Quantifying Error Disparities in Population Health Models

1 Introduction

Population health surveillance traditionally relies on surveys and administrative data, which are costly, temporally lagged, and often lack fine-grained spatial resolution. Recent work shows that community-aggregated social media language can predict health outcomes at the U.S. county level [Mangalik et al., 2024]. However, as with public health disparity analyses that guide fair resource allocation [Beck et al., 2014; Lemstra et al., 2006; Shavers, 2007], before such systems can inform public health policy, we must understand their error disparities-systematic differences in model performance across sociodemographic groups [Shah et al., 2020].

Error disparities have been extensively studied at the document- or person-level [Salinas et al., 2023; Garimella et al., 2022; Rawat et al., 2024], but remain poorly understood for community-level prediction tasks such as regional health and well-being. To address this gap, we systematically evaluate language-based predictive models across four community-level health outcomes, examining error disparities along three sociodemographic dimensions with known selection biases on Twitter [Giorgi et al., 2022a]: percentage of foreign-born, percentage of educated, and median household income.

We focus on sociodemographic ("human factor") inclusion techniques [Zamani et al., 2018] - methods that incorporate demographic factors to substantially improve model accuracy [Giorgi et al., 2023; Hovy, 2015] - though their impact on bias or error disparities is unexplored. While sociodemographic inclusion could theoretically increase bias, past studies indicate it can also reduce it [Shah et al., 2020]. We hypothesize this could depend on the inclusion strategy. We therefore evaluate two classes of methods: additive approaches, which account for baseline outcome differences across demographic groups [Zamani and Schwartz, 2017], and adaptive approaches, which allow language features to vary with sociodemographic context [Lynn et al., 2017; Zamani et al., 2018].

Our key contributions are three-fold: (1) Systematic bias assessment: We analyze which community health tasks and sociodemographic factors are most prone to error disparities in NLP models utilizing both traditional ngram and modern transformer LM approaches; (2) Evaluation of mitigation methods: We evaluate four sociodemographic factor inclusion strategies, spanning additive and adaptive approaches, and examine the relationship between accuracy and error disparities; and (3) Novel metric: We propose the Bilateral Concentration Index (BCI), inspired by the Gini coefficient, to quantify error disparities for continuous-valued community outcomes, capturing non-linear and non-monotonic sociodemographic-error relationships.

Our findings reveal a trade-off between accuracy and fairness in community-level prediction, with implications for the responsible deployment of NLP systems in policy-relevant settings.

Interdisciplinary Domain Expertise. This work was carried out in close collaboration with (i) a clinical psychologist with expertise in end-point bias and (ii) a clinical and public health biostatistician. The psychologist contributed to problem formulation and framing, leveraging their expertise in ethics and fairness to contextualize potential communitylevel harms, guide the analysis, and lead development of the paper's ethics section. This input shaped how we interpret model error disparities in terms of societal impact and policy relevance. The biostatistician contributed to the statistical methodology, including guidance on regression and correlation analyses, validation procedures, and population-level inference, and refined the methodological language to ensure statistical rigor and clarity. Overall, these collaborations informed both the technical design and the ethical framing of the study.

2 RelatedWork

Prior work has explored incorporating sociodemographic information into language-based models for over a decade [Hovy, 2015; Soni et al., 2024], primarily to improve predictive performance or language understanding [Lynn et al., 2017; Huang and Paul, 2019]. More recent studies have examined conditioning models on human traits such as empathy, emotion, or personas in dialog and generative settings [Rashkin et al., 2019; Roller et al., 2021; Hu and Collier, 2024]. However, the impact of such sociodemographic inclusion on error disparities has not been systematically studied.

Separately, a substantial body of work has documented demographic disparities in NLP model errors. Early evidence includes the "Wall Street Journal effect," where tagging errors increased for text authored by individuals demographically distant from the training data [Hovy and Søgaard, 2015]. More recent studies show persistent performance gaps in health-related prediction tasks [Rai et al., 2024] and in social media content moderation, where language from Black individuals is more likely to be mislabeled as hate speech [Sap et al., 2019]. Although these studies focus on individual- or document-level tasks, they motivate the need to examine and mitigate disparities in community-level modeling.

