Multilevel modelling for measuring interaction of effects between multiple categorical variables: An illustrative application using risk factors for preeclampsia

A tutorial for conducting intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA)

Intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (I-MAIHDA) is an innovative approach for investigating inequalities, including intersectional inequalities in health, disease, psychosocial, socioeconomic, and other outcomes. I-MAIHDA and related MAIHDA approaches have conceptual and methodological advantages over conventional single-level regression analysis. By enabling the study of inequalities produced by numerous interlocking systems of marginalization and oppression, and by addressing many of the limitations of studying interactions in conventional analyses, intersectional MAIHDA provides a valuable analytical tool in social epidemiology, health psychology, precision medicine and public health, environmental justice, and beyond. The approach allows for estimation of average differences between intersectional strata (stratum inequalities), in-depth exploration of interaction effects, as well as decomposition of the total individual variation (heterogeneity) in individual outcomes within and between strata. Specific advice for conducting and interpreting MAIHDA models has been scattered across a burgeoning literature. We consolidate this knowledge into an accessible conceptual and applied tutorial for studying both continuous and binary individual outcomes. We emphasize I-MAIHDA in our illustration, however this tutorial is also informative for understanding related approaches, such as multicategorical MAIHDA, which has been proposed for use in clinical research and beyond. The tutorial will support readers who wish to perform their own analyses and those interested in expanding their understanding of the approach. To demonstrate the methodology, we provide step-by-step analytical advice and present an illustrative health application using simulated data. We provide the data and syntax to replicate all our analyses.

What does the MAIHDA method explain?

Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) is a new approach to quantitative intersectional modelling. Along with an outcome of interest, MAIHDA entails the use of two sets of independent variables. These include group demographics such as race, gender, and poverty status as well as strata which are constructs such as Black female poor, Black female wealthy, and White female poor. These constructs represent the combination of the demographic variables. To operationalize the approach, an initial random intercepts model with strata as a level 2 context is specified. Then, another model is specified that includes the strata as well as the demographic variables as level 1 fixed effects. As such, it is argued that MAIHDA uniquely identifies the additive and intersectional effects for any given outcome. In this paper we show that MAIHDA falls short of this promise: the strata are an individual-level composite variable not a level 2 context. Rather than being analogous to neighborhoods as contexts, strata are analogous to socio-economic status which is a combination of individual-level demographic variables, albeit often presented as a group-level characteristic. The result is that the demographic variables are inserted in both level 2 and 1. This duplication across the levels in MAIHDA means that there is a built-in collinearity across the levels and that the models are mis-specified and, therefore, redundant. We conclude that single-level models with the demographic variables and interactions or with the strata as fixed effects are still the more accurate models for quantitative intersectional analyses.

Mapping socio-geographical disparities in the occurrence of teenage maternity in Colombia using multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA)

BACKGROUND

The prevalence of teenage pregnancy in Colombia is higher than the worldwide average. The identification of socio-geographical disparities might help to prioritize public health interventions.

AIM

To describe variation in the probability of teenage maternity across geopolitical departments and socio-geographical intersectional strata in Colombia.

METHODS

A cross-sectional study based on live birth certificates in Colombia. Teenage maternity was defined as a woman giving birth aged 19 or younger. Multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) was applied using multilevel Poisson and logistic regression. Two different approaches were used: (1) intersectional: using strata defined by the combination of health insurance, region, area of residency, and ethnicity as the second level (2) geographical: using geopolitical departments as the second level. Null, partial, and full models were obtained. General contextual effect (GCE) based on the variance partition coefficient (VPC) was considered as the measure of disparity. Proportional change in variance (PCV) was used to identify the contribution of each variable to the between-strata variation and to identify whether this variation, if any, was due to additive or interaction effects. Residuals were used to identify strata with potential higher-order interactions.

RESULTS

The prevalence of teenage mothers in Colombia was 18.30% (95% CI 18.20-18.40). The highest prevalence was observed in Vichada, 25.65% (95% CI: 23.71-27.78), and in the stratum containing mothers with Subsidized/Unaffiliated healthcare insurance, Mestizo, Rural area in the Caribbean region, 29.08% (95% CI 28.55-29.61). The VPC from the null model was 1.70% and 9.16% using the geographical and socio-geographical intersectional approaches, respectively. The higher PCV for the intersectional model was attributed to health insurance. Positive and negative interactions of effects were observed.

