From Averages to Heterogeneity: A Plain-Language Guide to MAIHDA in Epidemiology

Abstract

Many studies compare health averages between groups such as neighbourhoods or social categories. Averages are simple but can be misleading, since individuals within the same group often differ widely. We present MAIHDA (Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy) as a general framework to study how context structures health differences. MAIHDA is not a new statistical model but a way to reorganize standard multilevel analysis to look beyond averages. It integrates three perspectives: (1) Specific Contextual Effects (mean differences between groups), (2) General Contextual Effects (how strongly outcomes cluster within groups, eg the variance partition coefficient), and (3) Discriminatory Accuracy (how well group membership classifies individuals according to the outcome). Interpreting these dimensions together shows to which degree a context shapes outcome and whether interventions should be universal or targeted. Although intersectional studies have recently popularized MAIHDA, the framework predates its intersectional applications. It was first developed within contextual epidemiology to study geographical and institutional settings, and later extended to intersectionality and multicategorical analyses, which added visibility. By shifting attention from averages to heterogeneity and clustering, MAIHDA helps avoid group stigmatization and guides equitable strategies such as proportionate universalism. It offers a practical, theory-agnostic way to understand how contexts structure individual inequalities.

Introduction

The present essay is not a tutorial but a conceptual synthesis. We assume readers already have a basic knowledge of multilevel analysis, individuals nested within groups, with outcome variance decomposed into within- and between-group components.^1–4 Our aim is to situate Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) as a general framework for contextual epidemiology.

By contextual epidemiology we mean approaches that examine how health outcomes are shaped by social, organizational, and spatial contexts, ranging from neighbourhoods, schools, and workplaces to socioeconomic, racialized, and cultural groupings, rather than focusing solely on individual risk factors. ⁵

We highlight MAIHDA's applications across geographical, institutional, intersectional, and other multicategorical contexts. Our aim is conceptual and reflective: to trace the intellectual development of MAIHDA, clarify its methodological principles, and situate it as a framework for understanding context, heterogeneity, and inequality in population health research.

MAIHDA is not a new statistical model. Rather, it reorganizes and extends established concepts of multilevel modelling. Its distinctiveness lies in giving simultaneous interpretive weight to group-level differences in means and to the heterogeneity around those means.^6–9 This reframing is necessary to counter the dominance of means-centred, probabilistic risk-factor epidemiology, ⁷ which has long overshadowed variance-informed reasoning. By shifting attention from averages to heterogeneity, MAIHDA both improves analytic clarity and reduces the risk of stigmatizing populations, an all-too-common consequence of attributing group averages to each and all of their members.^10–12

In contemporary public health, the limits of average-based approaches are increasingly evident. ¹² While measures of association remain dominant, they fail to reflect the complexity of population health. This dissatisfaction has renewed interest in multilevel models that focus on variance and heterogeneity. ⁷ At the centre of this shift is MAIHDA. ¹³

In social epidemiology, one major strand is contextual epidemiology, which emphasizes how broader environments like households, schools, neighbourhoods, socioeconomic categories, or health-care systems, shape health outcomes. This tradition has often drawn on multilevel epidemiology, which provides the statistical framework for decomposing outcome variance into within- and between-context components. In this perspective, individuals and contexts are not separate but interlocked: the aim is to understand how contexts shape health differences across the life course. ¹⁴

This broader understanding was embedded in earlier work, ⁵ which proposed a longitudinal framework for studying inequalities across time and space. That framework explicitly called for measuring both general and specific contextual effects, using variance-informed approaches, across diverse contexts. Incorporating this perspective set the stage for MAIHDA as a flexible analytical framework in epidemology. ¹⁵

The acronym MAIHDA first appeared in the published literature through a tutorial commentary, ¹³ written to accompany an intersectional multilevel analysis. ¹⁶ Although Evans et al did not use the term MAIHDA itself, their intersectional application helped introduce variance-based multilevel analysis to a wider audience. Merlo's accompanying commentary consolidated and formally named the framework. In this light, Intersectional MAIHDA (I-MAIHDA) played a significant role in popularizing variance-informed reasoning, even though the conceptual foundations and scope of MAIHDA extend well beyond intersectional contexts. Properly, I-MAIHDA should be understood as one application alongside geographical, institutional, or other unidimensional and multidimensional uses of the framework. Indeed, as summarized in a recent systematic review, ¹⁷ MAIHDA has already been widely applied in intersectionality-informed research. Our aim in this essay is not to catalogue those applications but to reposition MAIHDA as a general framework for contextual epidemiology, showing how its principles predate and extend beyond intersectionality to geographical, institutional, and multicategorical settings.

As previously noted, ¹⁸ MAIHDA's roots lie in earlier multilevel analyses of geographical and institutional inequalities.^{3,8,13,19–21} Indeed, foundational work by Duncan, Jones, and Moon, ²² and Boyle and Willms, ²³ had already emphasized variance-based thinking. MAIHDA builds on this tradition by explicitly reframing variance-based reasoning and refining key concepts, not by introducing new statistical models, but by structuring their interpretation to address the persistent neglect of variance in applied multilevel research. History has shown that, despite its relevance, the variance approach has often been sidelined or overlooked. MAIHDA emerges as a necessary corrective, offering a perspective that makes contextual structuring visible and actionable.