In population health settings, evaluating bias remains challenging, particularly for regression-based community outcomes. Existing fairness metrics largely target binary classification or discrete groups [Pessach and Shmueli, 2022], and a comparatively small fraction of prior work addresses regression settings [Mehrabi et al., 2021]. Widely used measures such as statistical parity and bounded group loss [Agarwal et al., 2019] do not naturally extend to continuous outcomes or continuous sociodemographic attributes, while alternatives such as Individual Fairness [Berk et al., 2017] are difficult to operationalize for model evaluation. These limitations motivate the need for metrics tailored to continuous, communitylevel disparity analysis.

3 Data Set

We draw on county-level datasets during two distinct time periods that pair large-scale language use with sociodemographics and health outcomes. Below, we describe the language features, control variables, and outcome measures used in our analyses.

Community Language We use the County Tweet Lexical Bank (CTLB), which is an open-source dataset of U.S. county-level language features. We describe the details relevant to our experiments here, while other specifics can be found in [Giorgi et al., 2018]. This dataset is derived from a 10% sample of Twitter from 2009-2015. From this sample, Twitter users were mapped to U.S. counties - administrative regions within each state - via self-reported location (via a free-text field in their profile) and latitude/longitude coordinates associated with their tweets. To be included in the dataset, county-mapped Twitter users needed at least 30 tweets across the 10% sample, and counties were included if at least 100 such users were mapped to the county (we acknowledge as a limitation of this method that the 30 tweet a year minimum may under represent individuals who do not use online social media). A total of 6 million users across 2,041 counties met this threshold, for a final dataset of 1.5 billion tweets. From these tweets, lexical features (25,000 of the most frequent unigrams) were extracted and embeddings (RoBERTa-Large 1024 dimensional embeddings) were taken for each of the 6 million users. These user-level features were then averaged within each county to produce a set of U.S. county features (i.e., each county is represented by a vector of 25,000 unigram frequencies or a embedding vector of 1024 dimensions). This dataset has been validated across several studies and shown to predict community health [Matero et al., 2023; Abebe et al., 2020], well-being [Jaidka et al., 2020], and psychology [Giorgi et al., 2022b].

Community Controls We focus on three sociodemographic factors that have had high predictive value in past work [Giorgi et al., 2022a]: percentage of foreign-born residents, percentage of the county's population with a high school diploma, and the log of the county's median income. Five-year estimates (2011-2015) for percent of foreign-born population (percentage of a county's population that was born in another country), percent of high school graduate population (percentage of the population with a high school diploma), and median income of population (median log annual household income of a population) were obtained from the United States Census Bureau's 2015 American Community Survey (ACS).

Community Outcomes We consider prediction of four county health outcomes: heart disease mortality, life satisfaction, fair or poor health, and suicide mortality. We gathered age-adjusted mortality rates per 100,000 people for heart disease (HD; N = 1750, mean = 189.67, SD = 45.58) and suicide (SM; N = 1631, mean = 15.55, SD = 4.67) from the Centers for Disease Control and Prevention (CDC), averaged over the years 2010-2015. Life satisfaction (LS; N = 1745, mean = 3.39, SD = 0.03) was assessed using individual responses to the question: "In general, how satisfied are you with your life?" on a scale from 1 (very dissatisfied) to 5 (very satisfied), with scores averaged across 2009 and 2010 [Lawless and Lucas, 2011].

