Bayesian inference in racial health inequity analyses for noncommunicable diseases: a systematic review

Abstract

Background

Health inequalities are differences in health status or in the distribution of resources and opportunities between different population groups. Bayesian models are well-suited to address the special features and uncertainties in inequality analyses, making them useful for informing policymaking. This research reviewed the use of Bayesian models in racial health equity studies focused on non-communicable diseases.

Methodology

A systematic review was conducted to assess the applications and utility of Bayesian inference in racial health equity studies for non-communicable diseases (PROSPERO Registry No. CRD42024568708). A total of 2274 articles were identified through electronic databases, and 46 studies met inclusion criteria. All but three articles were from high-income countries, and all were published between 2008 and 2024. We summarized the information qualitatively, and each document included was assessed using the Bennett-Manuel checklist tool.

Findings

Studies on cancer and cardiovascular diseases were the most frequent. The most frequently used models were Poisson, spatial, and logistic regressions, with Markov-chain Monte Carlo and Integrated nested Laplace approximations being the dominant sampling strategies. The studies found that Black individuals, followed by those of Hispanic ethnicity, are the racial/ethnic groups most affected by health inequities. Data on other racial groups (e.g., Indigenous populations, people of Asian heritage) was insufficient for drawing definitive conclusions. The main factor contributing to these disparities lies within the health system, particularly in terms of access and quality, which can be understood in the context of each disease.

Interpretation

The integration of Bayesian modeling into health equity studies holds promise for developing methodologies that lead to insights and foster meaningful change.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13643-025-02898-w.

Introduction

Healthcare decisions have profound implications for human well-being. The search for accurate, efficient, and reliable methodologies is a constant challenge when studying racial inequalities in health. With the rise of computational advancements and the massive influx of health data, the demand for methodologies capable of navigating this complex landscape with precision has intensified. Among the statistical techniques used to study health inequities, Bayesian models provide a framework uniquely suited to address the intricacies and uncertainties involved in the analysis of health inequities.

According to the World Health Organization (WHO) [1], health inequalities are defined as differences in health status or the distribution of health resources and opportunities between diverse population groups that come from the contrasting social conditions in which individuals are exposed. These inequalities can come from specific variables in geographic location, ethnicity, gender, income level, and more, and can be highly affected by government policies. Therefore, these social determinants can pose significant threats to communities by affecting where people live, learn, work, worship, and play, and create inequities in access to a range of social and economic benefits, including access to health, housing, education, wealth, and employment.

Racial health inequalities are a persistent issue in healthcare systems worldwide, reflecting deeply rooted societal gaps. These inequalities manifest in various forms, including disparities in access to care, quality of treatment, and health outcomes across racial and ethnic groups. Addressing these inequalities is crucial for achieving health equity and improving overall public health outcomes [2, 3]. These unfortunate scenarios can be even more complex in developing countries, given their level of economic development and limited opportunities in the education, health, and quality of employment systems.

Regarding noncommunicable diseases (NCDs), nearly 41 million people every year die due to these health conditions, which also place an important burden on health expenditure and contribute to years lost to disability worldwide [4, 5]. These diseases often create a need for long-term treatment and care. Although progress has been made in recent decades in the fight against NCDs, the pace of improvement has been slower in low- and middle-income countries [6]. As a result, public health policies must rely on technical studies to support evidence-based decision-making, both qualitatively and quantitatively.

In this context, Bayesian methods offer valuable tools for studying health inequities. The Bayesian approach dates back to the eighteenth century [7] and has since transcended disciplinary boundaries, finding applications in fields as diverse as finance [8], healthcare [9], software engineering [10], manufacturing [11], supply chain [12], agriculture [13], and cybersecurity [14], among others.

The Bayesian approach involves using a sampling model along with a prior distribution on all unknown quantities, such as parameters and missing data. By combining the prior and likelihood, the posterior distribution is computed, which reflects the conditional distribution of the unknowns given the observed data and from which statistical inferences are made. In empirical Bayes, the observed data helps determine the prior distribution [15]. Bayesian procedures are evaluated through repeated sampling of unknowns from the posterior distribution for a specific dataset. On the other hand, the frequentist approach evaluates procedures based on imagined repeated sampling from a model (the likelihood), where unknown parameters are considered fixed [16].