This essay therefore revisits MAIHDA's conceptual foundations, traces its methodological evolution, and situates its relevance within social and contextual epidemiology. As noted, this essay is neither a tutorial nor focused on I-MAIHDA. Several recent papers have introduced MAIHDA in the context of intersectionality, including tutorials, systematic reviews, and debates about its interpretation.^13,17,24,25 These contributions have been essential for consolidating I-MAIHDA as a methodological tool within intersectional research. Our focus, however, is different. This essay seeks to reposition MAIHDA as a general conceptual framework within contextual epidemiology, and MAIHDA itself can be applied in many other fields beyond epidemiology. By tracing its intellectual roots, clarifying its variance-based orientation, and extending its relevance beyond intersectionality, we aim to highlight how MAIHDA can advance equity-oriented public health research in a broader sense.

We argue that general MAIHDA represents both a renaissance of original multilevel thinking and a forward-looking framework for ethically grounded, heterogeneity-aware public health. While our focus is to present MAIHDA as a general framework, we also locate it within the broader tradition of contextual epidemiology, highlighting how it builds upon and challenges earlier approaches, with implications for equity-oriented and anti-racist public health.

The Problem with Average-Based Epidemiology and MAIHDA as an Alternative

The standard approach to health inequality has been to compare group means, for example, neighbourhood-level obesity rates, hospital mortality rates after myocardial infarction, or ethnic disparities in disease prevalence. Yet this reliance on averages has a long and questioned history in both social and biological sciences and in clinical medicine: Claude Bernard warned that “averages confuse, while aiming to unify, and distort while aiming to simplify”. ²⁶ Later ²⁷ referred to the “tyranny of the average man” in ethics and social thought. In The Mismeasure of Man, ²⁸ Gould showed how averages reified in biology and human sciences conceal diversity and foster misleading conclusions. Similar critiques have appeared under labels such as the “mean-centric approach” ²⁹ and the “tyranny of the means”. ³⁰ In epidemiology, Himmelstein, Levins and Woolhandler ³¹ as well as Jones ³² stressed these ideas. In the same line ³³ Pepe has emphasized that reliance on mean values in the evaluation of diagnostic and prognostic tests can be misleading because averages obscure the underlying heterogeneity of test performance across patient groups and risk strata, thereby masking important differences in clinical utility; this concern is analogous to the ideas we advance here. In this line ³⁴ Kaufman shows that when researchers report only “average differences between races,” they commit the same mistake that Pepe warned against in diagnostics: relying on means that conceal heterogeneity and lead to misleading conclusions. Like Tabery, ³⁰ Merlo et al described this concept as the “tyranny of the averages”.^10–12

While descriptively useful, the mean-centric approach has critical limitations. First, it oversimplifies collapsing complex distributions into group averages that ignore the substantial heterogeneity within groups. This has practical implications: many high-risk individuals belong to low-risk groups, and many low-risk individuals belong to high-risk groups. Second, it misleads: policies based on mean differences risk being inefficient, by missing many cases, or inequitable, by stigmatizing entire groups on the basis of elevated averages. The problem is compounded by the fact that the mean, unlike the median, is highly sensitive to outliers. By ignoring within-group heterogeneity, the mean-centric approach also promotes narratives of blame and fosters statistical essentialism: treating group identity as fate. ³⁴ Another problem when comparing group means is that very different group sizes are often not given sufficient attention when one group mean is compared to another group.

Influential scholars^35–37 have offered important critiques of ecological inference and warned against overinterpreting variance components, citing their dependence on scale, prevalence, and model specification. While justified, this caution often led to neglect, and variance was too often treated as nuisance rather than as a substantive indicator of inequality. This tendency was reinforced by the popularity of specifying cluster-robust standard errors in conventional regression models or using generalized estimating equations (GEE), which estimate population-averaged associations with “correct” standard errors, but fail to quantify the degree of within- and between-group heterogeneity around them.

By contrast, Harvey Goldstein consistently championed the variance partition coefficient (VPC) as an interpretable summary measure of variance attributable to different levels.^38,39 Alongside co-authors such as Browne, Rasbash, and Leckie, he established the conceptual and computational foundation for using variance in educational and epidemiological studies. Raudenbush and Bryk ⁴⁰ and Snijders and Bosker, ⁴¹ similarly presented the VPC as a meaningful tool, though later editions ⁴² struck a more cautious tone, reflecting wider methodological debates and shifting disciplinary fashions.

These discussions also raised the question of whether variance could be understood causally. Contexts themselves often act as causal forces: exposure to environmental toxins produces clustering of disease, unequal resources across neighbourhoods or schools shape health and educational trajectories, and therapeutic traditions in primary health-care practices generate systematic disparities in treatment. Furthermore, structural processes such as racism or class stratification distribute risks across intersectional strata. In such cases, variance is not a statistical artefact but a signal of contextual influence.

Against this background, MAIHDA reframes variance as central. It asks not only whether context matters, but how much of total individual variation is structured by the context, and whether groupings meaningfully classify individual outcomes. By treating group-level variance as signal rather than noise, MAIHDA moves beyond ecological caution toward a deeper investigation of structural patterning in health.^8,9,43 This reframing challenges the dominance of “probabilistic risk-factor epidemiology”, ⁷ which has long privileged averages over heterogeneity and overlooked the causal role of contexts in producing inequality.

