A Review of the Causal Decomposition Framework for Modeling Interventions that Reduce Disparities

Abstract

Purpose of Review

This review summarizes recent developments in causal decomposition analysis (CDA), a modeling framework for reducing disparities. Rather than describing the current or past drivers of a disparity, CDA estimates the effect of an intervention to change the distribution of a variable or set of variables that are distributed differently or have different effects between groups. Furthermore, CDA clarifies how, through covariate adjustment, ethics and justice are implicit in any definition of disparity and may be incorporated into an intervention.

Recent Findings

CDA has been applied to disparities in health, sociology, education, and computer science. The CDA framework consists of four steps: formulating a meaningful estimand, articulating identification assumptions to link an appropriate dataset with the estimand, choosing an appropriate estimator, and conducting statistical inference. Estimators have been developed for various types of data and to address particular statistical challenges. However, some estimators adjust for all available covariates in all parts of the model, without discussing ethical implications. Meanwhile, the literature has covered some but not all potential violations of standard CDA modeling assumptions.

Summary

CDA builds on previous methods for studying disparities by articulating causal estimands that transparently reflect implicit value judgements about health disparities. This review outlines the broad framework of CDA methodology, selected implementations, practical considerations, and current limitations and alternatives.

Introduction

Disparate, potentially avoidable outcomes persist between historically disadvantaged and historically advantaged groups in the United States. For example, Black patients suffer higher rates of uncontrolled hypertension than white patients [1], which perpetuates an intergenerationally unequal burden of worse outcomes [2]. Causal decomposition analysis (CDA), formally introduced by [3], is a novel framework for modeling the effect of interventions to reduce disparities while incorporating value judgements about fairness and justice in the distribution of health outcomes. CDA has a number of advantages over previous methods.

Analytic methods developed in the twentieth century, namely decomposition and mediation analysis, sought to quantify disparities and associative pathways through which disparities arise [4–7]. However, as explained in previous papers [3,8,9], traditional decomposition and mediation analyses typically avoid making the causal identification assumptions necessary to robustly inform interventions. Similarly, the more recently developed technique of causal mediation analysis focuses on the effects of changing group membership, despite the fact that group membership is in many cases meaningful for individuals and not the focus of policymakers [10,11]. There are also long-standing debates about if, when, and how group membership may be modified [12]. In contrast, CDA is agnostic to the debate about whether group membership can be a cause modifiable by social forces [13]. Rather, CDA acknowledges the association between group membership and an outcome but focuses on changing the distribution of variables that, due to social stratification, may contribute to disparity due to their differential distribution or effects across groups. If the resulting disparity in outcomes changes considerably, then these variables may be important to prioritize in future interventions that attempt to reduce or eliminate disparity.

Additionally, many older and newer methods alike tend to adjust both the disparity measure and the intervention by every available covariate that is hypothesized to confound the relationship between the intervention and the outcome. Unfortunately, some covariates, e.g., societal resources like health insurance, income, or advanced educational programs, may not have an objectively fair distribution in the factual world, so defining disparity conditional on these covariates may over-adjust disparity for the very factors that are driving disparity [3,10]. Moreover, using such covariates to define conditional interventions may, in some cases, allow disparities that operate through these covariates to remain post-intervention. To avoid these issues, CDA carefully incorporates such confounding covariates into its identifying assumptions (to control for confounding and mitigate statistical bias) but excludes them from the disparity definition, the intervention, or both (to focus on a meaningful estimand).

This review outlines the CDA estimand, reviews several parametric and non-parametric estimators, discusses important considerations for practical analysis, and suggests directions for further methodological development. This review does not exhaustively cover the various applications or the performance of specific estimators on real or simulated datasets, which are both important areas for future research.

General Framework of CDA

Modeling a disparity in the CDA framework comprises four steps. First, morally and practically meaningful estimands (i.e., quantities to be modeled from data) are developed: the (i) observed disparity in expected outcomes between two or more groups, adjusted by so-called “outcome-allowable” covariates if any are specified, and the (ii) reduced disparity versus (iii) remaining disparity after a hypothetical intervention. The intervention may depend on “intervention-allowable” covariates, if any are specified.

Second, “identifying” assumptions are articulated, through which the average outcomes after intervention may be described in terms of observed data. This mapping to observed data may include additional confounding variables that are not used to define the estimand.