Bayesian analyses allow researchers to work with complex models and large datasets with unparalleled precision [15]. Researchers are increasingly aware of the limitations of traditional investigative methodologies, and Bayesian models offer a framework for quantifying and managing uncertainty, allowing them to incorporate preceding expertise, expert judgments, and evolving evidence into their analyses. This probabilistic approach provides a clearer understanding of research findings [17]. Thus, the aim of the present research is to review the application of Bayesian models in racial health equity studies for non-communicable diseases, where the quality of information systems often has significant opportunities for improvement.

Methodology

The systematic review protocol was registered on PROSPERO with registration number CRD42024568708, adhering to international quality standards according to those of the Cochrane Collaboration guidelines [18]. The research focused on the following research question: What are the applications and utility of Bayesian inference in racial health equity studies for NCDs?

Inclusion and exclusion criteria

Inclusion and exclusion criteria were defined based on the structured research question, encompassing studies employing Bayesian models to analyze racial health equity in NCDs. Language and time restrictions were not imposed and only studies with a clear methodology and data source details were considered, including both modeling and observational studies. The exclusion criteria defined were that the studies did not perform a quantitative application from a Bayesian approach, did not examine any type of health inequity, did not have a racial focus, did not address NCDs, or were grey literature.

Search strategy

The search employed indexed terms (MeSH and Emtree) tailored to each database (PubMed, Embase, LILACS, and Scielo). There were no restrictions regarding language or publication date. Documents published until May 9, 2024, were extracted. Search algorithms incorporated terms such as “Health equity,” “Health disparities,” “Health vulnerability,” “Bayesian models,” “Bayesian inference,” and “Bayesian statistics” within the relevant literature in MeSH, Emtree, and DeCS (exact search strings can be found in Supplement 1). Retrieved studies were managed using Mendeley, duplicates were removed, and the remaining studies were processed using Rayyan software.

Study selection

Study selection involved an initial screening of titles and abstracts by two reviewers (VB, AM), with disagreements resolved by a third reviewer (OE). Documents that met the inclusion criteria proceeded in the selection process. Full-text screening was then conducted independently by the same reviewers, with the PRISMA flow diagram used to document the selection and screening process.

Data extraction

Relevant data for this systematic review were extracted by two reviewers (VB, AM) and independently verified by a third reviewer (OE), using a data extraction form designed in Excel®, which was adjusted following a pilot extraction involving six articles (see information matrix in Supplement 2).

Analysis of the systematized papers

The synthesis of the information of all the included studies was carried out descriptively. All analyses were performed by category at the subgroup level, and descriptive statistics were provided when the available data can be grouped according to the degree of heterogeneity. On the other hand, due to methodological diversity (diversity of populations analyzed, study designs, health outcomes, etc.), we do not consider it appropriate to perform a meta-analysis.

Quality assessment

Given the lack of a specific tool for evaluating articles that apply Bayesian inference in health sciences, the quality of the included articles was assessed using the checklist proposed by Bennett and Manuel [19]. This tool seeks to evaluate the relevance of the articles with respect to different aspects of the Bayesian modeling process, such as the definition of the decision problem, the structural assumptions, the type of model applied and its construction process, internal and external consistency, among other factors.

Results

Figure 1 presents the PRISMA information flow diagram, illustrating that a total of 2274 articles were identified through electronic databases, leaving 1394 (61.3%) after excluding duplicates. Following the title and abstract screening from this, 85 (6.1%) proceed to full-text review, resulting in a total of 46 (54.1%) documents included in the final analysis.

Fig. 1.

PRISMA flow chart of the study

Bibliometric aspects

All but three articles (93.5%) were developed in high-income countries, with the majority (84.8%) from the United States of America. The exceptions were studies from Nigeria [20, 21] and Vietnam [22]. Other countries represented in the studies include Canada [23], Australia [24, 25], and Denmark [26]. The publication years range from 2008 to 2024 and show a rising trend over time (Fig. 2). Most articles (78.3%) were published in Q1-ranked journals (according to Scimago Journal & Country Rank), with the remainder in Q2-ranked journals.