Having outlined the limitations of average-based epidemiology in Section 2, we now turn to the intellectual tradition that most directly sets the stage for MAIHDA: contextual epidemiology. This field sought to move beyond methodological individualism by embedding individuals within the social and institutional environments that shape their health. Yet, as we will see, contextual epidemiology often reproduced some of the very shortcomings it aimed to overcome. Revisiting this tradition is essential for understanding both the origins of MAIHDA and the ways in which it reframes multilevel analysis.

Contextual Epidemiology Revisited: Reflections on MAIHDA as a General Framework

The intellectual roots of MAIHDA lie in the tradition of contextual epidemiology. While all epidemiology is inherently both social and biological (Krieger 2001), contextual epidemiology explicitly examines how social, spatial, and organizational contexts shape individual health and disease. Rather than focusing narrowly on individual-level risk factors, it highlights the influence of broader contexts, such as socioeconomic categories, neighbourhoods, schools, workplaces, and health-care systems, on health outcomes.

Seminal contributions over the last three decades,^35,44–48 alongside our own work^5,7,49,50 have emphasized that individuals cannot be treated as isolated units, but as embedded in households, schools, neighbourhoods, and institutions that structure health across the life course. This represented an important shift away from methodological individualism and the narrow logic of “probabilistic risk-factor epidemiology”. ⁷

Despite these advances, contextual epidemiology often reproduced some of the very limitations it sought to address. As noted in an invited commentary, ⁷ the focus on “risk factors” persisted, merely relocated from the individual to the contextual level. Analytical strategies frequently emphasized mean differences between groups (eg, between neighbourhoods), while neglecting the variability of outcomes around those means and the overlap between groups. Consequently, contexts were often treated as additional “risk factors” rather than as structuring mechanisms of inequality.

As discussed in the previous section, this reliance on averages has been described as the “tyranny of the averages”.^11,12 Beyond being analytically limiting, it stigmatizes whole groups by portraying them as uniformly high- or low-risk. ⁵¹ Measures of contextual variance such as the VPC were frequently overlooked or treated as mere technicalities, rather than recognized as key indicators of how social or geographical contexts condition inequality. ⁵¹ This neglect weakened contextual epidemiology's ability to capture the degree to which health inequalities are structured by contexts versus reflecting individual heterogeneity.

The marginalization of variance-based reasoning was further reinforced by a paradoxical phenomenon. ⁵² When the contextual clustering or general contextual effect (GCE) is weak (low VPC), group-level associations or specific contextual effects (SCE) can be estimated with greater precision, yielding “statistically significant” results that encourage a narrative of strong contextual influence, even when the GCE is negligible. Conversely, when clustering is strong (high VPC), SCE estimates become more uncertain, discouraging recognition of context precisely when it is most important.

The result was that contextual epidemiology, while rhetorically critical of individual risk-factor approaches, often remained tethered to their underlying logic. The contextual was frequently treated as simply another risk factor, and analyses of variance and heterogeneity were sidelined. As a result, opportunities to connect statistical modelling to broader theoretical debates in social epidemiology were underused.

Overcoming these limitations requires more than incremental methodological adjustments. What is needed is a reframing of multilevel analysis itself, one that systematically integrates measures of association (SCE), clustering (GCE), and discriminatory accuracy (DA), and treats them as substantively meaningful indicators of contextual structuring. Only then can contextual epidemiology move beyond the tyranny of averages and avoid the pitfalls of analytical blind spots and stigmatizing narratives. It is precisely this reframing that MAIHDA provides.

In sum, MAIHDA can be seen as both a continuation and an extension of contextual epidemiology. By reframing variance measures such as the VPC and DA as substantive evidence of contextual structuring, MAIHDA advances beyond the earlier focus on mean-based associations. Yet, while the framework is grounded in methodological innovation, it remains theory-agnostic. This openness is crucial: MAIHDA does not prescribe a specific explanation for health inequalities but provides an analytic platform that can be aligned with diverse traditions in social epidemiology or any field of quantitative science.

MAIHDA: An Evolution and a Renaissance in Multilevel Analysis

MAIHDA provides the reframing of multilevel analysis that contextual epidemiology has long needed. It is not a new statistical model but a systematic reorganization of established multilevel concepts, giving explicit interpretive weight to variance, heterogeneity, clustering, and discriminatory accuracy.^{5,7–9,13,21,22,44,53} Its distinctiveness lies not in statistical novelty but in interpretive orientation: variance components and DA are treated as substantively meaningful indicators of contextual structuring and inequality.

While intersectional applications have been especially influential in popularizing the approach, we stress that I-MAIHDA represents only one use of the general MAIHDA framework. Geographic, institutional, and other multicategorical applications are equally valid, and together they demonstrate that MAIHDA is not confined to intersectionality but rooted in a broader variance-based perspective.

To clarify, unidimensional MAIHDA refers to contexts defined by a single dimension (eg, neighbourhoods), while multidimensional MAIHDA uses cross-classification of several dimensions (eg, gender × ethnicity × income).