Bilateral Concentration Curve

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Lastly, data on poor or fair health (FP; N = 1703, mean = 17.15, SD = 5.71) came from the County Health Rankings, drawing on the Behavioral Risk Factor Surveillance System [Remington et al., 2015]. This age-adjusted metric reflects the percentage of adults who rated their health as "fair" or "poor" in response to the question: "In general, would you say that your health is Excellent/Very good/Good/Fair/Poor?" Replication To examine how generalizable the findings are to different time periods and approaches, we also rerun the experiment using a more recent set of 425 million tweets from 2019-2021 [Mangalik et al., 2024] across the same 2628 counties we call the County Tweet Lexical Bank 2 (CTLB2). Each of the sociodemographic factors and outcomes was sourced from the same databases as the first dataset but taken from 2020 to fit the recency of the dataset. Not all of the same data was collected for the more recent period, so this study does not analyze foreign born percentage or life satisfaction. Cumul pred. error

4 Metrics for Error Disparity

We study community-level disparity where sociodemographic attributes are continuous rather than categorical, requiring metrics that capture distributional error differences without binning.

Measuring Disparity Prior work on predictive bias in NLP often compares errors across discrete demographic groups (e.g., [Hovy and Søgaard, 2015; Zhao et al., 2017]); however, community-level sociodemographic attributes are typically continuous (e.g., percentages or averages). In social science, the Gini coefficient and Lorenz curve are commonly used to measure inequality, but they require ordering by the outcome variable itself and therefore cannot assess disparities conditioned on an external attribute. Concentration Curves [O'Donnell et al., 2007] generalize the Lorenz curve by allowing observations to be ranked by an auxiliary variable (e.g., median income), enabling the measurement of error disparities conditioned on continuous sociodemographic factors (Figure 1).

The concentration index does not however account for the non monotonic bias present in a concentration curve like the curve in Figure 1. To address this limitation, we introduce the Bilateral Concentration Index (BCI), a modification of the Concentration Index that captures disparity magnitude irrespective of directionality, enabling detection of nonlinear relationships between prediction error and sociodemographic variables. We clarify strengths of this metric in section 6.1. We define the BCI below.

0

0 0.2 0.4 0.6 0.8 in n Cumul. prop. of counties All disparity metrics are reported in Table 2 for Experiment 1 (language-only). Across experiments, metrics generally tracked similar disparity patterns, but differed in interpretability. The Anderson-Darling (AD) test yields unbounded values that are difficult to compare across settings, while the Concentration Index (CI) may understate disparity when opposing deviations cancel. In contrast, BCI remains bounded, direction-agnostic, and comparable across conditions.

Due to its bilateral and continuous formulation, BCI captures nonlinear relationships between prediction error and sociodemographic rank that are missed by KS and CI. For KS, this distinction appears empirically in Figure 4: disparity among counties with respect to income is low (BCI = 7.5%, KS = 0.072). Adaptation increases disparity primarily at the high-income end, reflected by a larger increase in BCI (10.6%) than KS (0.083). For CI, this is illustrated in Figure 3, where the concentration curve for predicting county-level suicide rates as a function of percent foreignborn crosses the line of equality multiple times, corresponding to a U-shaped relationship in the loess plot where the minimum error is in the center as opposed to either extreme. Figure 1 further illustrates how BCI accounts for opposing regions that cancel under CI.

BCI treats observations continuously without binning, enabling fine-grained measurement of disparity across the distribution. However, because CI encodes disparity directionality through its sign, it provides complementary information. Accordingly, BCI is best interpreted in conjunction with CI or the concentration curve to provide a complete view of community-level disparity.

5 Methods

We evaluate how sociodemographic information can be incorporated into language-based prediction using established factor inclusion techniques. Below, we describe the inclusion strategies and modeling pipeline used consistently across all experiments.

Factor Inclusion Methods. We examine four techniques for integrating sociodemographic factors into language-based predictive models, spanning two strategies: additive methods, which account for baseline outcome differences across sociodemographic variables, and adaptive methods, which allow linguistic meaning to vary by demographic context [Lynn et al., 2017]. For example, the word "mean" might have one sense as "cruel", but among more educated populations it could more often signify the mathematical average sense of the word [Lynn et al., 2017].