Fig. 2.

Number of articles by year of publication

Bayesian inference requires specialized knowledge and algorithmic skills, often found in developed countries with access to well-funded research and development (R&D) and highly trained human capital [27]. In addition, the complexity of Bayesian methods means that not all researchers venture into this demanding field of knowledge [27].

Health conditions

NCDs not only affect older populations but also account for 75% of premature deaths in adults aged 30–69, highlighting their widespread impact across age groups [28]. In this review, the main diseases studied are classified as follows: cancer with 19 articles [23, 25, 29–45], followed by cardiovascular diseases with 13 articles [26, 42, 43, 46–55], diabetes with 6 articles [24, 42, 53, 56–58] and respiratory diseases (including asthma, chronic low respiratory diseases, and influenza) with 4 articles [42, 59–61]. Additionally, there is another group of conditions that includes kidney disease [42, 53], Attention-deficit/hyperactivity disorder (ADHD) [62], Alzheimer’s disease [42], mental health and depression [4, 63], obesity [20, 64], underweight [21], posttraumatic stress disorder (PTSD) [65], epilepsy [66], and general non-communicable diseases1 [22, 43].

Bayesian inference

Table 1 summarizes the findings regarding the Bayesian models employed in the articles related to the classified diseases; these include mainly Poisson [4, 23, 26, 32, 36, 37, 40, 43, 50, 53, 61, 62, 66], spatial [20, 21, 23, 25, 26, 31, 35, 36, 39, 46, 47] and logistic [30, 57, 58, 63, 65] modeling. Most sampling methods used were Markov-chain Monte Carlo (MCMC) [4, 20–22, 24, 34–38, 40, 42, 44, 45, 47, 49, 52, 55, 57–60, 64, 66], followed by Integrated nested Laplace approximations (INLA) [23, 26, 30–32, 41, 46, 56]. Performance metrics were primarily assessed using deviance information criteria (DIC) although more than half of the articles did not report the measure used. R was the most commonly (63%) used statistical software.

Table 1.

Number of studies by characteristics of Bayesian models employed and type of disease

Characteristic	Cancer	Cardiovascular disease	Diabetes	Respiratory disease	Other	Total
	n (%)	n (%)	n (%)	n (%)	n (%)	n (%)
Bayesian model
Age-period-cohort	-	1 (2.17)	-	-	-	1 (2.17)
Intrinsic conditional autoregressive	-	-	1 (2.17)	-	-	1 (2.17)
Hierarchical	2 (4.35)	1 (2.17)	-	-	-	3 (6.52)
Linear regression	1 (2.17)	1 (2.17)	2 (4.35)	1 (2.17)	1 (2.17)	2 (4.35)
Logistic regression	1 (2.17)	-	2 (4.35)	-	2 (4.35)	5 (10.87)
Mixed-effects	-	-	-	-	1 (2.17)	1 (2.17)
Machine learning-augmented propensity score	-	1 (2.17)	-	-	-	1 (2.17)
Multilevel	1 (2.17)	2 (4.35)	-	-	-	3 (6.52)
Negative binomial regression	-	-	-	1 (2.17)	-	1 (2.17)
Network	2 (4.35)	-	-	-	-	2 (4.35)
Poisson	4 (8.7)	3 (6.52)	1 (2.17)	1 (2.17)	5 (10.87)	10 (21.74)
Poisson spatial	2 (4.35)	1 (2.17)	-	-	-	3 (6.52)
Profile regression	-	-	-	1 (2.17)	-	1 (2.17)
Smoothing	1 (2.17)	-	-	-	1 (2.17)	2 (4.35)
Spatial or geoadditive	4 (8.7)	3 (6.52)	-	-	2 (4.35)	9 (19.57)
Survival analysis	1 (2.17)	-	-	-	-	1 (2.17)
Sampling method
INLA	5 (10.87)	2 (4.35)	1 (2.17)	-	-	8 (17.39)
MCMC	9 (19.57)	5 (10.87)	4 (8.7)	3 (6.52)	7 (15.22)	24 (52.17)
Not defined	5 (10.87)	6 (13.04)	1 (2.17)	1 (2.17)	5 (10.87)	14 (30.43)
Software
Othera	1 (2.17)	2 (4.35)	-	-	2 (4.35)	5 (10.87)
Not defined	1 (2.17)	1 (2.17)	1 (2.17)	-	2 (4.35)	5 (10.87)
R	15 (32.61)	7 (15.22)	5 (10.87)	4 (8.7)	6 (13.04)	29 (63.04)
SAS	1 (2.17)	-	-	-	-	1 (2.17)
Stata	1 (2.17)	1 (2.17)	-	-	-	2 (4.35)
WinBUGS	-	2 (4.35)	-	-	2 (4.35)	4 (8.7)
Performance metrics
Deviance information criterion (DIC)	7 (15.22)	5 (10.87)	1 (2.17)	-	2 (4.35)	15 (32.61)
Not defined	10 (21.74)	8 (17.39)	4 (8.7)	3 (6.52)	8 (17.39)	25 (54.35)
Otherb	2 (4.35)	-	1 (2.17)	1 (2.17)	2 (4.35)	6 (13.04)
Watanabe–Akaike information criterion (WAIC)	2 (4.35)	-	-	-	-	2 (4.35)

