Mediation analysis when a continuous mediator is measured with error and the outcome follows a generalized linear model

Mediation analysis using incomplete information from publicly available data sources

Our work was motivated by the question whether, and to what extent, well-established risk factors mediate the racial disparity observed for colorectal cancer (CRC) incidence in the United States. Mediation analysis examines the relationships between an exposure, a mediator and an outcome. All available methods require access to a single complete data set with these three variables. However, because population-based studies usually include few non-White participants, these approaches have limited utility in answering our motivating question. Recently, we developed novel methods to integrate several data sets with incomplete information for mediation analysis. These methods have two limitations: (i) they only consider a single mediator and (ii) they require a data set containing individual-level data on the mediator and exposure (and possibly confounders) obtained by independent and identically distributed sampling from the target population. Here, we propose a new method for mediation analysis with several different data sets that accommodates complex survey and registry data, and allows for multiple mediators. The proposed approach yields unbiased causal effects estimates and confidence intervals with nominal coverage in simulations. We apply our method to data from U.S. cancer registries, a U.S.-population-representative survey and summary level odds-ratio estimates, to rigorously evaluate what proportion of the difference in CRC risk between non-Hispanic Whites and Blacks is mediated by three potentially modifiable risk factors (CRC screening history, body mass index, and regular aspirin use).

Causal mediation analysis with mediator values below an assay limit

Causal indirect and direct effects provide an interpretable method for decomposing the total effect of an exposure on an outcome into the indirect effect through a mediator and the direct effect through all other pathways. A natural choice for a mediator in a randomized clinical trial is the treatment's targeted biomarker. However, when the mediator is a biomarker, values can be subject to an assay lower limit. The mediator is affected by the treatment and is a putative cause of the outcome, so the assay lower limit presents a compounded problem in mediation analysis. We propose two approaches to estimate indirect and direct effects with a mediator subject to an assay limit: (1) extrapolation and (2) numerical optimization and integration of the observed likelihood. Since these estimation methods solely rely on the so-called Mediation Formula, they apply to most approaches to causal mediation analysis: natural, separable, and organic indirect, and direct effects. A simulation study compares the two estimation approaches to imputing with half the assay limit. Using HIV interruption study data from the AIDS Clinical Trials Group described in Li et al 2016, AIDS; Lok and Bosch 2021, Epidemiology, we illustrate our methods by estimating the organic/pure indirect effect of a hypothetical HIV curative treatment on viral suppression mediated by two HIV persistence measures: cell-associated HIV-RNA and single-copy plasma HIV-RNA.

Role of cardiovascular health factors in mediating social inequalities in the incidence of dementia in the UK: two prospective, population-based cohort studies

Background

The contribution of modifiable risk factors to social inequalities in dementia, observed in longitudinal studies, remains unclear. We aimed to quantify the role of cardiovascular health factors, assessed using Life's Essential 8 (LE8) score, in mediating social inequalities in incidence of dementia and, for comparison, in incidence of stroke, coronary heart disease, and mortality.

Methods

In this prospective, population-based cohort study, we collected data from the UK Whitehall II Study and UK Biobank databases. Participants were included if data were available on SEP, outcomes and LE8 (smoking, physical activity, diet, body mass index, blood pressure, fasting blood glucose, lipid levels, sleep duration). The primary outcome was incident dementia and secondary outcomes were stroke, coronary heart disease, and mortality. Outcomes were derived from electronic healthcare records. Socioeconomic position (SEP) was measured by occupation in Whitehall II and education in UK Biobank. Counterfactual mediation analysis was used to quantify the extent to which LE8 score explained the associations of SEP with all outcomes. Analyses involved Cox regression, accelerated failure time models, and linear regression; and were adjusted for age, sex, and ethnicity.

Findings

Between 10.09.1985 and 29.03.1988, a total of 9688 participants (mean age ± SD 44.9 ± 6.0; 67% men) from the Whitehall II study, and between 19.12.2006 and 01.10.2010, 278,215 participants (mean age ± SD 56.0 ± 8.1; 47% men) from the UK Biobank were included. There were 606 and 4649 incident dementia cases over a median (interquartile range) follow-up of 31.7 (31.1-32.7) and 13.5 (12.7-14.1) years respectively in Whitehall II and UK Biobank. In Whitehall II, the hazard ratio was 1.85 [95% CI 1.42, 2.32] for the total effect of SEP on dementia and 1.20 [1.12, 1.28] for the indirect effect via the LE8, the proportion mediated being 36%. In UK Biobank, the total effect of SEP on dementia was 1.65 [1.54, 1.78]; the indirect effect was 1.11 [1.09, 1.12], and the proportion mediated was 24%. The proportions mediated for stroke, coronary heart disease, and mortality were higher, ranging between 34% and 63% in Whitehall II and between 36% and 50% in UK Biobank.