Third, an estimator (i.e., a formula or algorithm applied to the observed data) is developed, which a researcher may optimize for efficiency, unbiasedness for the estimand, or other desired properties.

Lastly, the statistical uncertainty of the estimate is quantified, usually as a standard error or confidence interval.

In what follows, the Estimands and Assumptions sections are general to the CDA framework, while the Estimators and Statistical Inference sections review selected papers in the CDA literature thus far.

Estimands (i.e., Quantities to be Modeled)

The general CDA estimands are described below. The running example in [3]’s foundational paper is reused, but the notation is updated for clarity.

Let Y be the observed outcome and G denote group membership. In this basic example, G can take on values g₁ (a historically “disadvantaged” group) or g₀ (a historically “advantaged” group). G is not assumed to be a modifiable exposure or cause. Let A_y, called the outcome-allowable covariates, be the set of variables used to adjust the outcome for a fair comparison between groups. If A_y is non-empty, then both groups’ A_y are standardized to a within-sample standard population, which has probabilities P_Ay(A_y=a_y) for a range of possible values a_y.¹ After adjusting for A_y, we proceed with CDA if Y has a substantively greater expectation (denoted by $E_{{\mathit{A}}_{\mathit{y}}}$) in the G=g₁ group than in the G=g₀ group.

• The observed disparity is ${\text{E}}_{{\mathbf{A}}_{\mathbf{y}}}\left[\text{Y}\right|\text{G}={\text{g}}_1]-{\text{E}}_{{\mathbf{A}}_{\mathbf{y}}}[\text{Y}|\text{G}={\text{g}}_0]=\sum _{{\mathbf{a}}_{\mathbf{y}}}\left[\text{E}\right[\text{Y}|\text{G}={\text{g}}_1,{\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}}]-\text{E}\left[\text{Y}\right|\text{G}={\text{g}}_0,{\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}}\left]\right]{\text{P}}_{{\mathbf{A}}_{\mathbf{y}}}({\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}})$.

• For example: Y could be hypertension control, and A_y could consist of age and sex. Individuals from both groups could be sampled or adjusted according to the disadvantaged group’s empirical age and sex distribution, which would be P_Ay [14].

Now, let Z be a modifiable variable² that is hypothesized to affect the outcome. For instance, Z may be the dosage of a blood pressure medication or the availability or accessibility of a social service. Let Y(z) denote the outcome that would have been observed, if Z had been equal to the value z. To intervene, we assign Z according to a (deterministic or random) distribution P_Z*, which is a function of “intervention-allowable” covariates A_z and of A_y.³ Carrying on the “equalizing” tradition of decomposition analyses, P_Z* is typically the distribution of Z observed in the advantaged group. A_z are variables considered fair for an intervention to consider, such as a person’s baseline health status, e.g., baseline blood pressure and comorbidities. The A_z are distributed as they are in real world, with probabilities P_Az. (Thus, the intervention meets the study subjects “where they are”.)

• Then, the expected counterfactual outcome, for the disadvantaged group after intervention, still standardizing over a shared P_Ay, is ${\text{E}}_{\text{Z},{\mathbf{A}}_{\mathbf{z}},{\mathbf{A}}_{\mathbf{y}}}\left[\text{Y}\right(\text{z}\left)\right|\text{G}={\text{g}}_1]={\sum }_{{\mathbf{a}}_{\mathbf{y}}}{\sum }_{{\mathbf{a}}_{\mathbf{z}}}\sum _{\text{z}}\text{E}\left[\text{Y}\right(\text{z})|\text{G}={\text{g}}_1,\text{Z}=\text{z},{\mathbf{A}}_{\mathbf{z}}={\mathbf{a}}_{\mathbf{z}},{\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}}\left]P_z^{*}\right(\text{Z}=\text{z}|{\text{G}={\text{g}}_1,\mathbf{A}}_{\mathbf{z}}={\mathbf{a}}_{\mathbf{z}},{\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}}){\text{P}}_{{\mathbf{A}}_{\mathbf{z}}}({\mathbf{A}}_{\mathbf{z}}={\mathbf{a}}_{\mathbf{z}}|\text{G}={\text{g}}_1,{\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}}\left){\text{P}}_{{\mathbf{A}}_{\mathbf{y}}}\right({\mathbf{A}}_{\mathbf{y}}={\mathbf{a}}_{\mathbf{y}})$.