As additive approaches, we use: (1) Factor Concatenation (Factor Concat), where sociodemographic factors are concatenated with language features into a single feature vector; and (2) Residualized Controls (Res Control), where sociodemographic factors are first modeled independently and the language model predicts the residual from this controlonly model [Zamani et al., 2018]: Residualized Controls can be represented mathematically as follows

where ε is the residual, γ and λ are the coefficients and bias respectively for the linear prediction model, and ˆ YC represents the predictions of the controls model for the outcome variable, Y . The residual is minimized by a subsequent model that uses the language features, XL. This approach ensures that sociodemographic effects are preserved rather than overwhelmed by high-dimensional language features [Zamani and Schwartz, 2017].

As adaptive techniques, we utilize: (3) Factor Adaptation (Fact Adapt) - this approach augments linguistic features by transforming themwith control variables (C). This allows the model to use language features both independently, and in the context of controls [Lynn et al., 2017]. In Factor Adaptation, the adapted language features (XAi ) are combined as follows:

where controls are mean-centered prior to composition [Lynn et al., 2017]. (4) Residualized Factor Adaptation (Res Fact Adapt) - combining Fact Adapt and Res Control, a Fact Adapt model is fit to the residual of a control-only model offering the advantages of both [Zamani et al., 2018]. Residualized Factor Adaptation can be represented as

Baselines. We compare all factor inclusion methods against a language-only baseline (Language Alone) to isolate the effects of sociodemographic integration. Used alone, sociodemographic factors were generally weaker predictors than language, with foreign-born population performing substantially worse and education and income marginally worse.

Implementation Details. All experiments use a consistent feature selection and modeling pipeline across outcomes and factor inclusion methods. To emphasize inclusion strategies and disparity metrics, we employ a standard linear modeling pipeline commonly used in county-level language analysis [Eichstaedt et al., 2015; Giorgi et al., 2018], implemented using DLATK [Schwartz et al., 2017].

All experiments use the same modeling pipeline to isolate the effects of factor inclusion methods. Following prior county-level language prediction work [Eichstaedt et al., 2015; Giorgi et al., 2018], we use DLATK [Schwartz et al., 2017] to construct language-based predictors. Starting from 25,000 unigram features, we apply FWER-controlled univariate feature selection (threshold = 0.60) followed by PCA dimensionality reduction. For each factor inclusion method, the resulting language features are combined with the relevant sociodemographic factor and used to train one ℓ2-regularized linear regression (ridge) model to predict each outcome (HD, LS, FP, SM). Models are evaluated using 10-fold cross validation, with the regularization parameter α selected via nested cross validation. Experiments are conducted across all combinations of outcomes (4), sociodemographic factors (3), and inclusion methods (4).

The functions used are publicly released for reproducibility 1 . Additionally, we provide a web application 2 for computing BCI, accuracy metrics, significance tests, and related disparity measures from user-provided data.

6 Results

We first examine the characteristics of the BCI metric against other measures of bias, then, using the BCI, we systematically evaluate error disparities of language-based predictive models across four outcomes and three sociodemographic controls.

1 https://github.com/AaronMarker/AiFairnessPipeline

2 https://humanlanguage.org/BCI

6.1 BCI in Comparison with Alternative Metrics

An effective disparity metric should be globally sensitive to shifts anywhere in the distribution, interpretable, and capable of capturing nonlinear relationships between error and sociodemographic rank. We empirically compare common disparity metrics listed below, in Table 2.

The Kolmogorov-Smirnov (KS) statistic measures the maximum deviation (as a score between 0 and 1) between a concentration curve and the line of equality, making it intuitive but insensitive to global distributional differences, especially near the distribution's edges (see Figure 4).

The Anderson-Darling (AD) test addresses this limitation by weighting distribution tails more heavily, but produces unbounded values that are difficult to interpret and compare across settings.

The Concentration Index (CI) provides a bounded and interpretable measure by integrating the signed area between the concentration curve and the line of equality.

However, the CI assumes monotonic relationships between error and sociodemographic rank. As shown in Figure 1, non-monotonic disparities-where error is high in the middle of the distribution but low at both extremes-can result in cancellation of opposing areas, yielding a CI of zero despite substantial disparity.