Multidimensional MAIHDA is particularly suited for analyzing interaction effects, as highlighted by Evans ⁵³ and Rodriguez-Lopez et al. ⁵⁴

Unlike classical multilevel models that assume higher-level units are random samples, MAIHDA accommodates exhaustive classifications such as intersectional strata. This marks its evolution: extending multilevel analysis to multidimensional contexts that earlier traditions regarded as unsuitable. I-MAIHDA has proven especially valuable in mapping inequalities and clarifying whether joint effects reflect additivity or synergism (see section Intersectionality and interactions). It has even been proposed as a potential “gold standard” for the study of health inequalities. ¹³ At the same time, MAIHDA is theory-agnostic and not limited to intersectionality. It can operationalize diverse perspectives in social epidemiology (see section MAIHDA and Social Epidemiological Theories).

Another evolutionary step was the integration of discriminatory accuracy (DA) into multilevel models.^55,56 DA complements GCE by showing not just whether contexts structure individual variation, but whether they do so in ways that justify targeted versus universal interventions.

In a recent response to a commentary noting low DA, ⁵⁷ Borrell et al^58,59 suggested that attention to DA was misplaced, arguing that it pertains only to individual-level prediction whereas the authors’ focus was on population health. This dismissal of DA as ‘merely individual prediction’ reflects the same psychological bias that once led researchers to treat the variance partition coefficient as a nuisance: both measures disrupt the comfort of focusing exclusively on averages. Yet DA is highly relevant for population health, as it evaluates the practical utility of group classifications for interventions and guards against the ethical risk of stigmatization when average group differences are emphasized despite low discriminatory accuracy.

The discrepancy between VPC and AUC (Section 5) in situations of unequal group sizes should not be seen as a statistical limitation, but as relevant information: it distinguishes between contexts that matter in terms of explaining variance and those that truly discriminate between individuals. ⁵²

As a renaissance, MAIHDA restores variance-based measures such as the VPC to central interpretive status. MAIHDA repositions them as core tools for social epidemiology, demonstrating that variance is not noise but a signal of contextual structuring. The growing use of intersectional applications has contributed to this revival by making variance-based reasoning more visible and legitimate in public health (see section How Intersectional MAIHDA has Revitalized Geographical and Institutional Applications).

Core Components of MAIHDA

MAIHDA systematically combines three complementary elements.^5,7,8,13,52

- Specific Contextual Effects (SCE): Traditional group averages and associations (eg, means, risks, odds ratios). They ask whether belonging to a given stratum or context is associated with the outcome.

- General Contextual Effects (GCE): The degree to which outcomes are clustered within contexts, typically measured with the VPC. GCE indicate how much the contexts structure individual outcome variation in general, without specifying any contextual characteristic other than the cluster or group identity.

- Discriminatory Accuracy (DA): DA assesses how well group membership distinguishes individuals according to the outcome. For binary outcomes, it is often measured by the area under the receiver operating characteristic curve (AUC). In MAIHDA, the AUC is not used as a predictive marker in the conventional sense but as a contextual indicator of discriminatory accuracy—that is, the extent to which contextual grouping helps differentiate between cases and non-cases (or correctly rank individuals for continuous outcomes).

As discussed above, the variance partition coefficient (VPC) and the AUC may diverge when clusters differ in size. This discrepancy is not a flaw but informative: a context may account for much of the individual outcome variance (high VPC) yet still fail to meaningfully discriminate between individuals according their outcome (low AUC). Hence, measures of DA complement general contextual effects (GCE) by indicating whether contextual structuring has practical discriminatory value.

For continuous outcomes, analogous measures are needed that capture both contextual relevance and discriminatory balance across groups. For instance, rank-based statistics such as Harrell's concordance index (c-index, Somers’ D) extend the AUC logic to continuous data while remaining sensitive to both outcome range and group size. In contrast, R² measures provide complementary but weaker insights, as they depend mainly on total variance explained and only indirectly reflect discriminatory balance.

- Measures of DA remain uncommon in contextual epidemiology but are crucial for understanding inequality structures. Many published I-MAIHDA studies omit their interpretation, echoing the earlier neglect of the VPC, which was long treated as a technical nuisance because it challenged fixed-effects reasoning. Yet DA indicators such as the AUC are essential for describing the distributional structure of inequality; that is, how well models separate cases from non-cases rather than merely estimating mean differences. Ignoring DA risks overemphasizing average effects and overlooking Rose's insight ⁶⁰ that most cases arise among people at low or moderate risk simply because they constitute the majority

- Other measures: In addition, measures such as the Proportional Change in Variance (PCV) help us to understand how specific contextual effects (SCE) account for general contextual effects (GCE), and, in the case of multidimensional or intersectional MAIHDA, how much of the variance between strata is attributable to additive versus synergistic or super-additive components (with 1 – PCV reflecting the contribution of interactions).

It is true that in applied research, proportions or rates (eg, hospital mortality rates) are often used to “summarize” outcomes within each cluster. However, this approach is precisely what we and others have described as the “tyranny of the averages”.^10–12 Proportions collapse complex within-cluster heterogeneity into a single number, which can be misleading in two ways: (i) Many individuals with the outcome may belong to “low-rate” clusters simply because those clusters are large, (ii) Conversely, small clusters with extreme rates may strongly influence between-cluster variance estimates, even though they represent few individuals. Tiny groups will disproportionally appear at the extremes of the distribution of group differences (league table) due to the greater influence of chance and will get undue attention.

