Over the last several decades, U.S. life expectancy inequities across educational groups have grown 1–2 years.¹ Concomitantly, employment conditions have deteriorated as employers and states have eroded worker power and security, contributing to union-membership losses, stagnant wages, and debased benefits and hours.² Researchers hypothesize these adverse employment conditions mediate the education-mortality relationship (and mediate the relationship between other social exposures and mortality).^3,4 However, pathways linking employment conditions and health are intertwined with other social determinants,³ complicating analysis.^5–7 For example, occupation often confounds the relationship between employment conditions and health and is caused by social exposures like education. Moreover, social exposures may modify the health effects of employment conditions. This exposure-induced mediator-outcome confounding and exposure-mediator interaction, respectively, can compromise the validity of traditional mediation methods, like the difference or product methods.^8,9 Thus, although limited research has been conducted,^4,10 methodological barriers have hindered research on the role of employment conditions and hazards in mortality inequities, impeding identification of mediating mechanisms and the development of policy and organizing solutions.

In this paper, we outline and provide code for a marginal structural modeling (MSM) approach to mediation analysis that can be used to estimate policy-relevant effects in occupational health research, including in settings with exposure-induced mediator-outcome confounding and exposure-mediator interaction. We also cover the approach’s challenges, including the strong assumptions required for causal inference. Due to their apparent complexity, MSM approaches are rarely applied to occupational health research, particularly to mediation analyses.⁵ Thus, by outlining the approach in a didactic manner accessible to applied occupational health researchers, our paper makes an important methodological contribution. Our worked example assesses the extent to which disparities in employment quality (EQ) explained educational inequities in mortality.

This section describes a MSM mediation approach proposed elsewhere.^8,9 The approach can be used to estimate: 1) the total effect (TE) the exposure had on the outcome, with 2) the controlled direct effect (CDE) the exposure would have had on the outcome if the mediator had been constant across exposure groups.

Under the potential outcomes framework, the TE of a binary exposure E on a continuous outcome Y can be defined as:^8,9,11 TE=E(Ye=1)−E(Ye=0) where E (Y_e=1) is the expected value of Y in a sample if all respondents – possibly contrary to fact – had been exposed (e=1), while E (Y_e=0) is the expected value of Y in a sample if all respondents – again, possibly contrary to fact – had been unexposed (e=0). Contrasting these quantities captures every pathway through which the exposure affected the outcome, whether through the mediator or otherwise.^8,9

Meanwhile, the CDE of a binary exposure E on a binary outcome Y can be defined as:^8,9 CDE=E(Ye=1,m=m*)−E(Ye=0,m=m*) where E (Y_e=1,m=m*) is the expected value of Y in a sample if all respondents – possibly contrary to fact – had been exposed (e=1) and their mediator M had been at level m*, while E (Y_e=0,m=m*) is the expected value of Y in a sample if all respondents – again, possibly contrary to fact – had been unexposed (e=0) and their mediator M had been at level m*. Contrasting these quantities captures the effect the exposure would have had on the outcome if all respondents, regardless of their exposure, had the same mediator value, such as an occupational hazard compliant with a regulatory standard.^8,9

As defined above, the TE and CDE are counterfactual contrasts.^8,11 Because outcomes for respondents are only observable under one exposure-mediator combination at a given time, counterfactual contrasts cannot be measured directly.^8,11 Rather, they must be estimated using study design and modeling approaches.^8,11 In observational settings, such contrasts can be consistently estimated if one sufficiently controls for confounding of the exposure-outcome and mediator-outcome relationships such that the distribution of confounders is equal across exposure-mediator subgroups. In such settings, differences in observed outcomes across subgroups can be attributed to effects of the exposure and mediator rather than to effects of confounders.^8,11 The MSM approach described below is one method that can be used to consistently estimate TEs and CDEs in observational settings, given the validity of the requisite assumptions.

MSM mediation analyses proceed in three primary steps: 1) estimating exposure inverse probability weights (IPW), 2) estimating mediator IPW, and 3) estimating TEs and CDEs using weighted regression models.^8,9 eAppendix 1 contains R code and Table I contains a high-level overview of the approach.

