Natural direct and indirect effects on the exposed: effect decomposition under weaker assumptions

Nonparametric causal mediation analysis for stochastic interventional (in)direct effects

Causal mediation analysis has historically been limited in two important ways: (i) a focus has traditionally been placed on binary exposures and static interventions and (ii) direct and indirect effect decompositions have been pursued that are only identifiable in the absence of intermediate confounders affected by exposure. We present a theoretical study of an (in)direct effect decomposition of the population intervention effect, defined by stochastic interventions jointly applied to the exposure and mediators. In contrast to existing proposals, our causal effects can be evaluated regardless of whether an exposure is categorical or continuous and remain well-defined even in the presence of intermediate confounders affected by exposure. Our (in)direct effects are identifiable without a restrictive assumption on cross-world counterfactual independencies, allowing for substantive conclusions drawn from them to be validated in randomized controlled trials. Beyond the novel effects introduced, we provide a careful study of nonparametric efficiency theory relevant for the construction of flexible, multiply robust estimators of our (in)direct effects, while avoiding undue restrictions induced by assuming parametric models of nuisance parameter functionals. To complement our nonparametric estimation strategy, we introduce inferential techniques for constructing confidence intervals and hypothesis tests, and discuss open-source software, the $\texttt{medshift}$$\texttt{R}$ package, implementing the proposed methodology. Application of our (in)direct effects and their nonparametric estimators is illustrated using data from a comparative effectiveness trial examining the direct and indirect effects of pharmacological therapeutics on relapse to opioid use disorder.

An Introduction to Causal Mediation Analysis With a Comparison of 2 R Packages

Traditional mediation analysis, which relies on linear regression models, has faced criticism due to its limited suitability for cases involving different types of variables and complex covariates, such as interactions. This can result in unclear definitions of direct and indirect effects. As an alternative, causal mediation analysis using the counterfactual framework has been introduced to provide clearer definitions of direct and indirect effects while allowing for more flexible modeling methods. However, the conceptual understanding of this approach based on the counterfactual framework remains challenging for applied researchers. To address this issue, the present article was written to highlight and illustrate the definitions of causal estimands, including controlled direct effect, natural direct effect, and natural indirect effect, based on the key concept of nested counterfactuals. Furthermore, we recommend using 2 R packages, 'medflex' and 'mediation', to perform causal mediation analysis and provide public health examples. The article also offers caveats and guidelines for accurate interpretation of the results.

Testing Behavior Change Techniques to Increase Physical Activity in Middle-Aged and Older Adults: Protocol for a Randomized Personalized Trial Series

BACKGROUND

Being physically active is critical to successful aging, but most middle-aged and older adults do not move enough. Research has shown that even small increases in activity can have a significant impact on risk reduction and improve quality of life. Some behavior change techniques (BCTs) can increase activity, but prior studies on their effectiveness have primarily tested them in between-subjects trials and in aggregate. These design approaches, while robust, fail to identify those BCTs most influential for a given individual. In contrast, a personalized, or N-of-1, trial design can assess a person's response to each specific intervention.

OBJECTIVE

This study is designed to test the feasibility, acceptability, and preliminary effectiveness of a remotely delivered personalized behavioral intervention to increase low-intensity physical activity (ie, walking) in adults aged 45 to 75 years.

METHODS

The intervention will be administered over 10 weeks, starting with a 2-week baseline period followed by 4 BCTs (goal-setting, self-monitoring, feedback, and action planning) delivered one at a time, each for 2 weeks. In total, 60 participants will be randomized post baseline to 1 of 24 intervention sequences. Physical activity will be continuously measured by a wearable activity tracker, and intervention components and outcome measures will be delivered and collected by email, SMS text messages, and surveys. The effect of the overall intervention on step counts relative to baseline will be examined using generalized linear mixed models with an autoregressive model that accounts for possible autocorrelation and linear trends for daily steps across time. Participant satisfaction with the study components and attitudes and opinions toward personalized trials will be measured at the intervention's conclusion.

RESULTS

Pooled change in daily step count will be reported between baseline and individual BCTs and baseline versus overall intervention. Self-efficacy scores will be compared between baseline and individual BCTs and between baseline and the overall intervention. Mean and SD will be reported for survey measures (participant satisfaction with study components and attitudes and opinions toward personalized trials).

CONCLUSIONS

Assessing the feasibility and acceptability of delivering a personalized, remote physical activity intervention for middle-aged and older adults will inform what steps will be needed to scale up to a fully powered and within-subjects experimental design remotely. Examining the effect of each BCT in isolation will allow for their unique impact to be assessed and support design of future behavioral interventions. In using a personalized trial design, the heterogeneity of individual responses for each BCT can be quantified and inform later National Institutes of Health stages of intervention development trials.

TRIAL REGISTRATION

clinicaltrials.gov NCT04967313; https://clinicaltrials.gov/ct2/show/NCT04967313.

INTERNATIONAL REGISTERED REPORT IDENTIFIER (IRRID)

RR1-10.2196/43418.

The relationship between rurality, travel time to care and death by suicide

BACKGROUND

We previously found an association between rurality and death by suicide, where those living in rural areas were more likely to die by suicide. One potential reason why this relationship exists might be travel time to care. This paper examines the relationship between travel time to both psychiatric and general hospitals and suicide, and then determine whether travel time to care mediates the relationship between rurality and suicide.

METHODS

This is a population-based nested case-control study. Data from 2007 to 2017 were obtained from administrative databases held at ICES, which capture all hospital and emergency department visits across Ontario. Suicides were captured using vital statistics. Travel time to care was calculated from the resident's home to the nearest hospital based on the postal codes of both locations. Rurality was measured using Metropolitan Influence Zones.