This is where MAIHDA adds value. Instead of relying only on group-level averages, it integrates variance components and discriminatory accuracy (eg, AUC) to assess both how much outcomes are clustered (GCE) and how well cluster membership classifies individuals (DA). It should be noted that within the context of MAIHDA, the AUC serves not as a conventional predictive marker but rather as a contextual measure of discriminatory accuracy, indicating the degree to which group membership differentiates cases from non-cases. The AUC provides an individual-level perspective that avoids the pitfalls of average-based reasoning: it captures the overlap of individual distributions across groups and shows whether targeting interventions by cluster would meaningfully reduce inequities.

In short, MAIHDA reframes the analysis by combining group-level averages with measures of variance and classification, thus offering a fuller and less misleading picture of contextual effects.

Importantly, what distinguishes MAIHDA is not the statistical formulas themselves, since the VPC is a standard feature of multilevel models, but the interpretive framework. Rather than treating variance components and discriminatory accuracy as technical by-products, MAIHDA reframes them as substantive evidence of contextual structuring.^8,9,52 This interpretive orientation, developed over the past two decades, has gained wider visibility with the introduction of intersectional multilevel analyses ¹⁶ and their framing within the general MAIHDA paradigm. ¹³

This interpretive shift has sometimes been misunderstood. As Evans et al ²⁴ emphasize in their reply to Wilkes and Karimi, ²⁵ critiques of (Intersectional) MAIHDA often stem from misconceptions about the behaviour of variance components or the role of additive models. Their clarifications reinforce that the distinctive contribution of MAIHDA lies not in statistical novelty, but in elevating variance decomposition and discriminatory accuracy to central analytic dimensions within social epidemiology.

Taken individually, SCE, GCE, and DA illuminate different facets of contextual influence. Yet their greatest value lies in being interpreted together. It is precisely in the tensions and complementarities between them that MAIHDA reveals patterns invisible to conventional analyses. Using an empirical study as example, ⁸ the next section shows how the simultaneous interpretation of these three metrics provides a more nuanced understanding of multilevel risk heterogeneity and guides the design of equitable public health strategies.

The Simultaneous Interpretation of SCE, GCE, and DA

One of MAIHDA's core strengths is the joint interpretation of SCE, GCE, and DA. Each dimension highlights a different aspect of contextual structuring, and their combined reading prevents misleading conclusions. The Malmö study of neighbourhood effects on health behaviours provides a useful illustration. ⁸

In the case of psychotropic drug use in Malmö, ⁸ low individual income and living in a poor neighbourhood were both associated with higher prevalence (SCE). On average, the odds of use were about 30% higher in disadvantaged neighbourhoods. However, the general contextual effect was negligible: the VPC was only about 1%, and adding neighbourhood to the model hardly increased the AUC (from 0.616 to 0.630). In other words, outcomes were only weakly clustered within neighbourhoods, and the discriminatory accuracy of using neighbourhood membership to identify users was extremely low. This means that, although there was a measurable association at the group level, it was practically useless for identifying individuals at risk. A policy targeting “high-risk” neighbourhoods would miss most users and wrongly label many non-users as at risk. A universal intervention would be more justified.

By contrast, for choice of private versus public general practitioner (GP), ⁸ the interpretation was radically different. Here, neighbourhood residence showed a very strong general contextual effect: the VPC was nearly 60%, and the AUC jumped from 0.600 (using individual variables only) to 0.895 once neighbourhood clustering was accounted for. This meant that knowing someone's neighbourhood provided substantial additional discriminatory accuracy in classifying whether they would choose a private GP. At the same time, high neighbourhood income was strongly associated with private GP use (SCE, OR ≈ 3.5), but this variable explained only about 11% of the large between-neighbourhood variance. Thus, while the average association was clear, much of the heterogeneity across neighbourhoods remained unexplained, suggesting that additional contextual mechanisms (eg, availability of private providers) played a role.

Together, these two examples underscore why interpreting SCE, GCE, and DA jointly is essential. For psychotropic drug use, the SCE was statistically “significant” but of little practical value once low GCE and DA were considered. For private GP choice, SCE and GCE both pointed to strong contextual structuring, and DA confirmed that group membership was a powerful classifier. Relying on SCE alone in either case would have led to misleading conclusions, either overstating the relevance of neighbourhood for psychotropic drug use or overlooking the unexplained contextual heterogeneity in private GP choice. ⁸

This illustrates how SCE, GCE, and DA each reveal different facets of contextual influence. A low GCE necessarily implies low DA, but the reverse is not always true: a high GCE does not guarantee high DA, particularly when groups differ in size. This paradox highlights the importance of interpreting the three measures together. ⁵²

Also, in classical multilevel modelling the primary concern (to estimate contextual variance) is typically the number of upper-level units (eg, hospitals) rather than the size of each cluster. However, in MAIHDA the focus is somewhat different: cluster size becomes relevant for the quantification of discriminatory accuracy (DA) and also links to Rose's observation that most cases of disease often occur in groups with lower average risk simply because those groups contain the majority of individuals ⁶⁰ (see section Rose’s Legacy and MAIHDA’s Strategic Implications.).

From a causal perspective, a high GCE signals meaningful contextual influence. From a public health perspective, DA informs intervention strategies: low DA favours universal approaches, while high DA may justify targeted measures. This integration moves epidemiology beyond reliance on group averages alone.