• Therefore, the reduced disparity is ${\text{E}}_{{\mathbf{A}}_{\mathbf{y}}}\left[\text{Y}\right|\text{G}={\text{g}}_1\left]{-\text{E}}_{\text{Z},{\mathbf{A}}_{\mathbf{z}},{\mathbf{A}}_{\mathbf{y}}}\right[\text{Y}\left(\text{z}\right)|\text{G}={\text{g}}_1]$, and the remaining disparity is ${\text{E}}_{\text{Z},{\mathbf{A}}_{\mathbf{z}},{\mathbf{A}}_{\mathbf{y}}}\left[\text{Y}\right(\text{z}\left)\right|\text{G}={\text{g}}_1]-$ ${\text{E}}_{{\mathbf{A}}_{\mathbf{y}}}\left[\text{Y}\right|\text{G}={\text{g}}_0]$.

Note that the disparity could be defined as a ratio or other contrast between mean outcomes. Each mean outcome could also be transformed within this framework.

To recapitulate the main concept, the goal of CDA is to estimate the effect of an intervention (usually setting the disadvantaged group’s distribution of the variable Z to the advantaged group’s distribution) that can take into account an individual’s needs and circumstances. For CDA to find a significant reduction in disparity, Z must be distributed differently or have a differential effect on Y between groups [16].

Assumptions Needed to Identify (i.e., Estimate from Data) the Estimand

Since the expected counterfactual outcome in the estimand consists of unobserved quantities, we can only rely on assumptions to use observed, real-world data to estimate it accurately. (In statistics and epidemiology, such assumptions are called identification or causal inference assumptions.) If these assumptions hold, then the expected counterfactual outcome may be modeled according to an identifying formula, given in the Appendix, involving observed data.

The first and second assumptions (called positivity and consistency) explicitly ensure that the intervention and its effect on the outcome are reasonably well-defined. Positivity means that each group has a non-zero chance of having Z=z, for every combination of z, a_z, and a_y values considered together in the intervention. Consistency means that the counterfactual outcome, Y(z), is well-defined as the outcome that would happen in real life if Z=z.⁴

Thirdly, we assume that there is no unmeasured confounding between the point of intervention Z and the outcome Y. (This assumption is called exchangeability.) If any other variables N confound the relationship between the intervention and the outcome yet are inappropriate to define the disparity or the hypothetical intervention, then they need to be included in the estimation process, despite not appearing in the estimand. For instance, in a given dataset, both a patient’s medical treatment and whether their hypertension is successfully controlled may depend on their health insurance. A disparity-reducing intervention may not consider health insurance status, but when modeling its potential effect, such dependencies should be taken into account.

There are a few points of emphasis here. Firstly, identification assumptions are largely unconfirmable and untestable, but they may be conceptually falsifiable. For example, a substantive expert can assess whether the intervention definition seems realistic for a historically disadvantaged group or if all potential confounding variables seem to have been measured, even if imperfectly or by a proxy variable. Hence, having a good study design is important for identifiability. Cross-sectional data are the weakest for inferring causality, while longitudinal designs—where Z is measured before Y, and A is measured before both—are the strongest. Meanwhile, unmeasured confounding can be handled by sensitivity analyses for the strength of a hypothetical unmeasured confounder’s relationship with the intervention and with the outcome [15,18,19].⁵

Another important takeaway is that CDA can adjust for confounding by non-allowable covariates without adjusting the disparity measure or intervention for them.

Finally, we note that any estimator will have additional assumptions for statistical inference (such as linearity and correct model specification, if regression models are used in the estimation process), but this section discussed the causal inference assumptions in CDA.

A Review of Selected Estimators (i.e., Formulas or Algorithms) in CDA Literature

Multiple types of estimators have been proposed to estimate the expected counterfactual outcome in CDA. Each type of estimator tackles different statistical and data challenges. Selected recent papers are reviewed in Table 1. Several papers have publicly available software.

Table 1.

Selected recent CDA-compatible estimators.

