Status: A Longitudinal Analysis

Joshua D. MillerDepartment of Anthropology, Northwestern University, Evanston, Illinois;

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Kaitlyn G. FitzgeraldDepartment of Statistics, Northwestern University, Evanston, Illinois

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Abigail L. SmithDepartment of Statistics, Northwestern University, Evanston, Illinois

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Sera L. YoungDepartment of Anthropology, Northwestern University, Evanston, Illinois;

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Geophagy, the craving and purposive consumption of earth, is commonly reported during pregnancy. To date, most studies of geophagy have been cross-sectional and have not assessed its relationship with HIV infection. Therefore, to concurrently examine proposed etiologies of geophagy, a cohort of 371 women with mixed HIV status from Nyanza region, Kenya were recruited in late pregnancy and interviewed about pica at nine time points, through 21 months postpartum. Nutritional status (hemoglobin concentration and food insecurity), physical health (HIV infection and gastrointestinal distress), and psychosocial health (depression and perceived stress) were also repeatedly assessed. Prevalence of geophagy was greatest during pregnancy and decreased significantly postpartum. In a two-level hierarchical linear model, a one-unit increase in average hemoglobin (g/dL) was associated with a 35% decrease in the odds of geophagy. The adjusted odds ratios (CI) of geophagy were 3.98 (2.99, 5.29), 2.54 (1.13, 5.69), and 1.68 (1.15, 2.44) times higher if a woman was pregnant, reported diarrhea in the prior 24 hours, or was HIV positive, respectively. The adjusted odds ratio of geophagy was 1.61 (1.06, 2.45) times higher if a woman reported geophagy during childhood. Our results lend greatest plausibility to the protection hypothesis (i.e., that geophagy occurs in response to compromised immunity and/or infection). Given the high prevalence of geophagy, clinicians should regularly screen for the behavior and measure inflammatory biomarkers before treating geophagy with iron supplements, which can exacerbate some infections.

INTRODUCTION

Geophagy, the craving and purposive consumption of earth substances, is a quintessential form of pica. It is most commonly reported by pregnant women, but is also well documented among other vulnerable populations.1 Despite its considerable prevalence24 and association with both iron and zinc deficiencies,5 the causes and consequences of geophagy remain poorly understood.

Proposed causes of geophagy can be grouped into three domains: nutrition, protection, and psychosocial factors. Geophagy has mostly commonly been hypothesized to be a response to poor nutrition. Given the strong, clinically significant association between geophagy and lower iron, hemoglobin, and zinc concentrations,5 many researchers and health practitioners contend that geophagy is an adaptive strategy to supplement nutrients that are deficient in the diet.6 Alternatively, geophagy may be an epiphenomenon of micronutrient deficiency, that is, a maladaptive side effect.7 Indeed, geophagic earths can introduce heavy metals8 and pathogens9 that may negatively impact both maternal well-being and fetal development. In addition, geophagy has been proposed as a means to sate hunger.10

Geophagy may also be protective during times of impaired physical or immunological health. Many geophagic earths have a demonstrated capacity to reinforce the intestinal mucosa against or directly adsorb pathogens and harmful chemicals.11,12 Consumed earths may also increase immunological activity, introduce beneficial bacteria to the gut flora, and induce nutritional immunity by impeding the uptake of dietary iron, although these pathways have not been rigorously evaluated.13,14 Furthermore, individuals report consuming geophagic earths to quell gastrointestinal malaise.15 Most geophagic earths contain clay minerals that can reduce nausea, and some are alkaline, making them effective antacids.1618 Thus, during periods of impaired immune function (e.g., pregnancy and childhood), individuals may consume geophagic earths to protect against or reduce the effects of infection.