Interpretation

In two well-characterised cohort studies, up to one third of the social inequalities in incidence of dementia was attributable to cardiovascular health factors. Promotion of cardiovascular health in midlife may contribute to reducing social inequalities in risk of dementia, in addition to cardiovascular diseases and all-cause mortality. This study used adult measures of SEP, further research is warranted using lifecourse measures of SEP.

Funding

NIH (RF1AG062553).

Causal mediation for uncausally related mediators in the context of survival analysis

Objective

The study of the potential intermediate effect of several variables on the association between an exposure and a time-to-event outcome is a question of interest in epidemiologic research. However, to our knowledge, no tools have been developed for the evaluation of multiple correlated mediators in a survival setting.

Methods

In this work, we extended the multimediate algorithm, which conducts mediation analysis in the context of multiple uncausally correlated mediators, to a time-to-event setting using the semiparametric additive hazards model. We theoretically demonstrated that, under certain assumptions, indirect, direct and total effects can be calculated using the counterfactual framework with collapsible survival models. We also adapted the algorithm to accommodate exposure-mediator interactions.

Results and conclusions

Using simulations, we demonstrated that our algorithm performs better than the product of coefficients method, even for uncorrelated mediators. The additive hazards model quantifies the effects as rate differences, which constitute a measure of impact, with applications that can be highly informative for public health. Our algorithm can be found in the R package multimediate, which is available in Github.

Racial and ethnic disparities in preterm birth: a mediation analysis incorporating mixtures of polybrominated diphenyl ethers

Background

Racial and ethnic disparities persist in preterm birth (PTB) and gestational age (GA) at delivery in the United States. It remains unclear whether exposure to environmental chemicals contributes to these disparities.

Objectives

We applied recent methodologies incorporating environmental mixtures as mediators in causal mediation analysis to examine whether racial and ethnic disparities in GA at delivery and PTB may be partially explained by exposures to polybrominated diphenyl ethers (PBDEs), a class of chemicals used as flame retardants in the United States.

Methods

Data from a multiracial/ethnic US cohort of 2008 individuals with low-risk singleton pregnancies were utilized, with plasma PBDE concentrations measured during early pregnancy. We performed mediation analyses incorporating three forms of mediators: (1) reducing all PBDEs to a weighted index, (2) selecting a PBDE congener, or (3) including all congeners simultaneously as multiple mediators, to evaluate whether PBDEs may contribute to the racial and ethnic disparities in PTB and GA at delivery, adjusted for potential confounders.

Results

Among the 2008 participants, 552 self-identified as non-Hispanic White, 504 self-identified as non-Hispanic Black, 568 self-identified as Hispanic, and 384 self-identified as Asian/Pacific Islander. The non-Hispanic Black individuals had the highest mean ∑PBDEs, the shortest mean GA at delivery, and the highest rate of PTB. Overall, the difference in GA at delivery comparing non-Hispanic Black to non-Hispanic White women was -0.30 (95% CI: -0.54, -0.05) weeks. This disparity reduced to -0.23 (95% CI: -0.49, 0.02) and -0.18 (95% CI: -0.46, 0.10) weeks if fixing everyone's weighted index of PBDEs to the median and the 25th percentile levels, respectively. The proportion of disparity mediated by the weighted index of PBDEs was 11.8%. No statistically significant mediation was found for PTB, other forms of mediator(s), or other racial and ethnic groups.

Conclusion

PBDE mixtures may partially mediate the Black vs. White disparity in GA at delivery. While further validations are needed, lowering the PBDEs at the population level might help reduce this disparity.

Accommodating a Latent XM Interaction in Statistical Mediation Analysis

Statistical mediation analysis is used in the social sciences and public health to uncover potential mechanisms, known as mediators, by which a treatment led to a change in an outcome. Recently, the estimation of the treatment-by-mediator interaction (i.e., the XM interaction) has been shown to play a pivotal role in understanding the equivalence between the traditional mediation effects in linear models and the causal mediation effects in the potential outcomes framework. However, there is limited guidance on how to estimate the XM interaction when the mediator is latent. In this article, we discuss eight methods to accommodate latent XM interactions in statistical mediation analysis, which fall in two categories: using structural models (e.g., latent moderated structural equations, Bayesian mediation, unconstrained product indicator method, multiple-group models) or scoring the mediator prior to estimating the XM interaction (e.g., summed scores and factor scores, with and without attenuation correction). Simulation results suggest that finite-sample bias is low, type 1 error rates and coverage of percentile bootstrap confidence intervals and Bayesian credible intervals are close to the nominal values, and statistical power is similar across approaches. The methods are demonstrated with an applied example, syntax is provided for their implementation, and general considerations are discussed.