Estimator	Scale(s) of Disparity	Standardized over Allowable Covariates?	Variables Requiring Modeling	Type(s) of Estimator	Statistical Challenges Addressed
Jackson and VanderWeele (2018) [9]	Risk ratio; Difference in means	Yes	Y	Regression	Continuous intervention
Jackson (2021) [3]	Risk ratio; Difference in means	Yes	Y, Z, G	Weighting	Categorical intervention
Sudharsanan and Bijlsma (2021) [21]	Risk ratio	No	Y, Z	Imputation	Binary, count, or continuous outcome
Ben-Michael et al. (2024) [22]	Risk ratio; Difference in means	Yes	Y, Z	Weighting	Clustered data
Park et al. (2024b) [15]	Difference in means	No	Y, N, G	Imputation with weighting	Bivariate intervention; Unmeasured confounding
Park et al. (2024c) [23]	Difference in means	Yes	Y, Z	Q-learning; Weighting	Multiple interventions over time
Valeri et al. (2016) [24]	Difference in restricted mean survival times	No	Y	Kaplan-Meier	Censored, time-to-event outcome; Categorical intervention
Devick et al. (2022) [25]	Difference in mean survival times	No	Y, Z	Bayesian	Density shift intervention; Heterogeneous treatment effects
Valeri et al. (2023) [26]	Difference in restricted mean survival times	No	Stage transitions	Breslow with multistage model	Time-to-event intervention; Semi-competing risks
Smith et al. (2023) [27]	Difference in mean rates	No	Y, spatial random effect	Bayesian	Spatial data (dependence between neighbors); Small-area estimation

Some authors [3,9,22,28] show that their estimators are unbiased for both CDA and non-CDA estimands such as traditional decomposition. For many estimators, the allowability of covariates is not fully addressed, which may impact the size and interpretation of the observed and counterfactual disparity [29].

Meanwhile, estimators with the same estimand may have different statistical properties, strengths, and weaknesses. For example, regression methods tend to perform the most efficiently and interpretably if and only if they are correctly specified, i.e., if the intervention and covariates are linearly related to the outcome [30]. On the other hand, weighting methods can accommodate non-linear relationships between variables and do not extrapolate from observed data [22]. However, weighting can be less stable than regression due to the possibility of obtaining extremely large weights. Such imbalance can be mitigated by strategies such as “stabilizing” (i.e., normalizing) [31] and truncating weights [32]. Meanwhile, according to a simulation study [30], imputing the intervention tends to yield sensitive results when the correlation between the outcome and the intervention is much greater than the correlation between group membership and the intervention. Finally, to counter model misspecification, “doubly robust” estimators are theoretically (and asymptotically) unbiased for their estimands if at least one part of the model is correctly specified [33]. The best choice of estimator therefore depends on relationships in the data and desired statistical properties.

Statistical Inference

In science, it is always important to quantify the variance of estimates from data or modeling. Depending on how the data were collected or the structure of the model, there may be various approaches to estimate the variance. More mathematically derived models may come with mathematical forms for the variance, such as the asymptotic variance for an influence-function-derived estimator [34] or posterior quantiles for a Bayesian estimator [25]. More computationally, [33] recommended the bootstrap if the data were collected by a simple random sample but balanced repeated replication (BRR) if the data were collected by a stratified sample. Meanwhile, [22] used a simple weighted sum of squared residuals for their weighting estimator. Confidence intervals and variance estimates help audiences understand the reliability or uncertainty of an analytic result.

Important Considerations

The following sections discuss considerations throughout the CDA workflow, building on the discussion in [3].

Group Membership: Acknowledging Societal Identities and Intersectionality

When examining expected outcomes for a group of people, the definition of that group—for instance, race, ethnicity, or nationality—may be the result of historical classifications or social processes. Being a member of such a group may or may not reflect individuals’ lived experiences, and there may be substantial within-group heterogeneity. A well-established framework that addresses this limitation is intersectionality [35], which posits that the forces that shape disparate outcomes operate across many axes of disadvantage and can synergistically interact to produce altogether unique experience and outcomes for persons who stand at the intersection of various social groupings. Within the context of epidemiology and CDA, [36] discussed how including an interaction term for multiple dimensions of identity can reflect intersectionality, while [16] acknowledged the challenge in interpreting treatment effects across multiple groups.