The third explanation is that geophagy is a psychosocial phenomenon, that is, it is not driven by physiology. Indeed, some individuals report eating earth as a mechanism for reducing anxiety.19 There is also evidence that cultural norms can mediate the expression of geophagy.20

To date, most geophagy studies have been cross-sectional and have not been designed to rigorously examine proposed etiologies concurrently. Furthermore, although geophagy has been reported among individuals living with HIV,19,21 no study has collected data on both HIV-infected and -uninfected populations to explore if the behavior is associated with immunosuppression. Therefore, we examined geophagic behavior among a cohort of women with mixed HIV status in western Kenya across a period of 24 months, from approximately 6 months of pregnancy to 21 months postpartum. Our first objective was to explore the relationship between fluctuations in hemoglobin concentration across time and geophagy. Our second objective was to determine the most significant nutritional, physical health, and psychosocial covariates of geophagy. We hypothesized that decreasing hemoglobin concentrations among women in our study would be associated with greater odds of geophagy, and that HIV infection, pregnancy, and gastrointestinal upset would be most strongly associated with geophagy.

MATERIALS AND METHODS

Study setting and population.

Data are from Pith Moromo, a longitudinal cohort study examining the health consequences of food insecurity and HIV during the first 1,000 days (NCT02974972). Pregnant women (n = 371) were recruited from seven rural, periurban, and urban antenatal clinic sites in Nyanza region, Kenya (near Lake Victoria) between September 2014 and June 2015. Women were eligible for inclusion if they were within their first 7 months of pregnancy and intended to live in the catchment area until their infant(s) reached at least 9 months of age. Quota sampling was used to achieve equal numbers of HIV-infected and HIV-uninfected pregnant women by tertiles of food insecurity scores, as assessed using the nine-item Individual Food Insecurity Access Scale (IFIAS) (low: 0–9, moderate: 10–18, and severe: 19–27).22 Women with HIV were oversampled (approximately 6.9% of women of reproductive age in western Kenya have HIV23) to detect differences in primary study outcomes (e.g., maternal BMI) by HIV status at a power of 0.8. Participants still in the study at 9 months postpartum were enrolled into Pii En Ngima and surveyed through 21 months postpartum (NCT02979418).

This was an appropriate area to study geophagy during pregnancy because nearly 97% of women from this region attend at least one antenatal clinic during gestation.24 Geophagy is also common in western Kenya, with reported prevalence ranging from 27% to 75% among obstetric populations.4,25,26 In this region, Luo is both the predominant language spoken and ethnic group with which most individuals identify.

Ethics.

This study was approved by the Institutional Review Boards of Cornell and Northwestern Universities, and the Kenya Medical Research Institute. All participants provided written informed consent at enrollment.

Data collection.

Survey data were collected by local clinic-based study nurses using paper forms and tablet-based electronic surveys. Interviews were conducted at nine time points: twice during the index pregnancy and seven times after delivery, through 21 months postpartum (Figure 1). Most sociodemographic characteristics, including age, religion, and ethnic group, were collected at baseline. A principal component analysis was performed on reported household assets and used to represent household wealth.

Figure 1.
Figure 1.

Data collected in the Pith Moromo/Pii En Ngima pregnancy cohort, by study time point (n = 371).1 Individual food insecurity (IFIAS), 24-hour food frequency, use of iron supplements;2 HIV status, 24-hour gastrointestinal distress recall, pregnancy status;3 depression (Center for Epidemiologic Studies-Depression scale), stress (Perceived Stress Scale);4 age, ethnic group, religion, and clinic location.

Citation: The American Journal of Tropical Medicine and Hygiene 101, 3; 10.4269/ajtmh.19-0149

Data were collected at multiple time points on nutritional status (food security [IFIAS, 0–2722], 24-hour food frequency,27 and use of iron supplements), physical health (HIV status [colloidal gold rapid test], gastrointestinal distress [nausea, diarrhea in the prior 24 hours], pregnancy status [human chorionic gonadotropin urine tests], and hemoglobin concentration [HemoCue cuvettes]), and psychosocial health (depression [Center for Epidemiologic Studies-Depression scale, 0–6028] and stress [Perceived Stress Scale, 0–4029]) (Figure 1).

Participants were asked about pica in the prior 24 hours at each time point (Figure 1). Pica items queried about were based on formative qualitative work (unpublished) and established best practices,30 which included raw starches, charcoal, ash, earth, odowa (soft stones that are widely available for sale in Kenya), and other earth-like items (Supplemental File 1). Given that less than 2.0% of study participants reported any amylophagy or other forms of pica at any single time point (Supplemental Figure 1), geophagy is the focus of our analyses. Recall of pica during childhood was measured at 3 months postpartum. A woman’s classification as geophagic was determined for each visit and based on her recall of consuming earth in the prior 24 hours.