^aBayesian age-period-cohort modeling prediction (BAMP) software, BayesX, INLA and Java 9

^bExpected log predictive density, leave-one-out cross-validation error, miss-classification rates, posterior predictive check, potential scale reduction factor, and volume under the ROC surface

Socio-demographic characteristics

Table 2 provides details on the number of years covered by the studies, sample sizes, age ranges, sex distribution, and whether children were included in the studies. The longest study spanned 44 years [43], the largest sample size reported was 4,128,079 [26], while the smallest sample consisted of 175 participants [39]. The age range typically focused on individuals over 18 years of age from both sexes, while children were primarily studied in the context of asthma [60, 61], ADHD [62], hypertension [49], and mental health [4].

Table 2.

Number of studies by socio-demographic characteristics and disease

Characteristic	Cancer	Cardiovascular disease	Diabetes	Respiratory disease	Other	Total
	n (%)	n (%)	n (%)	n (%)	n (%)	n (%)
Number of years of collection
1	1 (2.17)	2 (4.35)	3 (6.52)	1 (2.17)	4 (8.7)	9 (19.57)
2–5	3 (6.52)	6 (13.04)	1 (2.17)	1 (2.17)	4 (8.7)	15 (32.61)
6–9	6 (13.04)	1 (2.17)	1 (2.17)	-	-	8 (17.39)
>=10	8 (17.39)	4 (8.7)	1 (2.17)	1 (2.17)	4 (8.7)	12 (26.09)
Not defined	1 (2.17)	-	-	1 (2.17)	-	2 (4.35)
Sample sizes (thousands)
<7	4 (8.7)	2 (4.35)	1 (2.17)	1 (2.17)	3 (6.52)	9 (19.57)
7–<20	2 (4.35)	4 (8.7)	1 (2.17)	2 (4.35)	-	9 (19.57)
20–<214	5 (10.87)	-	1 (2.17)	-	4 (8.7)	10 (21.74)
≥214	4 (8.7)	2 (4.35)	2 (4.35)	-	1 (2.17)	9 (19.57)
Not defined	4 (8.7)	5 (10.87)	1 (2.17)	1 (2.17)	4 (8.7)	9 (19.57)
Age rangea
<18	-	1 (2.17)	-	2 (4.35)	4 (8.7)	7 (15.22)
18–49	8 (17.39)	8 (17.39)	4 (8.7)	-	6 (13.04)	24 (52.17)
50–64	9 (19.57)	7 (15.22)	4 (8.7)	-	4 (8.7)	22 (47.83)
65–79	11 (23.91)	7 (15.22)	4 (8.7)	-	4 (8.7)	24 (52.17)
≥80	6 (13.04)	7 (15.22)	4 (8.7)	-	4 (8.7)	19 (41.3)
All ages	4 (8.7)	2 (4.35)	1 (2.17)	1 (2.17)	2 (4.35)	4 (8.7)
Not defined	4 (8.7)	2 (4.35)	1 (2.17)	1 (2.17)	2 (4.35)	10 (21.74)
Gender
Both	6 (13.04)	10 (21.74)	3 (6.52)	4 (8.7)	8 (17.39)	25 (54.35)
Men	3 (6.52)	1 (2.17)	1 (2.17)	-	-	5 (10.87)
Women	7 (15.22)	-	1 (2.17)	-	2 (4.35)	10 (21.74)
Not defined	3 (6.52)	2 (4.35)	1 (2.17)	-	2 (4.35)	6 (13.04)
Are children being studied?
No	11 (23.91)	10 (21.74)	5 (10.87)	-	4 (8.7)	28 (60.87)
Yes	2 (4.35)	2 (4.35)	-	2 (4.35)	6 (13.04)	10 (21.74)
Not defined	6 (13.04)	1 (2.17)	1 (2.17)	2 (4.35)	2 (4.35)	8 (17.39)