RESULTS

For every hour in travel time a male resides from a general hospital, their risk of death by suicide doubles (AOR = 2.08, 95% CI = 1.61-2.69). Longer travel times to psychiatric hospitals also increases risk of suicide among males (AOR = 1.03, 95%CI = 1.02-1.05). Travel time to general hospitals is a significant mediator of the relationship between rurality and suicide among males, accounting for 6.52% of the relationship between rurality and increased risk of suicide. However, we also found that there is effect modification, where the relationship between travel time and suicide is only significant among males living in urban areas.

CONCLUSIONS

Overall, these findings suggest that males who must travel longer to hospitals are at a greater risk of suicide compared to those who travel a shorter time. Furthermore, travel time to care is a mediator of the association between rurality and suicide among males.

The role of low educational attainment on the pathway from adolescent internalizing and externalizing problems to early adult labour market disconnection in the Dutch TRAILS cohort

Mental health challenges in adolescence may affect labour market transitions in young adulthood. Policies addressing early labour market disconnection largely focus on early school-leaving and educational attainment; however, the role of low educational attainment on the path from adolescent mental health to labour market disconnection is unclear. Using the TRacking Adolescents' Individual Lives Survey from the Netherlands (n = 1,197), we examined the extent to which achieving a basic educational qualification (by age 22) in the contemporary Dutch education system, mediates the effect of adolescent mental health (age 11-19) on early adult labour market disconnection, defined as 'not in education, employment, or training' (NEET, age 26). We estimated the total effect, the natural direct and indirect effects, and the controlled direct effects of internalizing and externalizing symptoms on NEET by gender. Among young men, clinical levels of adolescent externalizing symptoms were associated with a 0.093 higher probability of NEET compared with no symptoms (95% confidence interval, CI: 0.001, 0.440). The indirect effect through educational attainment accounted for 15.1% of the total effect. No evidence of mediation was observed for the relationship between externalizing symptoms and NEET in young women. No evidence of mediation was observed for the relationship between adolescent internalizing symptoms and NEET in either gender. The findings imply that adolescent externalizing symptoms disrupts the achievement of a basic educational qualification, leading to a higher probability of NEET in young men. This mechanism may play a smaller role in the risk of NEET associated with internalizing symptoms and in young women.

Identification and robust estimation of swapped direct and indirect effects: Mediation analysis with unmeasured mediator-outcome confounding and intermediate confounding

Counterfactual-model-based mediation analysis can yield substantial insight into the causal mechanism through the assessment of natural direct effects (NDEs) and natural indirect effects (NIEs). However, the assumptions regarding unmeasured mediator-outcome confounding and intermediate mediator-outcome confounding that are required for the determination of NDEs and NIEs present practical challenges. To address this problem, we introduce an instrumental blocker, a novel quasi-instrumental variable, to relax both of these assumptions, and we define a swapped direct effect (SDE) and a swapped indirect effect (SIE) to assess the mediation. We show that the SDE and SIE are identical to the NDE and NIE, respectively, based on a causal interpretation. Moreover, the empirical expressions of the SDE and SIE are derived with and without an intermediate mediator-outcome confounder. Then, a multiply robust estimation method is derived to mitigate the model misspecification problem. We prove that the proposed estimator is consistent, asymptotically normal, and achieves the semiparametric efficiency bound. As an illustration, we apply the proposed method to genomic datasets of lung cancer to investigate the potential role of the epidermal growth factor receptor in the treatment of lung cancer.

IBD Subtype-Regulators IFNG and GBP5 Identified by Causal Inference Drive More Intense Innate Immunity and Inflammatory Responses in CD Than Those in UC

Background: The pathological differences between Crohn’s disease (CD) and ulcerative colitis (UC) are substantial and unexplained yet. Here, we aimed to identify potential regulators that drive different pathogenesis of CD and UC by causal inference analysis of transcriptome data.

Methods: Kruskal–Wallis and Dunnett’s tests were performed to identify differentially expressed genes (DEGs) among CD patients, UC patients, and controls. Subsequently, differentially expressed pathways (DEPs) between CD and UC were identified and used to construct the interaction network of DEPs. Causal inference was performed to identify IBD subtype-regulators. The expression of the subtype-regulators and their downstream genes was validated by qRT-PCR with an independent cohort.

Results: Compared with the control group, we identified 1,352 and 2,081 DEGs in CD and UC groups, respectively. Multiple DEPs between CD and UC were closely related to inflammation-related pathways, such as NOD-like receptor signaling, IL-17 signaling, and chemokine signaling pathways. Based on the priori interaction network of DEPs, causal inference analysis identified IFNG and GBP5 as IBD subtype-regulators. The results with the discovery cohort showed that the expression level of IFNG, GBP5, and NLRP3 was significantly higher in the CD group than that in the UC group. The regulation relationships among IFNG, GBP5, and NLRP3 were confirmed with transcriptome data from an independent cohort and validated by qRT-PCR.

Conclusion: Our study suggests that IFNG and GBP5 were IBD subtype-regulators that trigger more intense innate immunity and inflammatory responses in CD than those in UC. Our findings reveal pathomechanical differences between CD and UC that may contribute to personalized treatment for CD and UC.

The association between pre-pregnancy body mass index and perinatal death and the role of gestational age at delivery

Introduction

The pathophysiology behind the association between obesity and perinatal death is not fully understood but may be in part due to higher rates of pregnancy complications at earlier gestation amongst obese women. We aimed to quantify the proportion of perinatal deaths amongst obese and overweight women mediated by gestational age at stillbirth or live birth.