Data cleaning and multiple imputation.

Data cleaning was performed using Stata 14.0 (StataCorp, College Station, TX). To account for missing data across items most salient to our proposed hypotheses, multiple imputation was performed using RStudio 1.1.442 (RStudio, Inc., Boston, MA). The three primary sources of missing data were attrition, nonresponse (e.g., participant refusal), and systematic missingness due to staggered data collection (Figure 1, Supplemental File 2). Ultimately, 10 complete datasets were generated for analysis; presented point estimates were computed by averaging across these datasets according to Rubin’s rules31 (see Supplemental File 2 for discussion of variable selection).

To evaluate the plausibility of the imputed data, we performed each statistical analysis using three sources of data: the original dataset with missing values, the imputed datasets, and the imputed datasets excluding visits where hemoglobin was not measured. All three analyses gave similar results (i.e., direction of associations and significance at P < 0.05) and differed only in the magnitude of coefficients.

Statistical analysis.

Descriptive statistics were performed using Stata 14.0 and RStudio 1.1.442 by pooling across the 10 imputed datasets. A two-level hierarchical generalized linear model (HGLM) of reported geophagy across time was conducted using HLM 7.01 (Scientific Software International, Inc., Lincolnwood, IL). Two-level HGLM is a preferred method because it accounts for the nonindependence of observations inherent in longitudinal data by nesting time-variant variables (level 1) within individual participants (level 2) (Supplemental Figure 2). Furthermore, HGLM can uniquely differentiate between within- and between-person variations across visits.

Model building followed the framework developed by Raudenbush and Bryk.32 Each variable was first included in a single-predictor exploratory model for reported geophagy. Variables were then added to an HGLM in a forward stepwise manner, beginning with the strongest predictor and building up. Variables were omitted if they had neither a significant fixed effect coefficient nor evidence of slope heterogeneity as a random effect (see Supplemental File 2 for a more thorough discussion about model building). Population-average models with robust standard errors are reported.

RESULTS

Cohort characteristics.

Three hundred seventy-one pregnant women were enrolled into the parent Pith Moromo study. Three hundred five of these participants were subsequently enrolled into the follow-up Pii En Ngima study. Ultimately, 298 participants completed both Pith Moromo and Pii En Ngima; total lost to follow-up was 11.3% (Figure 2).

Figure 2.
Figure 2.

Progress of participants through the Pith Moromo/Pii En Ngima study. Three hundred seventy-one women enrolled into the parent study; 11.3% were lost to follow-up.

Citation: The American Journal of Tropical Medicine and Hygiene 101, 3; 10.4269/ajtmh.19-0149

A majority of enrolled participants (85.6%) were Luo. Most participants were Christian (96.7%) and attended periurban antenatal care clinics (44.0%) (Table 1). At baseline, geophagy in the prior 24 hours was reported by 16.2% of the pregnant females and a majority (59.0%) were not anemic. Food insecurity, perceived stress, and probable depression scores were high in this cohort (Table 1).

Table 1

Characteristics of study participants (n = 371) at baseline

Participants at baseline (n = 371)
Age, mean (SD)24.8 (4.9)
Ethnic group, %
 Luo85.6
Religion, %
 Catholic17.2
 Seventh Day Adventist23.7
 Protestant35.2
 Christian-Other20.7
 African traditional3.3
Clinic location, %
 Urban19.0
 Periurban44.0
 Rural37.0
Wealth,* %
 Moderate24.2
 High32.7
Geophagy in prior 24 hours
 Yes16.2
Food insecurity score (0–27), mean (SD)13.9 (7.1)
GI distress in prior 24 hours, %
 Nausea21.7
 Diarrhea3.0
HIV
 Positive50.4
Hemoglobin (g/dL), mean (SD)11.1 (1.0)
Anemia, %
 Mild28.8
 Moderate12.2
Perceived stress score (0–40), mean (SD)20.0 (4.4)
CES-depression score (0–60), mean (SD)18.4 (8.3)

* Based on principal component analysis of reported assets.