Mediation analysis in the presence of continuous exposure measurement error

The difference method is used in mediation analysis to quantify the extent to which a mediator explains the mechanisms underlying the pathway between an exposure and an outcome. In many health science studies, the exposures are almost never measured without error, which can result in biased effect estimates. This article investigates methods for mediation analysis when a continuous exposure is mismeasured. Under a linear exposure measurement error model, we prove that the bias of indirect effect and mediation proportion can go in either direction but the mediation proportion is usually be less biased when the associations between the exposure and its error-prone counterpart are similar with and without adjustment for the mediator. We further propose methods to adjust for exposure measurement error with continuous and binary outcomes. The proposed approaches require a main study/validation study design where in the validation study, data are available for characterizing the relationship between the true exposure and its error-prone counterpart. The proposed approaches are then applied to the Health Professional Follow-up Study, 1986-2016, to investigate the impact of body mass index (BMI) as a mediator for mediating the effect of physical activity on the risk of cardiovascular diseases. Our results reveal that physical activity is significantly associated with a lower risk of cardiovascular disease incidence, and approximately half of the total effect of physical activity is mediated by BMI after accounting for exposure measurement error. Extensive simulation studies are conducted to demonstrate the validity and efficiency of the proposed approaches in finite samples.

Consistent inverse probability of treatment weighted estimation of the average treatment effect with mismeasured time-dependent confounders

In longitudinal studies, the inverse probability of treatment weighted (IPTW) method is commonly employed to estimate the effect of time-dependent treatments on an outcome of interest. However, it has been documented that when the confounders are subject to measurement error, the naive IPTW method which simply ignores measurement error leads to biased treatment effect estimation. In the existing literature, there is a lack of measurement error correction methods that fully remove measurement error effect and produce consistent treatment effect estimation. In this article, we develop a novel consistent IPTW estimation procedure for longitudinal studies. The key step of the proposed method is to use the observed data to construct a corrected function that is unbiased of the unknown IPTW function. Simulation studies reveal that the proposed method outperforms the existing consistent and approximate measurement error correction methods for IPTW estimation of the average treatment effect. Finally, we apply the proposed method to analyze a real dataset.

A unified mediation analysis framework for integrative cancer proteogenomics with clinical outcomes

MOTIVATION

Multilevel molecular profiling of tumors and the integrative analysis with clinical outcomes have enabled a deeper characterization of cancer treatment. Mediation analysis has emerged as a promising statistical tool to identify and quantify the intermediate mechanisms by which a gene affects an outcome. However, existing methods lack a unified approach to handle various types of outcome variables, making them unsuitable for high-throughput molecular profiling data with highly interconnected variables.

RESULTS

We develop a general mediation analysis framework for proteogenomic data that include multiple exposures, multivariate mediators on various scales of effects as appropriate for continuous, binary and survival outcomes. Our estimation method avoids imposing constraints on model parameters such as the rare disease assumption, while accommodating multiple exposures and high-dimensional mediators. We compare our approach to other methods in extensive simulation studies at a range of sample sizes, disease prevalence and number of false mediators. Using kidney renal clear cell carcinoma proteogenomic data, we identify genes that are mediated by proteins and the underlying mechanisms on various survival outcomes that capture short- and long-term disease-specific clinical characteristics.

AVAILABILITY AND IMPLEMENTATION

Software is made available in an R package (https://github.com/longjp/mediateR).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

High lifelong cognitive reserve prolongs disability-free survival: The role of cognitive function

INTRODUCTION

The association between cognitive reserve (CR) and survival with independence is unknown. We examined whether lifelong CR accumulation is associated with disability-free survival and explored the extent to which cognitive function mediates this association.

METHODS

Within the Rush Memory and Aging Project, 1633 dementia- and disability-free participants were followed annually for up to 22 years. Lifelong CR including education, early-/mid-/late-life cognitive activities, and late-life social activity was assessed and tertiled.

RESULTS

CR score was dose-dependently associated with disability/death (hazard ratio [HR] 0.96, 95% confidence interval [CI] 0.93-0.99). Compared to low CR, the HR (95% CI) of disability/death was 0.82 (0.70-0.95) for high CR. The median disability-free survival time was prolonged by 0.99 (95% CI 0.28-1.71) years for participants with high CR. Cognitive function mediated 35.7% of the association between CR and disability-free survival.

DISCUSSION

High lifelong CR was associated with prolonged disability-free survival. Cognitive function mediates about one-third of this association. Our findings underscore the importance of CR for healthy aging.