Methods

The study included all singleton births at ≥20 weeks’ gestation in British Columbia, 2004–2017, and excluded pregnancy terminations. The proportion of the association between BMI and perinatal death mediated by gestational age at delivery (in weeks) was estimated using natural effect models, with adjustment for potential confounders. Sensitivity analyses for unmeasured confounding and women missing BMI were conducted.

Results

Of 392,820 included women, 20.6% were overweight and 12.8% obese. Women with higher BMI had a lower gestational age at delivery. Perinatal mortality was 0.5% (1834 pregnancies); and was elevated in overweight (adjusted odds ratio [AOR] = 1.22, 95% confidence interval [CI] 1.08–1.37) and obese women (AOR = 1.55, 95% CI 1.36–1.77). Mediation analysis showed that 63.1% of the association between obesity and perinatal death was mediated by gestational age at delivery (natural indirect effect AOR = 1.32, 95% CI 1.23–1.42, natural direct effect AOR = 1.18, 95% CI 1.05–1.32). Similar, but smaller effects were seen when comparing overweight women vs. women with a normal BMI. Estimated effects were not affected by adjustment for additional risk factors for perinatal death or sensitivity analyses for missing data.

Conclusion

Obese pregnancies have a higher risk of perinatal death in part mediated by a lower gestational age at delivery.

Application of 4-way decomposition to the analysis of placental-fetal biomarkers as intermediary variables between maternal body mass index and birthweight

Human chorionic gonadotropin (hCG) is a placental hormone measured in pregnancy to predict individual level risk of fetal aneuploidy and other complications; yet may be useful in understanding placental origins of child development more generally. hCG was associated with maternal body mass index (BMI) and with birthweight. The primary aim here was to evaluate hCG as a mediator of maternal BMI effects on birthweight by causal mediation analysis. Subjects were 356 women from 3 U.S. sites (2010-2013). The 4-way decomposition method using med4way (STATA) was applied to screen for 5 types of effects of first trimester maternal BMI on birthweight: the total effect, the direct effect, mediation by hCG, additive interaction of BMI and hCG, and mediation in the presence of an additive interaction. Effect modification by fetal sex was evaluated, and a sensitivity analysis was performed to evaluate the assumption of unmeasured confounding. Additional placental-fetal biomarkers [pregnancy associated plasma protein A (PAPPA), second trimester hCG, inhibin-A, estriol, alpha fetoprotein] were analyzed for comparison. For first trimester hCG, there was a 0.20 standard deviation increase in birthweight at the 75th vs. 25th percentile of maternal BMI (95% CI 0.04, 0.36). Once stratified, the direct effect association was null in women carrying females. In women carrying males, hCG did not mediate the relationship. In women carrying females, there was a mediated effect of maternal BMI on birthweight by hCG in the reverse direction (-0.06, 95% CI: -0.12, 0.01), and a mediated interaction in the positive direction (0.06, 95% CI 0.00, 0.13). In women carrying males, the maternal BMI effect on birthweight was reverse mediated by PAPPA (-0.09, 95% CI: -0.17, 0.00). Sex-specific mediation was mostly present in the first trimester. Second trimester AFP was a positive mediator of maternal BMI effects in male infants only (0.06, 95% CI: -0.01, 0.13). Effect estimates were robust to potential bias due to unmeasured confounders. These findings motivate research to consider first trimester placental biomarkers and sex-specific mechanisms when quantifying the effects of maternal adiposity on fetal growth.

Clarifying causal mediation analysis: Effect identification via three assumptions and five potential outcomes

Causal mediation analysis is complicated with multiple effect definitions that require different sets of assumptions for identification. This article provides a systematic explanation of such assumptions. We define five potential outcome types whose means are involved in various effect definitions. We tackle their mean/distribution's identification, starting with the one that requires the weakest assumptions and gradually building up to the one that requires the strongest assumptions. This presentation shows clearly why an assumption is required for one estimand and not another, and provides a succinct table from which an applied researcher could pick out the assumptions required for identifying the causal effects they target. Using a running example, the article illustrates the assembling and consideration of identifying assumptions for a range of causal contrasts. For several that are commonly encountered in the literature, this exercise clarifies that identification requires weaker assumptions than those often stated in the literature. This attention to the details also draws attention to the differences in the positivity assumption for different estimands, with practical implications. Clarity on the identifying assumptions of these various estimands will help researchers conduct appropriate mediation analyses and interpret the results with appropriate caution given the plausibility of the assumptions.

Postoperative delirium mediates 180-day mortality in orthopaedic trauma patients

BACKGROUND

Frailty has been associated with increased incidence of postoperative delirium and mortality. We hypothesised that postoperative delirium mediates a clinically significant (≥1%) percentage of the effect of frailty on mortality in older orthopaedic trauma patients.

METHODS

This was a single-centre, retrospective observational study including 558 adults 65 yr and older, who presented with an extremity fracture requiring hospitalisation without initial ICU admission. We used causal statistical inference methods to estimate the relationships between frailty, postoperative delirium, and mortality.

RESULTS

In the cohort, 180-day mortality rate was 6.5% (36/558). Frail and prefrail patients comprised 23% and 39%, respectively, of the study cohort. Frailty was associated with increased 180 day mortality from 1.4% to 12.2% (11% difference; 95% confidence interval [CI], 8.4-13.6), which translated statistically into an 88.7% (79.9-94.3%) direct effect and an 11.3% (5.7-20.1%) postoperative delirium mediated effect. Prefrailty was also associated with increased 180 day mortality from 1.4% to 4.4% (2.9% difference; 2.4-3.4), which was translated into a 92.5% (83.8-99.9%) direct effect and a 7.5% (0.1-16.2%) postoperative delirium mediated effect.

CONCLUSIONS

Frailty is associated with increased postoperative mortality, and delirium might mediate a clinically significant, but small percentage of this effect. Studies should assess whether, in patients with frailty, attempts to mitigate delirium might decrease postoperative mortality.