Intersectionality and Interactions

Evaluating Interaction Effects

In addition to these three essential metrics (GCE, SCE, DA), intersectional and more generally multidimensional or multicategorical MAIHDA, where the clusters, groups or strata have been constructed from multiple categorical variables, offer a powerful approach for evaluating interaction effects. Rather than relying on traditional interaction terms, which can become unstable and difficult to interpret when multiple categorical variables are included, these applications of MAIHDA quantify interactions implicitly by performing strata specific predictions and modelling variance across the constructed strata. This allows researchers to detect whether specific combinations of social positions (eg, age, gender, and socioeconomic status) ⁶¹ or biomedical risk factors (eg, parity, BMI, and hypertension) ⁵⁴ have a synergetic effect on the outcome beyond what would be expected from the additive contributions of main effects alone.

Intersectionality Beyond Interaction

For more than 15 years, intersectionality has often been operationalized as statistical super-additivity. ⁶² Yet, as Bauer ⁶³ cautions, equating intersectionality with interaction risks oversimplification, since the framework also concerns power, history, and structures shaping inequalities. If intersectional effects are reduced to interactions, they appear small in most MAIHDA studies or may be underestimated.

To avoid this reduction, we propose the use of multidimensional MAIHDA for the study of socioeconomic inequalities. This approach distinguishes between additive components, reflecting the cumulative burden of belonging to multiple disadvantaged groups, and superadditive components, where disadvantages amplify one another. Even without interaction, additive burdens remain meaningful and require public health attention. However, there must also be sub-additive components. That is, strata that enjoy synergistic advantages. Intersectionality should work in both directions.

An “empty” MAIHDA model already maps how outcomes are distributed across multidimensional strata, showing where disease burden is concentrated regardless of interaction. Thus, what is often termed “intersectional MAIHDA” may be more accurately described as multidimensional or multicategorical MAIHDA, a flexible, theory-free analytic strategy open to diverse interpretations in social epidemiology.

MAIHDA and Social Epidemiological Theories

MAIHDA can be situated within and across different social epidemiological theories, providing a flexible framework to operationalize perspectives such as ecosocial theory, life course epidemiology, social stratification (Weberian tradition), fundamental cause theory psychosocial theories of stress and social hierarchy, and neo-materialist approaches to health inequalities.

Although since 2018 presented as an “intersectionality method,” multidimensional MAIHDA is in fact theory-agnostic and ideally suited to operationalize a wide range of perspectives on health inequities. MAIHDA can analyse contexts defined by isolated or combined socioeconomic, racialized/ethnic, geographical, and institutional dimensions to map average risks (SCE), quantify structural influences (GCE), and assess how individual outcomes are distributed across strata (DA).

Contemporary epidemiology must attend more deeply to the “embodied truths” produced through structural patterning.^44,64,65 MAIHDA responds by elevating variance-based reasoning, mapping how social, geographical, and health-care inequities become biologically embedded, while remaining open to diverse theoretical lenses.

For example, ecosocial theory emphasizes embodiment of injustice and racism across the life course;^44,64,65 life-course epidemiology highlights accumulation, timing, and sequencing of exposures;^66,67 and fundamental cause theory explains the persistence of disparities through enduring resource inequalities. ⁶⁸ The long-standing debate between psychosocial (eg, stress, comparison, hierarchies) ⁴⁷ and neo-materialist (eg, living conditions, access to resources) explanations ⁴⁶ can also be revisited through multidimensional MAIHDA, which moves beyond single-gradient analyses to explore how multiple social positions jointly structure inequality.

Newer approaches such as syndemic theory when two or more diseases or health conditions cluster within a population because of social and structural factors, leading to an excess burden of disease and continuing health disparities,^69,70 structural vulnerability frameworks, ⁷¹ and the political economy of health ⁷² can likewise be operationalized. Each emphasizes that inequities are systemic processes. Even less common sociological theories like ecological niche theories can be applied with a multidimensional MAIHDA framework ⁷³

In this way, multidimensional MAIHDA provides a flexible analytic bridge across theoretical traditions, enabling them to be tested, compared, and integrated within a single multilevel framework. It offers a stronger empirical basis for understanding the diverse pathways through which social determinants generate health inequalities.

Limitations and Critiques of MAIHDA

General Limitations Inherited from Multilevel Models

While the advantages of MAIHDA are many, the framework also inherits several limitations long associated with multilevel models. As discussed by Oakes and Merlo,^43,74 among others, these include sensitivity to assumptions about hierarchical structure, variance components, and boundary definitions, as well as risks of misspecification due to unmeasured confounding and selection bias Like all statistical approaches, MAIHDA requires careful design and transparent interpretation to avoid misleading conclusions.

Methodological and Practical Challenges in I-MAIHDA Applications

In its intersectional applications, a recurring critique highlighted by Wilkes and Karimi, ²⁵ is that I-MAIHDA should not be seen as a method that “explains” health inequalities on its own. Rather, it is a statistical framework that describes how inequalities are structured across contexts; explanation still requires theory and substantive interpretation. Similarly, Keller et al, ¹⁷ in their systematic review of I-MAIHDA applications, emphasized challenges that are common to most epidemiological methodologies such as the need for large datasets, instability of estimates in sparse strata, and reliance on shrinkage, which can obscure extreme risks in small disadvantaged groups. These concerns are especially relevant for intersectional MAIHDA, where the number of strata increases rapidly.