Mediation analysis method review of high throughput data

High-throughput technologies have made high-dimensional settings increasingly common, providing opportunities for the development of high-dimensional mediation methods. We aimed to provide useful guidance for researchers using high-dimensional mediation analysis and ideas for biostatisticians to develop it by summarizing and discussing recent advances in high-dimensional mediation analysis. The method still faces many challenges when extended single and multiple mediation analyses to high-dimensional settings. The development of high-dimensional mediation methods attempts to address these issues, such as screening true mediators, estimating mediation effects by variable selection, reducing the mediation dimension to resolve correlations between variables, and utilizing composite null hypothesis testing to test them. Although these problems regarding high-dimensional mediation have been solved to some extent, some challenges remain. First, the correlation between mediators are rarely considered when the variables are selected for mediation. Second, downscaling without incorporating prior biological knowledge makes the results difficult to interpret. In addition, a method of sensitivity analysis for the strict sequential ignorability assumption in high-dimensional mediation analysis is still lacking. An analyst needs to consider the applicability of each method when utilizing them, while a biostatistician could consider extensions and improvements in the methodology.

Contribution of smoking towards the association between socioeconomic position and dementia: 32-year follow-up of the Whitehall II prospective cohort study

Background

There is consistent evidence of social inequalities in dementia but the mechanisms underlying this association remain unclear. We examined the role of smoking in midlife in socioeconomic differences in dementia at older ages.

Methods

Analyses were based on 9951 (67% men) participants, median age 44.3 [IQR=39.6, 50.3] years at baseline in 1985-1988, from the Whitehall II cohort study. Socioeconomic position (SEP) and smoking (smoking status (current, ex-, never-smoker), pack years of smoking, and smoking history score (combining status and pack-years)) were measured at baseline. Counterfactual mediation analysis was used to examine the contribution of smoking to the association between SEP and dementia.

Findings

During a median follow-up of 31.6 (IQR 31.1, 32.6) years, 628 participants were diagnosed with dementia and 2110 died. Analyses adjusted for age, sex, ethnicity, education, and SEP showed smokers (hazard ratio [HR] 1.36 [95% CI 1.10-1.68]) but not ex-smokers (HR 0.95 [95% CI 0.79-1.14]) to have a higher risk of dementia compared to never-smokers; similar results for smoking were obtained for pack-years of smoking and smoking history score. Mediation analysis showed low SEP to be associated with higher risk of dementia (HRs between 1.97 and 2.02, depending on the measure of smoking in the model); estimate for the mediation effect was 16% for smoking status (Indirect Effect HR 1.09 [95% CI 1.03-1.15]), 7% for pack-years of smoking (Indirect Effect HR 1.03 [95% CI 1.01-1.06]) and 11% for smoking history score (Indirect Effect HR 1.06 [95% CI 1.02-1.10]).

Interpretation

Our findings suggest that part of the social inequalities in dementia is mediated by smoking.

Funding

NIH.

Risk of Type 2 Diabetes Among Individuals with Excess Weight: Weight Trajectory Effects

PURPOSE OF REVIEW

Increased risk of type 2 diabetes mellitus (T2D) among individuals with overweight or obesity is well-established; however, questions remain about the temporal dynamics of weight change (gain or loss) on the natural course of T2D in this at-risk population. Existing epidemiologic evidence is limited to studies that discretely sample and assess excess weight and T2D risk at different ages with limited follow-up, yet changes in weight may have time-varying and possibly non-linear effects on T2D risk. Predicting the impact of weight change on the risk of T2D is key to informing primary prevention. We critically review the relationship between weight change, trajectory groups (i.e., distinct weight change patterns), and T2D risk among individuals with excess weight in recently published T2D prevention randomized controlled trials (RCTs) and longitudinal cohort studies.

RECENT FINDINGS

Overall, weight trajectory groups have been shown to differ by age of onset, sex, and patterns of insulin resistance or beta-cell function biomarkers. Lifestyle (diet and physical activity), pharmacological, and surgical interventions can modify an individual's weight trajectory. Adolescence is a critical etiologically relevant window during which onset of excess weight may be associated with higher risk of T2D. Changes in insulin resistance and beta-cell function biomarkers are distinct but related correlates of weight trajectory groups that evolve contemporaneously over time. These multi-trajectory markers are differentially associated with T2D risk. T2D risk may differ by the age of onset and duration of excess body weight, and the type of weight loss intervention. A better understanding of the changes in weight, insulin sensitivity, and beta-cell function as distinct but related correlates of T2D risk that evolve contemporaneously over time has important implications for designing and targeting primary prevention efforts.