Insights into the Cross-world Independence Assumption of Causal Mediation Analysis

Causal mediation analysis is a useful tool for epidemiologic research, but it has been criticized for relying on a "cross-world" independence assumption that counterfactual outcome and mediator values are independent even in causal worlds where the exposure assignments for the outcome and mediator differ. This assumption is empirically difficult to verify and problematic to justify based on background knowledge. In the present article, we aim to assist the applied researcher in understanding this assumption. Synthesizing what is known about the cross-world independence assumption, we discuss the relationship between assumptions for causal mediation analyses, causal models, and nonparametric identification of natural direct and indirect effects. In particular, we give a practical example of an applied setting where the cross-world independence assumption is violated even without any post-treatment confounding. Further, we review possible alternatives to the cross-world independence assumption, including the use of bounds that avoid the assumption altogether. Finally, we carry out a numeric study in which the cross-world independence assumption is violated to assess the ensuing bias in estimating natural direct and indirect effects. We conclude with recommendations for carrying out causal mediation analyses.

The impact of adjusting for pure predictors of exposure, mediator, and outcome on the variance of natural direct and indirect effect estimators

It is now well established that adjusting for pure predictors of the outcome, in addition to confounders, allows unbiased estimation of the total exposure effect on an outcome with generally reduced standard errors (SEs). However, no analogous results have been derived for mediation analysis. Considering the simplest linear regression setting and the ordinary least square estimator, we obtained theoretical results showing that adjusting for pure predictors of the outcome, in addition to confounders, allows unbiased estimation of the natural indirect effect (NIE) and the natural direct effect (NDE) on the difference scale with reduced SEs. Adjusting for pure predictors of the mediator increases the SE of the NDE's estimator, but may increase or decrease the variance of the NIE's estimator. Adjusting for pure predictors of the exposure increases the variance of estimators of the NIE and NDE. Simulation studies were used to confirm and extend these results to the case where the mediator or the outcome is binary. Additional simulations were conducted to explore scenarios featuring an exposure-mediator interaction as well as the relative risk and odds ratio scales for the case of binary mediator and outcome. Both a regression approach and an inverse probability weighting approach were considered in the simulation study. A real-data illustration employing data from the Canadian Study of Health and Aging is provided. This analysis is concerned with the mediating effect of vitamin D in the effect of physical activity on dementia and its results are overall consistent with the theoretical and empirical findings.

Rural-to-urban migration, discrimination experience, and health in China: Evidence from propensity score analysis

This research examines how rural-to-urban migration influences health through discrimination experience in China after considering migration selection bias. We conducted propensity score matching (PSM) to obtain a matched group of rural residents and rural-to-urban migrants with a similar probability of migrating from rural to urban areas using data from the 2014 China Family Panel Studies (CFPS). Regression and mediation analyses were performed after PSM. The results of regression analysis after PSM indicated that rural-to-urban migrants reported more discrimination experience than rural residents, and those of mediation analysis revealed discrimination experience to exert negative indirect effects on the associations between rural-to-urban migration and three measures of health: self-reported health, psychological distress, and physical discomfort. Sensitivity analysis using different calipers yielded similar results. Relevant policies and practices are required to respond to the unfair treatment and discrimination experienced by this migrant population.

Nonparametric efficient causal mediation with intermediate confounders

Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficient influence function in the nonparametric statistical model. We use the efficient influence function to develop two asymptotically optimal nonparametric estimators that leverage data-adaptive regression for the estimation of nuisance parameters: a one-step estimator and a targeted minimum loss estimator. We further present results establishing the conditions under which these estimators are consistent, multiply robust, $n^{1/2}$-consistent and efficient. We illustrate the finite-sample performance of the estimators and corroborate our theoretical results in a simulation study. We also demonstrate the use of the estimators in our motivating application to elucidate the mechanisms behind the unintended harmful effects that a housing intervention had on risky behaviour in adolescent girls.

The multidimensional vulnerability of people with disability to HIV infection: Results from the handiSSR study in Bujumbura, Burundi

BACKGROUND

In resource-limited contexts, available data indicate that people with disability are disproportionally affected by the HIV epidemic. While disability resulting from chronic HIV infection has received some attention, few epidemiologic studies have examined the vulnerability of people with disability to HIV acquisition. The aims of the study were as follows: to estimate and compare HIV prevalence among people with and without disability living in Bujumbura, Burundi; to examine how the interaction among disability, gender and socioeconomic environment shapes vulnerability to HIV; and to identify potential pathways to higher HIV risk.

METHODS

In this cross-sectional population-based study, 623 persons with disability (302 with disability onset ≤10 years ["early disability"]) and 609 persons without disability matched for age, sex and location were randomly selected to be tested for HIV and to participate in an interview about their life history, their social environment and their knowledge of sexual health.

FINDINGS

A total of 68% of men and 75% of women with disability were affected by multidimensional poverty compared to 54% and 46% of their peers without disability (p<0.0001). Higher HIV prevalence was observed among women with disability (12.1% [8.2-16]) than among those without (3.8% [1.7-6], ORa 3.8, p<0.0001), while it was similar among men with disability and those without (p = 0·8). Women with disability were also at higher risk of sexual violence than were those without (ORa 2.7, p<0.0001). The vulnerability of women with early disability to HIV was higher among those who were socially isolated (HIV prevalence in this group: 19% [12-27]). In addition, education level and sexual violence mediated 53% of the association between early disability and HIV (p = 0.001).

INTERPRETATION

This study highlights how the intersection of disability, gender and social environment shapes vulnerability to HIV. It also shows that the vulnerability to HIV of women who grew up with a disability is mediated by sexual violence.