The first step involves estimating exposure IPW, which can be used to address confounding of the exposure-outcome relationship by creating a weighted pseudo-population in which measured confounders are unassociated with exposure.^8,9 For a binary exposure E, the exposure IPW wiE for each respondent i can be defined as: wiE=P(E=ei)P(E=ei|X=xi) where the denominator is the probability the respondent experienced their observed exposure value (E = e_i), given their values of any measured exposure-outcome confounders (X = x_i) suggested by theory and one’s directed acyclic graph (DAG).^8,9 Brookhart et al. provide further guidance on confounder/covariate selection.¹² The numerator can be the exposure’s marginal (unconditional) probability in the sample [P (E = e_i)] (which “stabilizes” the weight) or one (less common, since stabilization increases efficiency).^8,9 For binary exposures, numerator and denominator probabilities can be estimated using logistic models, while for ordinal or categorical exposures, probabilities can be estimated using ordinal or multinomial logistic models.^8,13 For continuous exposures, probabilities can be estimated using quantile-binning approaches or by replacing the probabilities with probability density functions estimated by linear or gamma models.^8,13 The final IPW should have a mean near one and moderate range.¹⁴ Using stabilized weights or truncating extreme weights can improve precision of the estimated TE and CDE, although truncation can increase residual confounding.^8,9,14 Confounder balance across exposure values after weighting can be examined using balance statistics; imbalance should be minimal post-weighting to mitigate residual confounding.¹⁵ Imbalance can be addressed by modifying one’s weighting model (e.g., by altering continuous-variable specification or including interactions).^14,15

The second step involves estimating mediator IPW to address confounding of the mediator-outcome relationship.^8,9 For a binary mediator M, the mediator IPW wiM for each respondent i can be defined as: wiM=P(M=mi)P(M=mi|E=ei,  X=xi,  Z=zi) where the denominator is the probability the respondent experienced their observed mediator value (M = m_i), given their exposure value (E = e_i), their values of exposure-outcome confounders (X = x_i), and their values of mediator-outcome confounders (Z = z_i). Again, the numerator can be the mediator’s marginal probability in the sample or one,^8,9 extreme weights can be truncated,¹⁴ weights should have a mean near one,¹⁴ and confounder balance can be assessed using balance statistics.¹⁵ Weights for ordinal, categorical, and continuous mediators can be estimated as described earlier.^8,13

The third step involves estimating the TE and the CDE. TEs can be estimated by fitting a regression model of the outcome as a function of the exposure, weighted by the vector of exposure IPW (w^E).¹⁶ For a continuous outcome Y and binary exposure E, this model can be written as: E(Y|E=e)=β0+β1e where β₁ is the TE of the exposure on the outcome.¹⁶ Meanwhile, CDEs can be estimated by fitting a regression model of the outcome as a function of the exposure, mediator, and an exposure-mediator interaction term, weighted by the product of the exposure and mediator weights (w^E *w^M).^8,9 For a continuous outcome Y, binary exposure E, and binary mediator M, this model can be written as: E(Y|E=e, M=0)=β0+β1e+β2m+β3em where β₁ is the CDE of the exposure on the outcome, holding M at 0 so that β₂ and β₃ drop from the model.^8,9 If there is exposure-mediator interaction, such as if EQ more strongly affected mortality among less-educated people than among more-educated people, the estimated CDE will vary with M’s reference level (0) – such as “high EQ” or “low EQ”.¹⁷. If exposure-mediator interaction is anticipated, one can calculate multiple CDEs with varying reference levels. Alternatively, one can choose the reference level based on real-world relevance. For example, if seeking to estimate whether reducing exposure to a chemical hazard could mitigate occupational inequities in lung-cancer mortality among workers in the manufacturing sector, one could choose the reference level based on a hypothetical or proposed regulatory standard for the hazard (e.g., elimination of the hazard or exposure below a given threshold). Likewise, if seeking to estimate whether increasing wages could reduce gender inequities in depression among workers in the service sector, one could choose the reference level based on proposed minimum-wage levels, such as the $15 minimum-wage level proposed by social movements.