^aThe studies can analyze more than one age range

For small race- and sex-specific populations in small areas, Bayesian methodology is the best choice due to its effectiveness in applying small sample corrections to improve statistical precision. Traditional methods fail to provide reliable estimates in small geographic areas with limited sample sizes, while Bayesian disease mapping leverages information from neighboring counties and similar demographic groups to stabilize extreme rates and produce more accurate estimates [37, 48].

Racial health inequities

Focusing on health inequities by race, most studies concentrated on White/Non-Hispanic White individuals (76.1%) [4, 29–31, 33–38, 40–43, 45–60, 62–66], Black/Non-Hispanic Black/African American individuals (71.7%) [29–31, 33–36, 38–41, 43–50, 52–62, 64–66], Hispanic or Latino individuals (37%) [31, 32, 35, 39, 40, 49, 50, 53–55, 57–61, 64, 66], and others (52.2%) generally involving minority ethnic groups such as Pacific Islanders or Asians [35, 36, 38, 40, 49, 53, 54, 58], American Indians or Alaskan Natives [37, 53, 54], Indigenous peoples [23–25], or Middle Eastern and North African (MENA) [59] populations. Three articles from Nigeria and Vietnam examined their respective ethnic groups [20–22].

A notable advantage of Bayesian modeling is its flexibility in modeling interactions, as demonstrated by Nguyen et al., where researchers stratified models by factors such as wealth quintile, educational level, urban-rural area, gender, and ethnic group to explore nuanced relationships and variations across subgroups, assessing random slopes to evaluate regional variations over time [22]. Furthermore, the ability to borrow information from neighboring counties, along with accounting for social determinants (i.e., the number of women at risk and a county-level area deprivation index [37]), enhanced the precision of estimates, facilitating a deeper understanding of how race/ethnicity interacts with these determinants to influence health outcomes.

We classify individual-level factors as those related to personal behavior such as physical activity, while multifactorial factors refer to the combination of several variables that are widely recognized in the literature. Neighborhood and geographical location factors relate to where people live, the schools or workplaces they attend, and their access to travel and transportation. Lastly, “not applicable” refers to populations where differences were either not significant compared to the majority group (mainly White population) or where no form of inequality was observed. Figure 3 provides the distribution by ethnic group for the inequality factors for each disease considered.

Fig. 3.

Distribution of racial/ethnic groups by inequality factor for each disease

The primary ethnic/racial group experiencing health inequities is the Black population, followed by those with Hispanic ethnicity, while data on other racial groups is often insufficient to draw conclusions. The main factor contributing to these disparities lies within the health system, particularly in terms of access and quality, which can be understood in the context of each disease. For instance, in cancer, this includes access to early detection [41], screening [39, 40], and therapy availability [38]. Geographical location and neighborhood conditions often reflect the public context of the population [34, 47] or state policies, which increasingly require attention on these differential groups, including environmental factors such as air quality [61]. Cultural barriers, particularly for Indigenous populations [25], also play a significant role. Socio-economic factors are well-known contributors, as they affect health insurance coverage and purchasing power [23, 44, 58, 59, 61].