FUNDING

This research was funded by the Netherlands Organization for Scientific Research (Grant W08.560.005) and the Initiative HIV-TB-Malaria (new name of the organisation).

Clarifying causal mediation analysis for the applied researcher: Defining effects based on what we want to learn

The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements-effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this article is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference between the causal inference and traditional approaches to mediation analysis and making a case for the need for explicit causal thinking and the causal inference approach in mediation analysis. It then explains in as-plain-as-possible language existing effect types, paying special attention to motivating these effects with different types of research questions, and using concrete examples for illustration. This presentation differentiates 2 perspectives (or purposes of analysis): the explanatory perspective (aiming to explain the total effect) and the interventional perspective (asking questions about hypothetical interventions on the exposure and mediator, or hypothetically modified exposures). For the latter perspective, the article proposes tapping into a general class of interventional effects that contains as special cases most of the usual effect types-interventional direct and indirect effects, controlled direct effects and also a generalized interventional direct effect type, as well as the total effect and overall effect. This general class allows flexible effect definitions which better match many research questions than the standard interventional direct and indirect effects. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

A More Efficient Causal Mediator Model Without the No-Unmeasured-Confounder Assumption

Mediator models have been developed primarily under the assumption of no-unmeasured-confounding. In many situations, this assumption is violated and may lead to the identification of mediator variables that actually are statistical artifacts. The rank preserving model (RPM) is an alternative approach to estimate controlled direct and mediator effects. It is based on the structural mean models framework and a no-effect-modifier assumption. The RPM assumes that unobserved confounders do not interact with treatment or mediators. This assumption is often more plausible to hold than the no-unmeasured-confounder assumption. So far, models using the no-effect-modifier assumption have been rarely used, which might be due to its low power and inefficiency in many scenarios. Here, a semi-parametric nonlinear extension, the nRPM, is proposed that overcomes this inefficiency using thin plate regression splines that both increase the predictive power of the model and decrease the misspecification present in many situations. In a simulation study, it is shown that the nRPM provides estimates that are robust against the violation of the no-effect-modifier assumption and that are substantively more efficient than those of the RPM. The model is illustrated using a data set on CD4 cell counts in a context of the human immunodeficiency virus (HIV).

Robust inference on population indirect causal effects: the generalized front door criterion

Standard methods for inference about direct and indirect effects require stringent no-unmeasured-confounding assumptions which often fail to hold in practice, particularly in observational studies. The goal of the paper is to introduce a new form of indirect effect, the population intervention indirect effect, that can be non-parametrically identified in the presence of an unmeasured common cause of exposure and outcome. This new type of indirect effect captures the extent to which the effect of exposure is mediated by an intermediate variable under an intervention that holds the component of exposure directly influencing the outcome at its observed value. The population intervention indirect effect is in fact the indirect component of the population intervention effect, introduced by Hubbard and Van der Laan. Interestingly, our identification criterion generalizes Judea Pearl's front door criterion as it does not require no direct effect of exposure not mediated by the intermediate variable. For inference, we develop both parametric and semiparametric methods, including a novel doubly robust semiparametric locally efficient estimator, that perform very well in simulation studies. Finally, the methods proposed are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health programme in Tanzania.

Estimation of Natural Indirect Effects Robust to Unmeasured Confounding and Mediator Measurement Error

The use of causal mediation analysis to evaluate the pathways by which an exposure affects an outcome is widespread in the social and biomedical sciences. Recent advances in this area have established formal conditions for identification and estimation of natural direct and indirect effects. However, these conditions typically involve stringent assumptions of no unmeasured confounding and that the mediator has been measured without error. These assumptions may fail to hold in many practical settings where mediation methods are applied. The goal of this article is two-fold. First, we formally establish that the natural indirect effect can in fact be identified in the presence of unmeasured exposure-outcome confounding provided there is no additive interaction between the mediator and unmeasured confounder(s). Second, we introduce a new estimator of the natural indirect effect that is robust to both classical measurement error of the mediator and unmeasured confounding of both exposure-outcome and mediator-outcome relations under certain no interaction assumptions. We provide formal proofs and a simulation study to illustrate our results. In addition, we apply the proposed methodology to data from the Harvard President's Emergency Plan for AIDS Relief (PEPFAR) program in Nigeria.

Causal Mediation Analysis for Standardized Mortality Ratios

Indirectly standardized mortality ratios (SMR) are often used to compare patient outcomes between health care providers as indicators of quality of care. Observed differences in the outcomes raise the question of whether these could be causally attributable to earlier processes or outcomes in the pathway of care that the patients received. Such pathways can be naturally addressed in a causal mediation analysis framework. Adopting causal mediation models allows the total provider effect on outcome to be decomposed into direct and indirect (mediated) effects. This in turn enables quantification of the improvement in patient outcomes due to a hypothetical intervention on the mediator. We formulate the effect decomposition for the indirectly standardized SMR when comparing to a health care system-wide average performance, propose novel model-based and semiparametric estimators for the decomposition, study the properties of these through simulations, and demonstrate their use through application to Ontario kidney cancer data.

Generalized causal mediation and path analysis: Extensions and practical considerations

Causal mediation analysis seeks to decompose the effect of a treatment or exposure among multiple possible paths and provide casually interpretable path-specific effect estimates. Recent advances have extended causal mediation analysis to situations with a sequence of mediators or multiple contemporaneous mediators. However, available methods still have limitations, and computational and other challenges remain. The present paper provides an extended causal mediation and path analysis methodology. The new method, implemented in the new R package, gmediation (described in a companion paper), accommodates both a sequence (two stages) of mediators and multiple mediators at each stage, and allows for multiple types of outcomes following generalized linear models. The methodology can also handle unsaturated models and clustered data. Addressing other practical issues, we provide new guidelines for the choice of a decomposition, and for the choice of a reference group multiplier for the reduction of Monte Carlo error in mediation formula computations. The new method is applied to data from a cohort study to illuminate the contribution of alternative biological and behavioral paths in the effect of socioeconomic status on dental caries in adolescence.