On the other hand, the BCI metric is defined as the total ab-

Predicting Fair Health

solute area between the concentration curve and the line of equality, aggregating disparities in either direction from the line of equality (See Figure 3):

6.2 Evaluation of Factor InclusionMethods

BCI Reference Points. To contextualize disparity magnitudes, we compare observed BCIs to two references: a random permutation of errors (noise-driven lower bound) and a sorted error ordering (high-inequality upper benchmark). Across models, lower-bound BCIs ranged from 0.01-0.03

and upper-bound BCIs from 0.44-0.46.

Disparity in Language Predictions. Table 3 shows significant error disparities for language-only models across all outcome-demographic pairs except suicide mortality with HS graduation. For example, life satisfaction predictions exhibit substantial disparity across foreign-born population share (BCI = 9.9% ngram, 7.6% embedding). Disparity magnitudes vary across outcomes for the same sociodemographic variable, indicating that prediction error is not solely determined by the demographic factor itself.

N-gram vs. Embedding Models. Embedding models generally exhibit higher error disparity than n-gram models, except for life satisfaction, while consistently achieving higher predictive accuracy (Table 1). Thus, disparity differences should be interpreted jointly with accuracy gains.

Factor Inclusion Methods. We next evaluate whether incorporating sociodemographic factors mitigates disparity. We find that all factor inclusion methods improve accuracy relative to language-only models, but often increase error disparity (Tables 1 and 4). For example, factor adaptation achieves the highest accuracy (Pearson r = 0.702 embedding) but increases average disparity relative to language-only baselines (BCIs 8.3% and 7.3% for embedding respectively).

Figure 2 shows that lower overall prediction error does not necessarily imply lower disparity. While factor inclusion often reduces error, the fitted error curves show a larger slope over varying income, corresponding to higher BCI values.

Replication with Recent Data. Using county-level RoBERTa embeddings from 2019-2021 tweets, we observe lower overall accuracy and disparity, but replicate the central finding: factor inclusion improves accuracy, but often increases disparity (Table 5).

7 Conclusion

We conducted a systematic evaluation of error disparities in community-level health prediction tasks, revealing substantial performance differences across sociodemographic variables and outcomes. To quantify these effects, we introduced the Bilateral Concentration Index (BCI), which captures asymmetric error distributions and highlights disparities not evident from aggregate accuracy alone.

Across both n-gram and transformer-based language models, we observed consistent disparities, with higher errors for counties with lower income or educational attainment on multiple health outcomes, and reduced accuracy for life satisfaction in counties with higher foreign-born populations. We further evaluated factor inclusion methods as potential mitigators and found a robust trade-off between accuracy and disparity. While incorporating sociodemographic factors generally improved predictive accuracy, methods that were most effective in this regard-particularly adaptive approaches-often increased error disparities. These patterns replicated across modeling approaches and time periods.

Overall, our findings suggest that sociodemographic disparities in model performance are pervasive at the county level, and that incorporating demographic factors does not yield universally beneficial effects. Instead, the impact of such factors depends on the outcome, demographic variable, and modeling approach, underscoring the need to evaluate fairness and accuracy jointly rather than in isolation. These findings are essential to consider when modeling public health via social media to make real world predictions for geographic areas with less available data.

Ethical Statement

This study was reviewed and approved by an academic institutional review board (found to be exempt, non-human subjects data). No individual-level data has been reported or released in the current study. We report only aggregate data at the community level, so there are no privacy concerns to individuals. It is important to consider and discourage the potential negative applications of this work. While our approach can uncover error disparities in systems such as targeted recommendations, we recognize it could also be misapplied to amplify algorithmic biases and exacerbate inequities. The results described could reinforce existing biases contributing to additional stigma towards a group. Our work is intended for researchers and practitioners of Social Science, and we don't condone the usage of such algorithms for malicious purposes.

Acknowledgements

This research was, in part, funded by the National Institutes of Health (NIH) Agreement NO. 1OT2OD032581-01. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the NIH.