Quantifying direct and indirect effect for longitudinal mediator and survival outcome using joint modeling approach

Longitudinal biomarkers are widely used in biomedical and translational researches to monitor the progressions of diseases. Methods have been proposed to jointly model longitudinal data and survival data, but its causal mechanism is yet to be investigated rigorously. Understanding how much of the total treatment effect is through the biomarker is important in understanding the treatment mechanism and evaluating the biomarker. In this work, we propose a causal mediation analysis method to compute the direct and indirect effects, when a joint modeling approach is used to take the longitudinal biomarker as the mediator and the survival endpoint as the outcome. Such a joint modeling approach allows us to relax the commonly used "sequential ignorability" assumption. We demonstrate how to evaluate longitudinally measured biomarkers using our method with two case studies, an AIDS study and a liver cirrhosis study.

Simulation extrapolation method for measurement error: A review

Measurement error is pervasive in statistics due to the non-availability of authentic data. The reasons for measurement error mainly relate to cost, convenience, and human error. Measurement error can result in non-negligible bias due to attenuated estimates, reduced power of statistical tests, and lower coverage probabilities of the coefficient estimators in a regression model. Several methods have been proposed to correct for measurement error, all of which can be grouped into two broad categories based on the underlying model-functional and structural. Functional models provide flexibility and robustness to estimators by placing minimal or no assumptions on the distribution of the mismeasured covariate or by treating them as a fixed entity, as opposed to a structural model which treats the underlying mismeasured covariates as random with a specified structure. The simulation extrapolation method is one method that is used for the partial correction of measurement error in both structural and functional models. Reviews of measurement error correction techniques are available in the literature. However, none of the previously conducted reviews has exclusively focused on simulation extrapolation and its application in continuous measurement error models, despite its widespread use and ease of application. We attempt to close this gap in the literature by highlighting its development over the past two and a half decades.

Accounting for Patient Engagement in Randomized Controlled Trials Evaluating Digital Cognitive Behavioral Therapies

Background: Cognitive behavioral therapy (CBT) can be a useful treatment option for various mental health disorders. Modern advances in information technology and mobile communication enable delivery of state-of-the-art CBT programs via smartphones, either as stand-alone or as an adjunct treatment augmenting traditional sessions with a therapist. Experimental CBTs require careful assessment in randomized clinical trials (RCTs). Methods: We investigate some statistical issues for an RCT comparing efficacy of an experimental CBT intervention for a mental health disorder against the control. Assuming a linear model for the clinical outcome and patient engagement as an influential covariate, we investigate two common statistical approaches to inference—analysis of covariance (ANCOVA) and a two-sample t-test. We also study sample size requirements for the described experimental setting. Results: Both ANCOVA and a two-sample t-test are appropriate for the inference on treatment difference at the average observed level of engagement. However, ANCOVA produces estimates with lower variance and may be more powerful. Furthermore, unlike the t-test, ANCOVA allows one to perform treatment comparison at the levels of engagement other than the average level observed in the study. Larger sample sizes may be required to ensure experiments are sufficiently powered if one is interested in comparing treatment effects for different levels of engagement. Conclusions: ANCOVA with proper adjustment for engagement should be used for the for the described experimental setting. Uncertainty on engagement patterns should be taken into account at the study design stage.

Testing Black-White Disparities in Biological Aging Among Older Adults in the United States: Analysis of DNA-Methylation and Blood-Chemistry Methods

Biological aging is a proposed mechanism through which social determinants drive health disparities. We conducted proof-of-concept testing of 8 DNA-methylation (DNAm) and blood-chemistry quantifications of biological aging as mediators of disparities in healthspan between Black and White participants in the 2016 wave of the Health and Retirement Study (n = 9,005). We quantified biological aging from 4 DNAm "clocks" (Horvath, Hannum, PhenoAge, and GrimAge clock), a DNAm pace-of-aging measure (DunedinPoAm), and 3 blood-chemistry measures (PhenoAge, Klemera-Doubal method biological age, and homeostatic dysregulation). We quantified Black-White disparities in healthspan from cross-sectional and longitudinal data on physical performance tests, self-reported limitations in activities of daily living, and physician-diagnosed chronic diseases, self-rated health, and survival. DNAm and blood-chemistry quantifications of biological aging were moderately correlated (Pearson's r = 0.1-0.4). The GrimAge clock, DunedinPoAm, and all 3 blood-chemistry measures were associated with healthspan characteristics (e.g., mortality effect-size hazard ratios were 1.71-2.32 per standard deviation of biological aging) and showed evidence of more advanced/faster biological aging in Black participants than in White participants (Cohen's d = 0.4-0.5). These measures accounted for 13%-95% of Black-White differences in healthspan-related characteristics. Findings suggest that reducing disparities in biological aging can contribute to building health equity.