Finally, the proportion of the exposure’s effect on the outcome that would have been eliminated if the mediator had been held at a certain value (i.e., “proportion eliminated”) for absolute measures of effect (e.g., risk differences) can be defined as:^9,18 Proportioneliminatedforabsolutemeasuresofeffect=(TE−CDE)TE Meanwhile, for relative measures of effect (e.g., risk ratios), the proportion eliminated can be defined as:¹⁸ Proportioneliminatedforrelativemeasuresofeffect=(TE−CDE)(TE−1)

Robust or bootstrap standard errors should be used to calculate confidence intervals for TEs and CDEs.⁹ The proposed approach can accommodate common outcome types, including continuous, binary, and survival (provided the outcome is rare) via weighted linear, logistic, and Cox proportional hazards regression, respectively,^8,9,16,19,20 and can extend to time-varying settings.⁸ Additionally, if desired, missing data can be addressed via multiple imputation by chained equations (MICE). The IPW, TE, and CDE should be estimated on each of the multiply imputed datasets and the TE and CDE estimates from each of the datasets pooled using Rubin’s Rules.²¹

As in non-mediation settings, consistently estimating TEs using the approach requires no uncontrolled exposure-outcome confounding (among other assumptions, including no selection bias and no information bias).^8,9 Consistently estimating CDEs additionally requires no uncontrolled mediator-outcome confounding.^8,9 However, unlike traditional methods, mediator-outcome confounders can be exposure-induced (Figure I). This is because the approach does not condition on confounders via covariate adjustment or stratification and thus does not inherently induce overadjustment and collider bias.^8,9 Nonetheless, the no-unmeasured-confounding assumptions are strong and their validity cannot be directly tested; rather, researchers must assess their validity (or near-validity) using theory and background knowledge.^8,9,17 Additionally, if desired, researchers can conduct sensitivity analyses that assess how strong unmeasured confounding would need to be to meaningfully alter conclusions drawn from one’s TE and CDE estimates.^20,22,23 Consistently estimating TEs and CDEs additionally requires no model misspecification and positivity.^8,9 No model misspecification requires that the IPW models are adequately specified to address confounding of the exposure-outcome and mediator-outcome relationships.^9,14,15 Weights with a mean far from one or large range can indicate model misspecification, as can confounder imbalance after weighting.^9,14,15 Meanwhile, positivity assumes each respondent has a nonzero probability of receiving each exposure-mediator combination, given their covariates.^8,9,14,15 Positivity violations – or near violations, which occur if there are rare exposure-mediator-covariate combinations and which can produce weights with a large range – can cause imprecision and bias.^9,14 Additionally, as in all mediation analyses, consistently estimating CDEs requires the exposure preceded the mediator, which preceded the outcome.²⁴

Our sample included 6,507 respondents, followed for a median, maximum, and total of 12, 18, and 78,282 years, respectively. There were 380 deaths (≤HS: 235; >HS: 145); the Kaplan-Meier survival probability at 18 years was 90%. See Figure III for a flow diagram.

Forty-six percent of respondents had ≤HS degree at baseline (Table II). Less-educated respondents had similar distributions of age, gender, marital status, and division to more-educated respondents (Table II). However, they were less often White and more often low income and employed in industries of “manufacturing” and occupations of “operators, fabricators, and laborers”, “precision production, craft, and repair”, and “services” (Table II). Less-educated respondents had lower median EQ than more-educated respondents, driven by less-educated respondents’ greater likelihood of being uninsured, waged, pension-less, short-tenured, and low-income (Table II). Lower-EQ respondents were disproportionately Black or “other”, low-income, less-educated, disabled, and employed in industries of “services” and “wholesale and retail trade” and occupations of “operators, fabricators, and laborers” and “services” (eAppendix 3).

eAppendix 4 displays IPW distributions, which had means near one and moderate ranges. After weighting, differences in confounder distributions across exposure and mediator values were minimal (eAppendix 5).

Regarding the TE, the mortality hazard was 67% greater (HR: 1.67, 95% CI: 1.34, 2.09) among those with ≤HS degree than among those with >HS degree (Figure IV and eAppendix 6).

Regarding the CDE, when holding EQ at the 80^th percentile (100^th=best) across educational groups, the mortality hazard was 15% greater (HR: 1.15; 95% CI: 0.81, 1.64) among those with ≤HS degree than among those with >HS degree (Figure IV and eAppendix 6). End-of-follow-up survival also increased across subgroups.

Holding EQ at lower percentiles increased the CDE, indicating an exposure-mediator interaction in which EQ decreases were more strongly related to increased mortality among the less-educated than among the more-educated, although estimates were imprecise. Indeed, when holding EQ at the 20^th percentile (1^st=worst), the CDE nearly equaled the TE (HR: 1.66, 95% CI: 1.19, 2.31) (Figure IV and eAppendix 6).

Sensitivity analyses yielded similar estimates (eAppendices 7–9).