Causal Mediation Analysis With Observational Data: Considerations and Illustration Examining Mechanisms Linking Neighborhood Poverty to Adolescent Substance Use

Understanding the mediation mechanisms by which an exposure or intervention affects an outcome can provide a look into what has been called a "black box" of many epidemiologic associations, thereby providing further evidence of a relationship and possible points of intervention. Rapid methodologic developments in mediation analyses mean that there are a growing number of approaches for researchers to consider, each with its own set of assumptions, advantages, and disadvantages. This has understandably resulted in some confusion among applied researchers. Here, we provide a brief overview of the mediation methods available and discuss points for consideration when choosing a method. We provide an in-depth explication of 2 of the many potential estimators for illustrative purposes: the Baron and Kenny mediation approach, because it is the most commonly used, and a recently developed approach for estimating stochastic direct and indirect effects, because it relies on far fewer assumptions. We illustrate the decision process and analytical procedure by estimating potential school- and peer-based mechanisms linking neighborhood poverty to adolescent substance use in the National Comorbidity Survey Adolescent Supplement.

The role of socioeconomic status in the relationship between detention and self-rated health among prison detainees in Belgium

Prisoners are known to report worse health than the general population. Research has also shown that the prison population counts disproportionally more people with a lower socioeconomic status (SES), making it difficult to determine whether the worse self-reported health of prisoners is an effect of their detention or of their lower SES. This study assesses the influence of being in prison on self-rated health and if (and how) this relationship is mediated by SES. Data from detainees were collected in 12 Flemish prisons. To compare with the general population, data from the Belgian national health survey 2013 were used. To estimate the direct and indirect effect of being in prison on self-reported health, mediation analysis was carried out by means of natural effect models using nested counterfactuals. Following previous literature we find that prisoners report worse health than the general population and that SES has a significant influence on subjective health. Our results showed that the direct effect (exp(B) = 3.43; [95% CI: 2.924-4.024]) of being in prison on self-reported health is larger than the indirect effect (through SES) (exp(B) = 1,236; [95% CI: 1.195-1.278]), thus contradicting the hypotheses in previous literature that the SES is the main explanation for variation in self-reported health among prisoners. Lastly, the effect of SES on health is more important for the general population compared to detainees, suggesting that for prisoners the effect of being in prison seems to surpass the effect of SES on health.

Attributing diseases to multiple pathways: a causal-pie modeling approach

Characterizing the relations between exposures and diseases is the central tenet of epidemiology. Researchers may want to evaluate exposure-disease causation by assessing whether the disease under concern is induced by the various exposures – the so-called “attribution”. In this paper, the authors propose a method to attribute diseases to multiple pathways based on the causal-pie model. The method can also be used to evaluate the potential impact of an intervention strategy and to allocate responsibility in tort-law liability issues.

Interventional Effects for Mediation Analysis with Multiple Mediators

The mediation formula for the identification of natural (in)direct effects has facilitated mediation analyses that better respect the nature of the data, with greater consideration of the need for confounding control. The default assumptions on which it relies are strong, however. In particular, they are known to be violated when confounders of the mediator-outcome association are affected by the exposure. This complicates extensions of counterfactual-based mediation analysis to settings that involve repeatedly measured mediators, or multiple correlated mediators. VanderWeele, Vansteelandt, and Robins introduced so-called interventional (in)direct effects. These can be identified under much weaker conditions than natural (in)direct effects, but have the drawback of not adding up to the total effect. In this article, we adapt their proposal to achieve an exact decomposition of the total effect, and extend it to the multiple mediator setting. Interestingly, the proposed effects capture the path-specific effects of an exposure on an outcome that are mediated by distinct mediators, even when-as often-the structural dependence between the multiple mediators is unknown, for instance, when the direction of the causal effects between the mediators is unknown, or there may be unmeasured common causes of the mediators.

Estimating causal contrasts involving intermediate variables in the presence of selection bias

An important goal across the biomedical and social sciences is the quantification of the role of intermediate factors in explaining how an exposure exerts an effect on an outcome. Selection bias has the potential to severely undermine the validity of inferences on direct and indirect causal effects in observational as well as in randomized studies. The phenomenon of selection may arise through several mechanisms, and we here focus on instances of missing data. We study the sign and magnitude of selection bias in the estimates of direct and indirect effects when data on any of the factors involved in the analysis is either missing at random or not missing at random. Under some simplifying assumptions, the bias formulae can lead to nonparametric sensitivity analyses. These sensitivity analyses can be applied to causal effects on the risk difference and risk-ratio scales irrespectively of the estimation approach employed. To incorporate parametric assumptions, we also develop a sensitivity analysis for selection bias in mediation analysis in the spirit of the expectation-maximization algorithm. The approaches are applied to data from a health disparities study investigating the role of stage at diagnosis on racial disparities in colorectal cancer survival. Copyright © 2016 John Wiley & Sons, Ltd.

Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding

It is often of interest to decompose the total effect of an exposure into a component that acts on the outcome through some mediator and a component that acts independently through other pathways. Said another way, we are interested in the direct and indirect effects of the exposure on the outcome. Even if the exposure is randomly assigned, it is often infeasible to randomize the mediator, leaving the mediator-outcome confounding not fully controlled. We develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator-outcome confounding.