Pica and hemoglobin across time.

Geophagy was the most common form of pica practiced. Across all time points, 51.5% of women reported pica and 45.1% reported geophagy in the prior 24 hours at least once (Supplemental Figure 1). A greater proportion of women living with HIV reported geophagy in the prior 24 hours at least once (53.8%) than women who were HIV negative (36.3%).

Geophagy was more common during pregnancy and peaked during the third trimester; 23.0% of the 256 women interviewed between 8 and 9 months of pregnancy recalled eating earth items in the prior 24 hours (Figure 3). Reported geophagy decreased significantly postpartum (P < 0.001). A greater proportion of HIV-infected women engaged in geophagy at 4–5 months of pregnancy, 1–2 months postpartum, and 18–20 months postpartum than HIV-uninfected women (Figure 3).

Figure 3.
Figure 3.

Proportion of women engaging in geophagy in the prior 24 hours by reproductive status relative to index pregnancy and HIV status (bars; black = HIV positive, gray = HIV negative); mean hemoglobin concentration (g/dL) by reproductive status relative to index pregnancy and geophagy in the prior 24 hours (lines; black line with diamond = geophagous, gray line with circle = nongeophagous). Mean hemoglobin was significantly lower among geophagous women than nongeophagous women during pregnancy and postpartum (P < 0.001). *P < 0.05.

Citation: The American Journal of Tropical Medicine and Hygiene 101, 3; 10.4269/ajtmh.19-0149

On average, hemoglobin concentration increased by 0.32 (±1.09) g/dL across the sampling interval (Figure 3); this did not differ significantly by any reported geophagy. However, mean hemoglobin concentration was significantly lower among geophagous women relative to nongeophagous women, both during pregnancy (10.66 ± 0.13 versus 11.34 ± 0.07 g/dL, P < 0.001) and postpartum (10.88 ± 0.16 versus 11.42 ± 0.06 g/dL, P < 0.001).

Modeling geophagy and hemoglobin across time.

Individual fluctuations (i.e., within-person changes) in hemoglobin (Figure 4, dashed line) across time were not associated with geophagy in a single-predictor HGLM (P = 0.203, Supplemental File 2). Given the consistently strong relationship between geophagy and hemoglobin concentration in prior studies,5 the between-person effects of hemoglobin were then investigated (Figure 4, solid line). In a single-predictor HGLM of geophagy, between-person differences in hemoglobin were statistically significant (P = 0.006, Supplemental File 2), suggesting that an individual’s hemoglobin concentration relative to others in the cohort was a stronger predictor of geophagy than individual variations over time. Therefore, in the final HGLM of geophagy, hemoglobin was operationalized as an individual’s average concentration across visits and included as a time-invariant, level 2 predictor.

Figure 4.
Figure 4.

Logarithmic probability of engaging in geophagy based on hemoglobin concentration (g/dL). Between-person variations in hemoglobin (solid line) are more strongly associated with geophagy than within-person changes (dashed lines).

Citation: The American Journal of Tropical Medicine and Hygiene 101, 3; 10.4269/ajtmh.19-0149

Covariates of geophagy across time.

In the final multivariable HGLM of geophagy, a one-unit increase in average hemoglobin (g/dL) was associated with a 35% decrease in the odds of geophagy (P < 0.001) (Table 2). Being pregnant, having diarrhea in the prior 24 hours, or having HIV was associated with a 298%, 154%, and 68% increase in the odds of geophagy (P < 0.001, P = 0.025, P = 0.007), respectively. Reporting geophagy during childhood was also associated with a 61% increase in the odds of current geophagy (P = 0.027). Sociodemographic characteristics, individual food insecurity, consumption of iron-rich foods in the prior 24 hours, stress, and depression were not significantly associated with geophagy when controlling for pregnancy.