Quality assessment results

Following the guidelines by Bennet and Manuel [19], we adjusted the proposed checklist items for reporting modeling studies to align with the relevant items that applied to our literature review, as the models do not account for economic evaluation. The final checklist was applied to the 46 articles included in the review (see Supplement 3). It is important to highlight that all articles made a clear statement of the decision problem, as well as the model’s perspective, using a Bayesian framework with a consistent structure grounded in coherent theory and methodology. These studies also employed justifiable statistical techniques, demonstrating that the underlying mathematical logic had been thoroughly tested before use. Moreover, the selected model types were appropriate for the specified problems, with variables defined and justified, data identification methods both transparent and appropriate, and outcomes aligned with the model’s perspective, scope, and overall objective. Most articles effectively employed data and methods that ideally support the identification and establishment of these key modeling steps.

While not every article mentioned the software used (93.5%), the source of the data (93.5%), or provided an explicit objective consistent with the problem (95.7%), 44 articles (95.7%) justified the model scope and assessed parameter uncertainty (using credible intervals). Credible intervals, widely used within Bayesian frameworks, are a standard feature of all analyses, as is the software used to reproduce results, contributing to open science. More than 50% of the articles adhered to key practices such as describing search algorithms (78.3%), clearly stating and justifying structural assumptions (73.9%), addressing mutually inconsistent data (67.4%), disclosing relationships between study sponsors and researchers (67.4%), explaining the choice of distribution for each parameter (60.9%), and providing relevant appendices (52.2%). Additionally, they ran alternative versions of the models to address uncertainties (54.3%) and reported goodness-of-fit metrics (50%). Many articles also included model equations in supplemental material, although we acknowledge the challenges of running different versions due to the time-consuming nature of model development.

However, some areas need improvement. Less than 17 articles (37%) explained counterintuitive results, provided transparency in the data incorporation process (37%), reported results in a way that allowed assessment of parameter and assumption appropriateness (21.7%), conducted sensitivity analyses (15.2%), indicated parsimony in their models (15.2%), or compared results with previous models (13%). Given the complexity of Bayesian models and the number of parameters involved, it is understandable that some studies did not report detailed parameter estimation or sensitivity analysis, such as adjusting prior structures or values. Since data incorporation is critical for reproducibility, future research should place greater emphasis on addressing these issues.

Discussion

The multivariable root causality of disparities includes not only social determinants of health, but also intrinsic characteristics of the population, including age, gender, and family history, which play an important role in the case of NCDs. Bayesian models are increasingly being used to inform health policy decisions. For example, these methods can be used to calibrate health policy models that represent the social and biological mechanisms driving health and economic outcomes. By combining multiple sources of evidence and synthesizing outcomes, these models can provide valuable insights for policy decisions. Bayesian methods help improve the accuracy of model predictions and provide face validity by fitting empirical data [67].

One of the hallmark benefits of Bayesian models lies in their exceptional flexibility and adaptability to diverse healthcare scenarios, from diagnostic assessments and treatment evaluations to epidemiological analyses and predictive modeling [68]. In contrast, classical (frequentist) statistical methods are often constrained by rigid assumptions and limited adaptability to complex data structures, proving not always to be the best option for capturing the multifaceted nature of health disparities. Bayesian models offer a realistic approach to scientific thinking, incorporating prior expert knowledge into statistical inference [69].

Bayesian inference has a powerful framework for reasoning under uncertainty. Unlike classical statistics, which typically relies on frequentist methods, Bayesian models adopt a probabilistic approach by incorporating antecedent beliefs and updating them based on observed data [7]. This iterative process results in posterior probability distributions, representing updated beliefs about the parameters of interest. One of the key strengths of Bayesian modeling is its flexibility in handling complex data structures and integrating knowledge effectively. By combining prior information with observed data, Bayesian models can provide more robust and interpretable results, especially in scenarios with limited data or high-dimensional settings. Furthermore, Bayesian techniques excel in uncertainty quantification, offering probabilistic predictions that account for various sources of uncertainty inherent in the data [68].