CONCLUSION

Disparities were observed between intersectional socio-geographical strata but not between geo-political departments. Our results indicate that if resources for prevention are limited, using an intersectional socio-geographical approach would be more effective than focusing on geopolitical departments especially when focusing resources on those groups which show the highest prevalence. MAIHDA could potentially be applied to many other health outcomes where resource decisions must be made.

Intersectional analysis of social disparities in type 2 diabetes risk among adults in Germany: results from a nationwide population-based survey

BACKGROUND

Differences in type 2 diabetes risk have been reported for several sociodemographic determinants including sex/gender or socioeconomic status. From an intersectional perspective, it is important to not only consider the role of social dimensions individually, but also their intersections. This allows for a deeper understanding of diabetes risk and preventive needs among diverse population groups.

METHODS

As an intersectionality-informed approach, multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) was used in a population-based sample of adults without known diabetes in Germany from the cross-sectional survey "Disease knowledge and information needs- Diabetes mellitus (2017)". Diabetes risk was assessed by the German Diabetes Risk Score (GDRS, range 0-122 points), estimating the individual risk of developing type 2 diabetes within the next 5 years based on established self-reported risk factors. Nesting individuals in 12 intersectional strata defined by combining sex/gender, educational level, and history of migration, we calculated measures to quantify the extent to which individual differences in diabetes risk were explained at strata level, and how much this was due to additive or multiplicative intersectional effects of social determinants.

RESULTS

Drawing on data of 2,253 participants, we found good discriminatory accuracy of intersectional strata (variance partition coefficient = 14.00% in the simple intersectional model). Model-predicted GDRS means varied between 29.97 (corresponding to a "low risk" of < 2%) in women with high educational level and a history of migration, and 52.73 ("still low risk" of 2-5%) in men with low educational level without a history of migration. Variance in GDRS between strata was mainly explained by additive effects of social determinants (proportional change in variance to intersectional interaction model = 77.95%) with being male and having low educational level being associated with higher GDRS. There was no evidence of multiplicative effects in individual strata.

CONCLUSIONS

Type 2 diabetes risk differed between intersectional strata and can to some extent be explained at strata level. The role of intersectional effects was minor and needs to be further investigated. Findings suggest a need for specific preventive measures targeted at large groups with increased diabetes risk, such as men and persons with low educational level.

Overcoming combination fatigue: Addressing high-dimensional effect measure modification and interaction in clinical, biomedical, and epidemiologic research using multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA)

Growing interest in precision medicine, gene-environment interactions, health equity, expanding diversity in research, and the generalizability results, requires researchers to evaluate how the effects of treatments or exposures differ across numerous subgroups. Evaluating combination complexity, in the form of effect measure modification and interaction, is therefore a common study aim in the biomedical, clinical, and epidemiologic sciences. There is also substantial interest in expanding the combinations of factors analyzed to include complex treatment protocols (e.g., multiple study arms or factorial randomization), comorbid medical conditions or risk factors, and sociodemographic and other subgroup identifiers. However, expanding the number of subgroup category combinations creates combination fatigue problems, including concerns over small sample size, reduced power, multiple testing, spurious results, and design and analytic complexity. Creative new approaches for managing combination fatigue and evaluating high-dimensional effect measure modification and interaction are needed. Intersectional MAIHDA (multilevel analysis of individual heterogeneity and discriminatory accuracy) has already attracted substantial interest in social epidemiology, and has been hailed as the new gold standard for investigating health inequities across complex intersections of social identity. Leveraging the inherent advantages of multilevel models, a more general multicategorical MAIHDA can be used to study statistical interactions and predict effects across high-dimensional combinations of conditions, with important advantages over alternative approaches. Though it has primarily been used thus far as an analytic approach, MAIHDA should also be used as a framework for study design. In this article, I introduce MAIHDA to the broader health sciences research community, discuss its advantages over conventional approaches, and provide an overview of potential applications in clinical, biomedical, and epidemiologic research.