Table 2

Predictors of current geophagy across time among pregnant and postpartum Kenyan women, modeled as a 2-level multivariable hierarchical model (n = 371)

VariableAdjusted odds ratio95% CIP-value
Average hemoglobin (g/dL)*0.65(0.53, 0.80)< 0.001
Pregnancy†3.98(2.99, 5.29)< 0.001
Diarrhea in prior 24 hours†2.54(1.13, 5.69)0.025
HIV infection*1.68(1.15, 2.44)0.007
Geophagy during childhood*1.61(1.06, 2.45)0.027

* Level 2 time-invariant variable.

† Level 1 time-variant variable.

DISCUSSION

In this first study to concurrently examine nutritional, physical health, and psychosocial covariates of geophagy across pregnancy and HIV infection status, 45.1% of women within the cohort (n = 371) reported geophagy at least once in the prior 24 hours. The prevalence of geophagy was highest during pregnancy (Figure 3), which is consistent with previous findings from Kenya and elsewhere.11,26 However, the prevalence of geophagy in this cohort was lower than that reported in other studies.3,4 This may be due to our shorter recall period (prior 24 hours); other studies had recall periods spanning the entire pregnancy.

In terms of nutrition, our data suggest that hunger was not a significant motivator of geophagy. Individual food insecurity was not associated with geophagy when controlling for pregnancy, which is consistent with most,1,33 but not all,34 previous work.

Previous studies have found a strong, biologically significant association between geophagy and lower hemoglobin concentrations.5 Although many researchers have theorized that this relationship is driven by individual fluctuations in hemoglobin, our study is the first to rigorously measure both geophagy and hemoglobin concentration across time to explore this hypothesis. In a 2-level hierarchical model, we found that individual fluctuations in hemoglobin concentration were not related to initiation or cessation of geophagy. However, between-person variations in average hemoglobin (i.e., hemoglobin concentrations relative to others in the cohort) were highly predictive of geophagy (Figure 4), such that a one-unit increase in average hemoglobin concentration was associated with a 35% decrease in the odds of geophagy (Table 2). The fact that geophagy is not associated with individual changes in hemoglobin concentrations across time does not support the supplementation hypothesis.

With respect to the protection hypothesis, our data suggest that immunosuppression is positively associated with geophagy. We found that HIV infection was associated with a 68% increase in the odds of geophagy. Although previous studies have documented geophagy among individuals living with HIV,19,21 this is the first study to include HIV-negative individuals as a comparison. In addition, we found that pregnancy was associated with a 298% increase in the odds of engaging in geophagy (Table 2); the relationship between pregnancy and geophagy has been well documented across numerous studies and ecological settings.35 Having diarrhea in the prior 24 hours was also associated with a 154% increase in the odds of geophagy. This is consistent with both qualitative and quantitative data, in which many individuals report engaging in geophagy to quell gastrointestinal upset, such as nausea and heartburn.17,36

We found no association between psychosocial health indicators (perceived stress, depression) and geophagy when controlling for pregnancy status, which does not support the psychosocial hypothesis of geophagy. This differs from several reports in which stress is described as a motivator for engaging in the behavior19 or is associated with greater stress scores,37,38 but is consistent with a case–control study that found no association between pica and postpartum depression.39 Future studies of geophagy should include validated measures of stress or depression to more robustly explore this relationship.

Reported geophagy during childhood was associated with a 61% increase in the odds of geophagy. Previous work among obstetric populations has also found associations between current pica and reported family histories of pica.40,41 Given these trends, it is theorized that culture or personal attitudes may modify the expression of geophagy.11 Alternatively, these associations may be reflective of biological or genetic predispositions to pica. Future studies should more robustly examine the influence of cultural and social relationships on the expression of pica by querying about family histories, personal histories, and any stigma or provocations experienced in relation to pica.

Taken together, these results suggest greatest plausibility for the protection hypothesis. Although iron deficiency anemia is the most common form of anemia globally, and is often hypothesized to be a cause of geophagy, emergent literature suggests that a large proportion of anemia among women of reproductive age is attributable to chronic infection.42 Given the causal links between infection and anemia,43 it is possible that infection independently influences geophagy and may be confounding the observed relationship between geophagy and hemoglobin concentration. Thus, the strong association observed between geophagy and indicators of compromised immune systems (HIV infection, pregnancy, and diarrhea) suggests that geophagy may be a marker of infection.