Bayesian models have also been an excellent support in various worldwide problematics, including the COVID-19 pandemic, and so on. A recent study directed by Aouissi et al. [70] demonstrates how the given modeling was used to analyze the pandemic’s behavior in several regions of Algeria. Similarly, in the de Oliveira et al. [71] article, it can be seen how Bayesian modeling was used during the pandemic, representing a pivotal advancement in infectious disease epidemiology. In addition, Bayesian models can represent a significant step in disease modeling, as shown in Lawson et al. [72], by offering advanced statistical methodologies that hold promise in shaping effective strategies for prevention, containment, and mitigation, ultimately safeguarding public health on a global scale.

Among their many advantages, several health sciences researches have established that Bayesian models are more flexible for the analysis of public health surveillance systems or the modeling of vital statistics, which enables better detection of health inequalities [40]. It has also demonstrated its potential advantage over the possible estimation of relatively small populations in terms of sex, age, and race groups, taking advantage of information from nearby geographic areas, other demographic groups, or nearby time periods [48]. This allows accurate conclusions to be drawn from research, especially in small populations with few frequent health events (e.g., some low-prevalence cancers) [37].

From a more conceptual point of view, Nguyen et al. [22] highlight the strength of Bayesian models in allowing the calculation of probabilities of predictions within specific ranges (credibility intervals), a feature not possible with classical frequentist approaches (confidence intervals). About the features of the Bayesian models, we hypothesize that the MCMC sampling method is more frequently used due to its ease of application to estimate posterior distributions that are not analytically known [73]. However, the use of INLA has been increasing as computational algorithms continue to improve [74]. In terms of statistical software, R is widely adopted because it is a free, open-source platform with contributions from researchers globally, offering a strong focus on statistical analysis rather than solely on data science tools.

The main disadvantages of Bayesian modeling are related to the intense use of computational resources and the complexity of statistical analyses. These factors increase the training and mentorship needed for a valid Bayesian analysis and expand the expertise needed to interpret Bayesian models and their more complex assumptions. In contrast to the frequentist approach, Bayesian analysis uses more statistical assumptions that need much more research experience to grasp in this entirely. This is an especial disadvantage for decision-makers and policymakers untrained in Bayesian analyses. However, initial frameworks or guidelines have been developed that facilitate partially overcoming this gap [68]. A limitation of our work is that only the biases on the statistical heterogeneity of the included studies were evaluated, without analyzing the biases of possible ecological and atomistic fallacies (responsible for the heterogeneity of causal effects). Despite these challenges, the advantages of Bayesian analysis are plentiful, especially on issues related to small samples, where frequentist analyses are frequently intractable.

Our study is limited in scope as we only review a narrow topic in literature. Despite this, our results highlight the broad applicability of Bayesian modeling to answer specific research questions within the field.

Conclusion

Health equity remains an elusive goal, primarily due to the complex interplay of socioeconomic, environmental, and biological factors that influence health outcomes across diverse racial and ethnic groups. Looking ahead, the integration of Bayesian modeling into health equity research holds immense promise for driving actionable insights and fostering meaningful change. Encourage authors of future studies to report comprehensively the different technical aspects involved in Bayesian modeling, following the minimum guidelines recommended in the field [75].

As researchers continue to refine methodologies and expand the applications of Bayesian inference, the journey toward achieving health equity for all stands to benefit from the transformative power of these models.

Authors’ contributions

Conceptualization: OE; data curation: OE, VB, AM; formal analysis: OE, VB, AM, AP; investigation: OE; methodology: OE; project administration: OE; resources: OE; software: OE, VB, AM; supervision: OE; validation: OE, HC, AP; visualization: OE, VB; writing—original draft: OE, VB, AM, HC, AP, and writing—review and editing: OE, VB, AM, HC, AP.

Funding

None.

Data availability

Not applicable.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

All authors agree with the content of this manuscript.

Competing interests

None.