Mediation analysis to estimate direct and indirect milk losses associated with bacterial load in bovine subclinical mammary infections

Milk losses associated with mastitis can be attributed to either effects of pathogens per se (i.e. direct losses) or to effects of the immune response triggered by the presence of mammary pathogens (i.e. indirect losses). Test-day milk somatic cell counts (SCC) and number of bacterial colony forming units (CFU) found in milk samples are putative measures of the level of immune response and of the bacterial load, respectively. Mediation models, in which one independent variable affects a second variable which, in turn, affects a third one, are conceivable models to estimate direct and indirect losses. Here, we evaluated the feasibility of a mediation model in which test-day SCC and milk were regressed toward bacterial CFU measured at three selected sampling dates, 1 week apart. We applied this method on cows free of clinical signs and with records on up to 3 test-days before and after the date of the first bacteriological samples. Most bacteriological cultures were negative (52.38%), others contained either staphylococci (23.08%), streptococci (9.16%), mixed bacteria (8.79%) or were contaminated (6.59%). Only losses mediated by an increase in SCC were significantly different from null. In cows with three consecutive bacteriological positive results, we estimated a decreased milk yield of 0.28 kg per day for each unit increase in log2-transformed CFU that elicited one unit increase in log2-transformed SCC. In cows with one or two bacteriological positive results, indirect milk loss was not significantly different from null although test-day milk decreased by 0.74 kg per day for each unit increase of log2-transformed SCC. These results highlight the importance of milk losses that are mediated by an increase in SCC during mammary infection and the feasibility of decomposing total milk loss into its direct and indirect components.

Mediation Analysis: A Practitioner's Guide

This article provides an overview of recent developments in mediation analysis, that is, analyses used to assess the relative magnitude of different pathways and mechanisms by which an exposure may affect an outcome. Traditional approaches to mediation in the biomedical and social sciences are described. Attention is given to the confounding assumptions required for a causal interpretation of direct and indirect effect estimates. Methods from the causal inference literature to conduct mediation in the presence of exposure-mediator interactions, binary outcomes, binary mediators, and case-control study designs are presented. Sensitivity analysis techniques for unmeasured confounding and measurement error are introduced. Discussion is given to extensions to time-to-event outcomes and multiple mediators. Further flexible modeling strategies arising from the precise counterfactual definitions of direct and indirect effects are also described. The focus throughout is on methodology that is easily implementable in practice across a broad range of potential applications.

Causal mediation analysis with multiple causally non-ordered mediators

In many health studies, researchers are interested in estimating the treatment effects on the outcome around and through an intermediate variable. Such causal mediation analyses aim to understand the mechanisms that explain the treatment effect. Although multiple mediators are often involved in real studies, most of the literature considered mediation analyses with one mediator at a time. In this article, we consider mediation analyses when there are causally non-ordered multiple mediators. Even if the mediators do not affect each other, the sum of two indirect effects through the two mediators considered separately may diverge from the joint natural indirect effect when there are additive interactions between the effects of the two mediators on the outcome. Therefore, we derive an equation for the joint natural indirect effect based on the individual mediation effects and their interactive effect, which helps us understand how the mediation effect works through the two mediators and relative contributions of the mediators and their interaction. We also discuss an extension for three mediators. The proposed method is illustrated using data from a randomized trial on the prevention of dental caries.

Causal mediation analysis with multiple mediators

In diverse fields of empirical research-including many in the biological sciences-attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways. For example, we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure (SBP) into effects via body mass index (BMI), via gamma-glutamyl transpeptidase (GGT), and via other pathways. Much progress has been made, mainly due to contributions from the field of causal inference, in understanding the precise nature of statistical estimands that capture such intuitive effects, the assumptions under which they can be identified, and statistical methods for doing so. These contributions have focused almost entirely on settings with a single mediator, or a set of mediators considered en bloc; in many applications, however, researchers attempt a much more ambitious decomposition into numerous path-specific effects through many mediators. In this article, we give counterfactual definitions of such path-specific estimands in settings with multiple mediators, when earlier mediators may affect later ones, showing that there are many ways in which decomposition can be done. We discuss the strong assumptions under which the effects are identified, suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified. These ideas are illustrated using data on alcohol consumption, SBP, BMI, and GGT from the Izhevsk Family Study. We aim to bridge the gap from "single mediator theory" to "multiple mediator practice," highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed.

Mediation analysis to estimate direct and indirect milk losses due to clinical mastitis in dairy cattle

Milk losses associated with mastitis can be attributed to either effects of pathogens per se (i.e., direct losses) or effects of the immune response triggered by intramammary infection (indirect losses). The distinction is important in terms of mastitis prevention and treatment. Regardless, the number of pathogens is often unknown (particularly in field studies), making it difficult to estimate direct losses, whereas indirect losses can be approximated by measuring the association between increased somatic cell count (SCC) and milk production. An alternative is to perform a mediation analysis in which changes in milk yield are allocated into their direct and indirect components. We applied this method on data for clinical mastitis, milk and SCC test-day recordings, results of bacteriological cultures (Escherichia coli, Staphylococcus aureus, Streptococcus uberis, coagulase-negative staphylococci, Streptococcus dysgalactiae, and streptococci other than Strep. dysgalactiae and Strep. uberis), and cow characteristics. Following a diagnosis of clinical mastitis, the cow was treated and changes (increase or decrease) in milk production before and after a diagnosis were interpreted counterfactually. On a daily basis, indirect changes, mediated by SCC increase, were significantly different from zero for all bacterial species, with a milk yield decrease (ranging among species from 4 to 33g and mediated by an increase of 1000 SCC/mL/day) before and a daily milk increase (ranging among species from 2 to 12g and mediated by a decrease of 1000 SCC/mL/day) after detection. Direct changes, not mediated by SCC, were only different from zero for coagulase-negative staphylococci before diagnosis (72g per day). We concluded that mixed structural equation models were useful to estimate direct and indirect effects of the presence of clinical mastitis on milk yield.