Our findings have important implications for the treatment of geophagy and future clinical research. First, reported geophagy may be a useful indicator of chronic infection and low hemoglobin concentration in low-resource medical settings, although research that more rigorously examines geophagy, iron status, and biomarkers of infection is required to validate this method. In addition, clinicians have commonly treated geophagy by prescribing iron supplements,44 which can exacerbate some underlying infections.45 Therefore, we implore clinicians to consider biomarkers of infection, as well as hemoglobin concentration, before prescribing iron supplements to treat geophagy. Given that pregnant women and individuals living with HIV have suppressed immune systems,4648 it is important to understand how their health can best be protected. Finally, some geophagic earths can bind antibiotics and other medicines49,50 and may decrease the efficacy of important antiretroviral medicines. Research investigating the impact of geophagy on both drug pharmacokinetics and infection is needed, including rigorous measurement of disease status and inflammatory cytokines [e.g., interleukin (IL)-1, IL-6, and tumor necrosis factor-alpha].

Strengths of our study include its longitudinal design and unique examination of geophagy in relation to HIV. In addition, our findings are robust, given the relatively large sample size and repeat measurement of relevant covariates, including hemoglobin concentration. However, there are several limitations. First, our imputed datasets may mask true within-person trends because some data were systematically missing (Supplemental File 2), which no statistical methods can recover. Second, caution is warranted when generalizing our findings to other populations. Although a quota sampling strategy was useful for detecting differences in the primary exposures of Pith Moromo/Pii En Ngima, our nonprobability sample is systematically different than the broader Kenyan population.23

In conclusion, we found that geophagy was commonly practiced among pregnant women in the cohort and strongly associated with lower average hemoglobin concentrations, pregnancy, HIV infection, diarrhea, and childhood geophagy, which lends support to the protection hypothesis. Taken together, these data suggest that geophagy may be an indicator of increased susceptibility to infection. Clinicians should, therefore, measure inflammatory biomarkers before treating geophagy with iron supplements, which can exacerbate some infections. In addition, given the strong associations with negative health outcomes and high prevalence of the behavior among obstetric populations, clinicians and public health professionals should regularly screen for geophagy. Ultimately, longitudinal studies, especially control trials, are needed to understand the biochemical pathways that are involved in the strong relationships we observed between geophagy and periods of increased vulnerability.

Supplemental materials

Acknowledgments:

We would like to thank the Kenya Medical Research Institute (KEMRI) for providing space within the FACES clinics for the work to be conducted, ethical and logistic support to conduct this research, and oversight in Kenya. We would also like to warmly thank study nurses and study trackers, as well as the mothers and their infants who participated in this study. We are also grateful to Dr. Kimberly O’Brien (Cornell Unviersity), Dr. Asher Rosinger (Pennsylvania State University), and Jean Cox (University of New Mexico) for providing feedback on earlier versions, as well as statistical guidance from Dr. Bruce Spencer (Northwestern University).

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Author Notes

Address correspondence to Sera L. Young, Department of Anthropology, Northwestern University, Evanston, 1819 Hinman Ave., Evanston, IL 60208. E-mail: sera.young@northwestern.edu

Financial support: Research activities and S. L. Y. were supported by the National Institute of Mental Health (K01 MH098902 and R21 MH108444). K. G. F. was supported by the U.S. Department of Education, Institute of Education Sciences, Multidisciplinary Program in Education Sciences (R305B140042). Authors had full access to all study data and had final responsibility for the decision to submit for publication.

Authors’ addresses: Joshua D. Miller and Sera L. Young, Department of Anthropology, Northwestern University, Evanston, IL, E-mails: josh.miller@northwestern.edu and sera.young@northwestern.edu. Kaitlyn G. Fitzgerald and Abigail L. Smith, Department of Statistics, Northwestern University, Evanston, IL, E-mails: kgfitzgerald@u.northwestern.edu and abigailsmith2021.1@u.northwestern.edu.

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