Scale of Disparity Measurement and Size of Intervention Effect

There may be more than one possible scale to measure the average outcome within one group against the average outcome within another group. In the case of binary outcomes, for example, a disparity may be measured as a risk difference or a risk ratio or an odds ratio. A scale meaningful to stakeholders should be chosen. For instance, if the number of cases matters more than the proportion of cases, then a difference may be more meaningful than a ratio between groups because it can be multiplied by the population of a disadvantaged group to calculate the number of cases prevented by an intervention.

A CDA estimand can be formulated for any scale, but the choice of scale impacts the size of the observed, reduced, and remaining disparities [37]. For regression-based estimators, it also impacts which models may be most stable and accurate in estimating them. Regression-based estimators have a unique link function that constrains the effect of the intervention and of the covariates to be linear on that scale. For example, if the outcome is on the log scale, then the effect of an increase in the intervention or in a covariate is multiplicative on the original scale of the outcome.

Options for Intervention

Choosing a substantively meaningful intervention to study is key in CDA. The intervention should be modifiable, ethical to act upon, measurable, and respect individuals’ autonomy and well-being. The ideal intervention, especially in the context of historically disadvantaged subjects and communities, would be developed by a community-based participatory research approach, wherein the individuals to be studied have a partner role in defining the research question, model, and implementation. Considerations from social epidemiology may also be helpful [38]. In health settings, it is not usually necessary to assume that a binary intervention has a limited prevalence, as some alternative frameworks discussed later in this review [39,40] assume. Meanwhile, the non-substantive, causal inference considerations for defining an intervention have already been discussed in the Assumptions section of this review.

The results of CDA, comprising the disparity reduced and the disparity remaining, can inform whether the intervention studied would substantially decrease the (allowably-adjusted) difference in expected outcomes between disadvantaged and advantaged groups.

Allowable Covariates: Definition, Standard Population, and Overlap Requirements

Through a framework of allowability, CDA defines disparities according to explicit conceptions of fairness and agency [3,29]. Past literature has discussed nuances for choosing allowable covariates to align with the Institute of Medicine’s definition for a health disparity [41–43]. The set of allowable covariates may differ by context and application area.

Choosing a standard population for the outcome-allowable covariates should also align with moral justifications, such as equal opportunity or patient autonomy. Past studies that used matching designs to study disparities [44] used a disadvantaged group’s observed distribution for standardizing outcome-allowable covariates. Even though the CDA framework does not match patients across groups explicitly⁶, centering the causal and statistical inference on a disadvantaged group’s distribution of experiences (as measured by the outcome-allowable covariates) has a consistent interpretation with CDA’s framework of intervening on disadvantaged group(s).

Finally, just as in the long-standing descriptive method of decomposition, CDA results may be unstable (from a statistical inference perspective, meaningful that confidence intervals may be wide or results may change easily from small perturbations in the data) when advantaged and disadvantaged groups’ outcome-, intervention-, or non-allowable covariates have insufficient overlap [40]. This instability occurs under poor overlap because the results are driven by a small number of data points. There are a few possible strategies to overcome the overlap challenge. For weighting estimators, weights may be stabilized (i.e., normalized, bringing their average to approximately one) [31] and/or truncated [32]. Alternatively, the study and inferential population could be trimmed to include only people within a certain range of A_y and A_z values. As a descriptive diagnostic, the overlap of outcome-allowable, intervention-allowable, and non-allowable covariates between advantaged and disadvantaged groups—both before and after outcome-allowable standardization and balancing efforts such as weighting—should be plotted visually, as done in [22].

Choosing a Dataset

Several considerations should be made when selecting a dataset for CDA. For example, what purpose were the data were collected for? Do the measured variables (group designation, outcome, hypothetical intervention, covariates) align with the research question of interest? Who is missing from the dataset?

Time ordering—between the outcome, the hypothetical intervention, and the covariates—also matters. Depending on when the hypothetical intervention is measured, the causal path and interpretation may be different. To use [25]’s example, BMI measured at the beginning of cancer could hypothetically be a point of intervention, whereas BMI measured at a late stage of cancer may have already been influenced by cancer. To avoid introducing “collider-stratification” bias, the best study design is longitudinal with time-varying covariates, where the allowable and non-allowable covariates are measured first, then the hypothetical intervention, then the outcome.