Bayesian kernel machine regression-causal mediation analysis

Greater understanding of the pathways through which an environmental mixture operates is important to design effective interventions. We present new methodology to estimate natural direct and indirect effects and controlled direct effects of a complex mixture exposure on an outcome through a mediator variable. We implement Bayesian Kernel Machine Regression (BKMR) to allow for all possible interactions and nonlinear effects of (1) the co-exposures on the mediator, (2) the co-exposures and mediator on the outcome, and (3) selected covariates on the mediator and/or outcome. From the posterior predictive distributions of the mediator and outcome, we simulate counterfactuals to obtain posterior samples, estimates, and credible intervals of the mediation effects. Our simulation study demonstrates that when the exposure-mediator and exposure-mediator-outcome relationships are complex, BKMR-Causal Mediation Analysis performs better than current mediation methods. We applied our methodology to quantify the contribution of birth length as a mediator between in utero co-exposure to arsenic, manganese, and lead, and children's neurodevelopmental scores, in a prospective birth cohort in Bangladesh. Among younger children, we found a negative (adverse) association between the metal mixture and neurodevelopment. We also found evidence that birth length mediates the effect of exposure to the metal mixture on neurodevelopment for younger children. If birth length were fixed to its 75 t h percentile value, the harmful effect of the metal mixture on neurodevelopment is attenuated, suggesting nutritional interventions to help increase fetal growth, and thus birth length, could potentially block the harmful effect of the metal mixture on neurodevelopment.

A Difference-in-Difference Study Evaluating the Effect of Minimum Wage Policy on Body Mass Index and Related Health Behaviors

Minimum wage laws are a promising policy lever to promote health equity, but few rigorous evaluations have tested whether and how minimum wage policy affects health outcomes. This paper describes an ongoing difference-in-difference study evaluating the health effects of the 2017 Minneapolis Minimum Wage Ordinance, which incrementally increases the minimum wage to $15/hr. We present: (1) the conceptual model guiding the study including mediating mechanisms, (2) the study design, and (3) baseline findings from the study, and (4) the analytic plan for the remainder of the study. This prospective study follows a cohort of 974 low-wage workers over four years to compare outcomes among low-wage workers in Minneapolis, Minnesota, and those in a comparison city (Raleigh, North Carolina). Measures include height/weight, employment paystubs, two weeks of food purchase receipts, and a survey capturing data on participant demographics, health behaviors, and household finances. Baseline findings offer a profile of individuals likely to be affected by minimum wage laws. While the study is ongoing, the movement to increase local and state minimum wage is currently high on the policy agenda; evidence is needed to determine what role, if any, such policies play in improving the health of those affected.

Estimation of Controlled Direct Effects in Longitudinal Mediation Analyses with Latent Variables in Randomized Studies

In a randomized study with longitudinal data on a mediator and outcome, estimating the direct effect of treatment on the outcome at a particular time requires adjusting for confounding of the association between the outcome and all preceding instances of the mediator. When the confounders are themselves affected by treatment, standard regression adjustment is prone to severe bias. In contrast, G-estimation requires less stringent assumptions than path analysis using SEM to unbiasedly estimate the direct effect even in linear settings. In this article, we propose a G-estimation method to estimate the controlled direct effect of treatment on the outcome, by adapting existing G-estimation methods for time-varying treatments without mediators. The proposed method can accommodate continuous and noncontinuous mediators, and requires no models for the confounders. Unbiased estimation only requires correctly specifying a mean model for either the mediator or the outcome. The method is further extended to settings where the mediator or outcome, or both, are latent, and generalizes existing methods for single measurement occasions of the mediator and outcome to longitudinal data on the mediator and outcome. The methods are utilized to assess the effects of an intervention on physical activity that is possibly mediated by motivation to exercise in a randomized study.

Comparing self-reported and O*NET-based assessments of job control as predictors of self-rated health for non-Hispanic whites and racial/ethnic minorities

The Occupational Information Network (O*NET) database has been used as a valuable source of occupational exposure information. Although good agreement between O*NET and self-reported measures has been reported, little attention has been paid to O*NET's utility in racially/ethnically diverse samples. Because O*NET offers job-level information, if different racial groups have different experiences under the same job title, O*NET measure would introduce systematic measurement error. Using the General Social Survey data (n = 7,041; 437 occupations), we compared self-report and O*NET-derived measures of job control in their associations with self-rated health (SRH) for non-Hispanic whites and racial/ethnic minorities. The correlation between self-report and O*NET job control measures were moderate for all gender-race groups (Pearson's r = .26 - .40). However, the logistic regression analysis showed that the association between O*NET job control and SRH was markedly weaker for racial/ethnic minorities than for non-Hispanic whites. The self-reported job control was associated with SRH in similar magnitudes for both groups, which precluded the possibility that job control was relevant only for non-Hispanic whites. O*NET may not capture job experience for racial/ethnic minorities, and thus its utility depends on the racial/ethnic composition of the sample.