Interaction Effects and the ARDI Approach

Another common concern is that I-MAIHDA does not estimate interaction terms within the traditional “main effects plus interactions” framework. Some authors have suggested that this might obscure potential synergistic or antagonistic effects between factors.^75,76 However, MAIHDA enables the calculation of indicators such as the Absolute Risk Due to Interaction (ARDI), defined as the difference between the predicted absolute risk including both main additive fixed effects and interaction random effects (AR) and the risk predicted from main additive fixed effects only (ARDM). These differences can be visualized through interaction maps, which display stratum-specific deviations from additive predictions. ⁵⁴ Moreover, Evans et al ²⁴ in their reply to Wilkes & Karimi, emphasized that the purpose of MAIHDA is not to produce abstract coefficients but to provide empirically grounded predictions for intersectional strata and assess departures from additivity.

Shrinkage and the Risk of Dilution

Bingenheimer and Raudenbush, ⁷⁷ as well as Leckie, Bell et al, ⁷⁸ raised a more general concern regarding multilevel models: while shrinkage helps stabilize estimates for small units or strata by reducing random noise, it may also ‘dilute’ true but extreme risks present in small groups

Limited Familiarity with Variance-Based Measures

Across all MAIHDA applications, variance-informed measures such as the VPC, or DA for random effects remain less familiar to applied researchers than regression coefficients or mean differences. ³⁵ This may limit uptake in practice and reinforce reliance on averages, even when variance-based reasoning would be more appropriate.

Theoretical Concerns: Intersectionality and Structural Processes

Finally, some critics argue that: I-MAIHDA risks simplifying intersectionality by focusing on variance decomposition rather than broader structural processes of power, history, and oppression. ⁷⁵ While this is a valid caution, it reflects the need to embed MAIHDA analyses within appropriate theoretical frameworks, not a flaw of the statistical approach itself. ⁷⁶

Summary and Broader Implications

Taken together, these critiques do not undermine MAIHDA but highlight the conditions under which it should be applied and interpreted. The framework's strength lies in its ability to integrate variance-based description of contextual structuring with the potential for causal interpretation when supported by appropriate design and assumptions. MAIHDA thus bridges the gap between descriptive mapping of inequalities and causal reasoning about how contexts produce them.

The joint interpretation of its components: GCE, SCE, and DA offers a powerful means of understanding how contexts structure health inequalities. When carefully implemented, MAIHDA can inform both descriptive assessments of inequality patterns and causal explanations of the mechanisms that sustain them. In the following section, we discuss how recent developments in multidimensional MAIHDA, and I-MAIHDA in particular, have reinvigorated applications in geographical, institutional, and other contextual domain

How Intersectional MAIHDA has Revitalized Geographical and Institutional Applications

As discussed above, MAIHDA is applicable across diverse contexts. Although it is now most closely linked with intersectionality-informed research, its conceptual origins lie in earlier multilevel analyses of geographical and institutional inequalities.^6,13,18–20 Geographical MAIHDA, in fact, predates its intersectional applications.

Yet despite this early promise, variance-informed approaches such as geographical MAIHDA were long marginalized. In our opinion, a central reason was the frequent observation of small contextual variances (VPCs), which many researchers dismissed as statistical nuisances rather than as substantively meaningful indicators of weak contextual structuring; though not all agreed, see Riva, Gauvin et al. ⁷⁹ The problem was compounded by a paradox: when contextual clustering (GCE) is small, SCEs can be estimated with greater precision and are more likely to be highlighted, whereas strong clustering reduces precision and discourages recognition of context precisely when it is most important We believe, this statistical asymmetry reinforced the dominance of average-focused models and contributed to the neglect of variance-based reasoning. ⁵²

Scientific narratives also played a role. In public health, the claim that “neighbourhoods matter” became dominant. When variance-based measures such as the VPC yielded small values, these were often downplayed or reframed as “not the intended use” rather than examined for their substantive meaning. This reflects a broader tendency in science, where results that challenge prevailing narratives are disqualified or overlooked. For example, while Ana Diez Roux was instrumental in bringing multilevel methods into public health, her influential applications generally emphasized fixed effects and associations with contextual covariates over variance-based metrics such as the VPC.^35,80,81 In this sense, MAIHDA represents a methodological and conceptual renaissance, reclaiming variance-based reasoning as central to the analysis of health inequalities. ⁷

This situation shifted with the emergence of I-MAIHDA, particularly the influential paper by Evans et al ¹⁶ and the accompanying commentary. ¹³ By offering a coherent way to estimate joint effects across intersecting identities, I-MAIHDA drew renewed attention to variance decomposition. Importantly, its empty models often revealed substantial VPCs, frequently between 8% and 24%,^24,82,83 demonstrating that multidimensional social groupings could yield contextually meaningful patterns. ⁴³

Equally significant was a shift in how small VPCs were interpreted. Within MAIHDA, low values are not dismissed but understood as meaningful, indicating overlapping group distributions or contexts where universal rather than targeted interventions may be appropriate. ⁴³ What once discouraged variance-based reasoning now provides substantive insight, including the recognition that administrative boundaries or conventional categorizations may fail to capture relevant exposures.^21,43

Moreover, MAIHDA accommodates flexible modelling, including cross-classified structures such as spatial–demographic combinations. ⁸⁴ This capacity expands its reach beyond geography or intersectionality, positioning it as a general-purpose framework for analysing structured heterogeneity.