Finally, a common statistical challenge when studying disparities is that one or more groups may have a small sample size, decreasing the confidence of modeling results for both internal and external validity. [27] uses small-area estimation and Bayesian techniques to incorporate prior and neighboring information to supplement a small sample size.

Space for Further Methodological Development

More work can be done to incorporate allowability into existing models for decomposing and intervening on disparities. Meanwhile, several authors have started exploring methods for complex data settings, where causal and statistical assumptions may be violated. Future research can compare such methods on simulated or real data.

Alternative Frameworks to CDA

Many other causal frameworks for reducing disparities have been proposed recently. Here, we briefly explain why they differ from CDA.

Despite their other advantages (i.e., handling differently sized comparison groups and being flexibly data-driven, respectively), matching methods [44–46] and graphical discovery approaches [47,48] both treat group membership like a root cause or exposure. As discussed earlier in this review, this can lead to difficulties in interpretation, implementation, and causal inference.

Several frameworks [33,34,39,40] differ from CDA in at least two ways. Firstly, the interventions are applied to all individuals rather than to historically disadvantaged groups. Secondly, the interventions in [33,34,39,40] depend on all potentially confounding covariates, rather than only allowable covariates.

[34]’s decomposition adds an additional lever for a binary intervention: “selection”, denoting how likely it is that the individuals within a group who would most benefit from the intervention receive the intervention. Here, there are three steps: (i) to first randomize the intervention within groups while maintaining the same within-group prevalence (to remove selection); (ii) to subsequently equalize the prevalence of the intervention across groups (to remove disparities in intervention prevalence); (iii) subsequently withhold the intervention from everyone (to exclude effect heterogeneity) similar to [10,11], where changes in disparity are assessed after each step. This is an effort to describe and isolate the explanatory contributions of the intervention in terms of within-group selection, differential prevalence, and differential effect rather than an effort to prescribe the impact of removing disparities in the intervention (which in practice will affect each of these components collectively [13]). Meanwhile, [40] and [39] discuss three classes of binary interventions (“lottery”, “affirmative action”, and “antidiscrimination” or “conditional equalization”⁷, as labeled by their respective papers), all of which—unlike CDA—assume that the prevalence (i.e., distribution) of the intervention should be kept at a pre-fixed level. Such interventions may not be reasonable in public health and medical contexts, where interventions must be medically appropriate, and it is plausible to increase the availability of the intervention.

Additionally, to address the causal inference challenge of non-overlap of covariates between disadvantaged and advantaged groups, [40] transforms the values of a hypothesized confounder while preserving the order of values within each group. However, transforming intervention-allowable covariates may not make sense in all settings. For instance, in a medical setting, weight is an objective measurement that may be necessary for an intervention to consider, so transforming it differently within different groups may dismiss an already disadvantaged group’s greater medical need. Furthermore, in medical settings, interventions are unlikely to be guided by an individuals within-group ranking of a confounding variable as socioeconomic status.

Conversely, [49] uses allowability for a different purpose than CDA. To evaluate effects of an actual intervention on a health outcome, it balances baseline allowable covariates across groups, while balancing all confounders across intervention arms within each group. To evaluate effects on an actual intervention on disparate decision-making, [49] creates an additional hypothetical intervention on post-intervention “decision-making”, i.e., the allowable criteria by which a decision-based outcome (e.g., a medical treatment) is determined. [49] also considers effects for treated individuals had they received control (e.g., the ATT for disparity in outcomes).

Conclusion

By taking a prescriptive, interventional approach that differentiates between adjustment for allowable covariates versus non-allowable confounding covariates, CDA builds on past descriptive methods for decomposing disparities. To perform CDA, analysts should: construct a meaningful, substantively informed research question; use a dataset where causal assumptions are plausible; weigh the statistical strengths and weaknesses of any estimation strategy; and diagnose the model fit and uncertainty. Assuming sufficient statistical power, CDA will find a significant reduction in disparity if a historically advantaged and a historically disadvantaged group experience different distributions of the variable to be intervened on or if the effect of the intervention differs by group. By reviewing the CDA framework and recent implementations by various authors, we hope that this review will inform disparity-reducing interventions in any field.