High-dimensional mediation analysis in survival models

Mediation analysis with high-dimensional DNA methylation markers is important in identifying epigenetic pathways between environmental exposures and health outcomes. There have been some methodology developments of mediation analysis with high-dimensional mediators. However, high-dimensional mediation analysis methods for time-to-event outcome data are still yet to be developed. To address these challenges, we propose a new high-dimensional mediation analysis procedure for survival models by incorporating sure independent screening and minimax concave penalty techniques for variable selection, with the Sobel and the joint method for significance test of indirect effect. The simulation studies show good performance in identifying correct biomarkers, false discovery rate control, and minimum estimation bias of the proposed procedure. We also apply this approach to study the causal pathway from smoking to overall survival among lung cancer patients potentially mediated by 365,307 DNA methylations in the TCGA lung cancer cohort. Mediation analysis using a Cox proportional hazards model estimates that patients who have serious smoking history increase the risk of lung cancer through methylation markers including cg21926276, cg27042065, and cg26387355 with significant hazard ratios of 1.2497(95%CI: 1.1121, 1.4045), 1.0920(95%CI: 1.0170, 1.1726), and 1.1489(95%CI: 1.0518, 1.2550), respectively. The three methylation sites locate in the three genes which have been showed to be associated with lung cancer event or overall survival. However, the three CpG sites (cg21926276, cg27042065 and cg26387355) have not been reported, which are newly identified as the potential novel epigenetic markers linking smoking and survival of lung cancer patients. Collectively, the proposed high-dimensional mediation analysis procedure has good performance in mediator selection and indirect effect estimation.

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.

Impact of an early childhood intervention on the home environment, and subsequent effects on child cognitive and emotional development: A secondary analysis

The objective of this study was to use secondary data from the Preparing for Life (PFL) trial to test (1) the impact of a prenatal-to-age-five intervention targeting women from a disadvantaged Irish community on the quality of the home environment; (2) whether any identified changes in the home environment explain the positive effects of the PFL program on children’s cognitive and emotional development at school entry which have been identified in previous reports of the PFL trial (ES = .72 and .50, respectively). Pregnant women were randomized into a treatment (home visits, baby massage, and parenting program, n = 115) or control (n = 118) group (trial registration: ISRCTN04631728). The home environment was assessed at 6 months, 1½, and 3 years using the Home Observation for Measurement of the Environment (responsiveness, acceptance, organization, learning material, involvement, variety). Cognitive skills were assessed at 5 years using the British Ability Scales. Emotional problems were teacher-reported at 5 years using the Short Early Development Inventory. Latent growth modeling was used to model changes in the home environment, and mediation analyses to test whether those changes explained children outcomes. Compared to controls, treatment children were exposed to more stimulating environments in terms of learning material (B = -1.62, p = 0.036) and environmental variety (B = -1.58, p = 0.009) at 6 months, but these differences faded at 3 years. Treatment families were also more likely to accept suboptimal child behaviors without using punishment (acceptance score, B = 1.49, p = 0.048) and were more organized at 3 years (B = 1.08, p = 0.033). None of the changes mediated children’s outcomes. In conclusion, we found that the program positively impacted different home environment dimensions, but these changes did not account for improvements in children’s outcomes. Exploratory analyses suggest that the impact of improvements in the home environment on child outcomes may be limited to specific groups of children. Limitations of the study include the potential lack of generalizability to other populations, the inability to assess the individual treatment components, and sample size restrictions which precluded a moderated mediation analysis.

Global test for high-dimensional mediation: Testing groups of potential mediators

We address the problem of testing whether a possibly high-dimensional vector may act as a mediator between some exposure variable and the outcome of interest. We propose a global test for mediation, which combines a global test with the intersection-union principle. We discuss theoretical properties of our approach and conduct simulation studies that demonstrate that it performs equally well or better than its competitor. We also propose a multiple testing procedure, ScreenMin, that provides asymptotic control of either familywise error rate or false discovery rate when multiple groups of potential mediators are tested simultaneously. We apply our approach to data from a large Norwegian cohort study, where we look at the hypothesis that smoking increases the risk of lung cancer by modifying the level of DNA methylation.