In this way, the intersectional applications of MAIHDA played a key role in giving variance-based approaches new empirical legitimacy and broader visibility. Whether mapping intersectional inequalities, evaluating health care systems, or refining spatial epidemiology, MAIHDA now provides a unified, robust framework for modelling heterogeneity across social, geographical, and biomedical domains.

The interpretation of heterogeneity and clustering has direct implications for public health strategies. These insights resonate strongly with Geoffrey Rose's foundational distinction between individual and population approaches to prevention. ⁶⁰ In the next section, we revisit Rose's legacy and show how MAIHDA provides new tools to operationalize his ideas in ways that strengthen both equity and effectiveness.

Rose's Legacy and MAIHDA's Strategic Implications

One of the most compelling reasons to adopt MAIHDA is its alignment with Geoffrey Rose's foundational insights in preventive medicine.^60,85 Rose distinguished between two strategies of public health intervention: the high-risk approach, which targets individuals or groups with elevated risk, and the population strategy, which seeks to shift the overall distribution of risk factors. While the high-risk approach may appear intuitive, Rose showed that it, paradoxically, fails to reduce the population burden of disease, since most cases arise among the far more numerous individuals at “low” or “average” risk.

MAIHDA formalizes this dilemma. It demonstrates how a group with a high average risk may account for only a minority of cases, while lower-risk but larger groups carry much of the burden. This is where Discriminatory Accuracy (DA) becomes critical: it evaluates how well group membership classifies individual outcomes, thereby clarifying when targeted versus universal strategies are appropriate.^7,11,86

The distinction between average risk and classification accuracy is not merely methodological, it reshapes how resources are allocated, how interventions are designed, and how public health messages are framed. MAIHDA brings empirical precision to Rose's qualitative vision by quantifying the mismatch between group-level risk and the distribution of cases across the population. This helps reduce the risk of stigmatization, strengthens ethical justification, and improves the strategic allocation of public health resources. Still, translating these insights into interventions requires more than variance decomposition: it also entails weighing the costs and consequences of false positives and false negatives in specific settings.

Geoffrey Rose's classic distinction between high-risk and population strategies has been further developed by Michael Marmot and colleagues in the Marmot Review (Fair Society, Healthy Lives, 2010). Their principle of proportionate universalism adapts Rose's insights to contemporary equity concerns, emphasizing that interventions should be universal in scope but scaled in intensity according to the level of disadvantage. MAIHDA provides an empirical tool to operationalize this continuum, clarifying when universal measures are most effective, when targeted approaches are warranted, and how both can be combined. In this sense, MAIHDA extends Rose's preventive logic while also offering practical means to realize Marmot's equity-focused framework. ⁸⁷

Conclusion and the Future

MAIHDA marks an important step forward in how we study health inequalities. Instead of focusing mainly on group averages, it highlights how health varies both within and between groups, and what this variation reveals about the role of context. In this sense, MAIHDA is more than just another modelling tool, it is a general framework within contextual epidemiology that makes inequalities visible in a clearer and more structured way.

By combining three key elements, specific contextual effects (SCE), general contextual effects (GCE), and discriminatory accuracy (DA), as well as the Proportional Change of Variance (PCV), MAIHDA enables sharper questions. Group differences are not defined by contrasts in averages but by how much of the total individual variation is structured at the group level. This allows us to ask: Are group differences substantial? Do contexts meaningfully shape individual outcomes? And how well group boundaries identify who has the disease. These shifts turn long-standing debates about group differences into empirical questions about the structuring of inequality and the design of interventions.

Intersectional applications gave MAIHDA much of its recent visibility, but its roots lie in earlier work on geographical and institutional contexts. I-MAIHDA should therefore be seen as a major force in reviving variance-based reasoning, rather than the origin of the approach.

Looking ahead, MAIHDA is well positioned to connect with emerging developments in epidemiology and data science. Its logic fits naturally with advances in causal inference, machine learning, and fairness-aware analytics. Rather than replacing conventional regression, multidimensional MAIHDA extends it: mapping health inequalities across multiple strata, linking with diverse social theories, and testing whether contexts classify outcomes in ways that matter for prevention and policy.

MAIHDA thus both continues and renews the tradition of multilevel thinking. It offers a framework that is rigorous yet flexible, attentive to both heterogeneity and equity. In this way, it provides a promising path toward public health that is not only more precise but also more just.

Recent extensions of I-MAIHDA to longitudinal frameworks ⁶⁷ illustrate how the approach can be used to model individual health trajectories and capture how inequalities unfold dynamically across the life course. Such innovations expand the potential of MAIHDA to integrate with life-course epidemiology, ecosocial perspectives, and structural analyses of inequality.

Our contribution complements existing methodological tutorials on I-MAIHDA by reframing MAIHDA as a broader framework for contextual epidemiology. This perspective links MAIHDA to long-standing debates in social epidemiology about variance, heterogeneity, and contextual causality, while clarifying that I-MAIHDA is one important application rather than the sole focus of the approach. Further reflection on the potential role of the MAIHDA approach in current and future epidemiology, where broader ethical and civic implications are discussed, is presented elsewhere. ¹⁵