Mediation analysis with intermediate confounding: structural equation modeling viewed through the causal inference lens

The study of mediation has a long tradition in the social sciences and a relatively more recent one in epidemiology. The first school is linked to path analysis and structural equation models (SEMs), while the second is related mostly to methods developed within the potential outcomes approach to causal inference. By giving model-free definitions of direct and indirect effects and clear assumptions for their identification, the latter school has formalized notions intuitively developed in the former and has greatly increased the flexibility of the models involved. However, through its predominant focus on nonparametric identification, the causal inference approach to effect decomposition via natural effects is limited to settings that exclude intermediate confounders. Such confounders are naturally dealt with (albeit with the caveats of informality and modeling inflexibility) in the SEM framework. Therefore, it seems pertinent to revisit SEMs with intermediate confounders, armed with the formal definitions and (parametric) identification assumptions from causal inference. Here we investigate: 1) how identification assumptions affect the specification of SEMs, 2) whether the more restrictive SEM assumptions can be relaxed, and 3) whether existing sensitivity analyses can be extended to this setting. Data from the Avon Longitudinal Study of Parents and Children (1990-2005) are used for illustration.

A principal stratification approach for evaluating natural direct and indirect effects in the presence of treatment-induced intermediate confounding

Recently, several authors have shown that natural direct and indirect effects (NDEs and NIEs) can be identified under the sequential ignorability assumptions, as long as there is no mediator-outcome confounder that is affected by the treatment. However, if such a confounder exists, NDEs and NIEs will generally not be identified without making additional identifying assumptions. In this article, we propose novel identification assumptions and estimators for evaluating NDEs and NIEs under the usual sequential ignorability assumptions, using the principal stratification framework. It is assumed that the treatment and the mediator are dichotomous. We must impose strong assumptions for identification. However, even if these assumptions were violated, the bias of our estimator would be small under typical conditions, which can be easily evaluated from the observed data. This conjecture is confirmed for binary outcomes by deriving the bounds of the bias terms. In addition, the advantage of our estimator is illustrated through a simulation study. We also propose a method of sensitivity analysis that examines what happens when our assumptions are violated. We apply the proposed method to data from the National Center for Health Statistics.

Effect decomposition in the presence of an exposure-induced mediator-outcome confounder

Methods from causal mediation analysis have generalized the traditional approach to direct and indirect effects in the epidemiologic and social science literature by allowing for interaction and nonlinearities. However, the methods from the causal inference literature have themselves been subject to a major limitation, in that the so-called natural direct and indirect effects that are used are not identified from data whenever there is a mediator-outcome confounder that is also affected by the exposure. In this article, we describe three alternative approaches to effect decomposition that give quantities that can be interpreted as direct and indirect effects and that can be identified from data even in the presence of an exposure-induced mediator-outcome confounder. We describe a simple weighting-based estimation method for each of these three approaches, illustrated with data from perinatal epidemiology. The methods described here can shed insight into pathways and questions of mediation even when an exposure-induced mediator-outcome confounder is present.

Theory and Analysis of Total, Direct, and Indirect Causal Effects

Mediation analysis, or more generally models with direct and indirect effects, are commonly used in the behavioral sciences. As we show in our illustrative example, traditional methods of mediation analysis that omit confounding variables can lead to systematically biased direct and indirect effects, even in the context of a randomized experiment. Therefore, several definitions of causal effects in mediation models have been presented in the literature (Baron & Kenny, 1986 ; Imai, Keele, & Tingley, 2010 ; Pearl, 2012 ). We illustrate the stochastic theory of causal effects as an alternative foundation of causal mediation analysis based on probability theory. In this theory we define total, direct, and indirect effects and show how they can be identified in the context of our illustrative example. A particular strength of the stochastic theory of causal effects are the causality conditions that imply causal unbiasedness of effect estimates. The causality conditions have empirically testable implications and can be used for covariate selection. In the discussion, we highlight some similarities and differences of the stochastic theory of causal effects with other theories of causal effects.

Advances in mediation analysis: a survey and synthesis of new developments

Mediation processes are fundamental to many classic and emerging theoretical paradigms within psychology. Innovative methods continue to be developed to address the diverse needs of researchers studying such indirect effects. This review provides a survey and synthesis of four areas of active methodological research: (a) mediation analysis for longitudinal data, (b) causal inference for indirect effects, (c) mediation analysis for discrete and nonnormal variables, and (d) mediation assessment in multilevel designs. The aim of this review is to aid in the dissemination of developments in these four areas and suggest directions for future research.

Flexible Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula

In the social sciences, mediation analysis has typically been formulated in the context of linear models using the Baron & Kenny (1986) approach. Extensions to nonlinear models have been considered but lack formal justification. By placing mediation analysis within the counterfactual framework of causal inference one can define causal mediation effects in a way that is not tied to a specific statistical model and identify them under certain no unmeasured confounding assumptions. Corresponding estimation procedures using parametric or nonparametric models, based on the so-called mediation formula, have recently been proposed in the psychological literature and made accessible through the R-package mediation. A number of limitations of the latter approach are discussed and a more flexible approach using natural effects models is proposed as an alternative. The latter builds on the same counterfactual framework but enables interpretable and parsimonious modeling of direct and mediated effects and facilitates tests of hypotheses that would otherwise be difficult or impossible to test. We illustrate the approach in a study of individuals who ended a romantic relationship and explore whether the effect of attachment anxiety during the relationship on unwanted pursuit behavior after the breakup is mediated by negative affect during the breakup.