High dimensional mediation analysis with latent variables

We propose a model for high dimensional mediation analysis that includes latent variables. We describe our model in the context of an epidemiologic study for incident breast cancer with one exposure and a large number of biomarkers (i.e., potential mediators). We assume that the exposure directly influences a group of latent, or unmeasured, factors which are associated with both the outcome and a subset of the biomarkers. The biomarkers associated with the latent factors linking the exposure to the outcome are considered "mediators." We derive the likelihood for this model and develop an expectation-maximization algorithm to maximize an L1-penalized version of this likelihood to limit the number of factors and associated biomarkers. We show that the resulting estimates are consistent and that the estimates of the nonzero parameters have an asymptotically normal distribution. In simulations, procedures based on this new model can have significantly higher power for detecting the mediating biomarkers compared with the simpler approaches. We apply our method to a study that evaluates the relationship between body mass index, 481 metabolic measurements, and estrogen-receptor positive breast cancer.

Estimating causal effects from a randomized clinical trial when noncompliance is measured with error

Noncompliance or non-adherence to randomized treatment is a common challenge when interpreting data from randomized clinical trials. The effect of an intervention if all participants were forced to comply with the assigned treatment (i.e., the causal effect) is often of primary scientific interest. For example, in trials of very low nicotine content (VLNC) cigarettes, policymakers are interested in their effect on smoking behavior if their use were to be compelled by regulation. A variety of statistical methods to estimate the causal effect of an intervention have been proposed, but these methods, including inverse probability of compliance weighted (IPCW) estimators, assume that participants' compliance statuses are reported without error. This is an untenable assumption when compliance is based on self-report. Biomarkers (e.g., nicotine levels in the urine) may provide more reliable indicators of compliance but cannot perfectly discriminate between compliers and non-compliers. However, by modeling the distribution of the biomarker as a mixture distribution and writing the probability of compliance as a function of the mixture components, we show how the probability of compliance can be directly estimated from the data even when compliance status is unknown. To estimate the causal effect, we develop a new approach which re-weights participants by the product of their probability of compliance given the observed data and the inverse probability of compliance given confounders. We show that our proposed estimator is consistent and asymptotically normal and show that in some situations the proposed approach is more efficient than standard IPCW estimators. We demonstrate via simulation that the proposed estimator achieves smaller bias and greater efficiency than ad hoc approaches to estimating the causal effect when compliance is measured with error. We apply our method to data from a recently completed randomized trial of VLNC cigarettes.

Socioeconomic and Tobacco Mediation of Ethnic Inequalities in Mortality over Time: Repeated Census-mortality Cohort Studies, 1981 to 2011

Supplemental Digital Content is available in the text.

Background:

Racial/ethnic inequalities in mortality may be reducible by addressing socioeconomic factors and smoking. To our knowledge, this is the first study to estimate trends over multiple decades in (1) mediation of racial/ethnic inequalities in mortality (between Māori and Europeans in New Zealand) by socioeconomic factors, (2) additional mediation through smoking, and (3) inequalities had there never been smoking.

Methods:

We estimated natural (1 and 2 above) and controlled mediation effects (3 above) in census-mortality cohorts for 1981–1984 (1.1 million people), 1996–1999 (1.5 million), and 2006–2011 (1.5 million) for 25- to 74-year-olds in New Zealand, using a weighting of regression predicted outcomes.

Results:

Socioeconomic factors explained 46% of male inequalities in all three cohorts and made an increasing contribution over time among females from 30.4% (95% confidence interval = 18.1%, 42.7%) in 1981–1984 to 41.9% (36.0%, 48.0%). Including smoking with socioeconomic factors only modestly altered the percentage mediated for males, but more substantially increased it for females, for example, 7.7% (5.5%, 10.0%) in 2006–2011. A counterfactual scenario of having eradicated tobacco in the past (but unchanged socioeconomic distribution) lowered mortality for all sex-by-ethnic groups and resulted in a 12.2% (2.9%, 20.8%) and 21.2% (11.6%, 31.0%) reduction in the absolute mortality gap between Māori and Europeans in 2006–2011, for males and females, respectively.

Conclusions:

Our study predicts that, in this high-income country, reducing socioeconomic disparities between ethnic groups would greatly reduce ethnic inequalities in mortality over the long run. Eradicating tobacco would notably reduce ethnic inequalities in absolute but not relative mortality.

Med4way: a Stata command to investigate mediating and interactive mechanisms using the four-way effect decomposition

The overall effect of an exposure on an outcome, in the presence of a mediator with which the exposure may interact, can be decomposed into four components that correspond to the portion of the effect that is due: (i) to neither mediation nor interaction; (ii) to just interaction (but not mediation); (iii) to both mediation and interaction; and (iv) to just mediation (but not interaction). This four-way decomposition unifies methods to attribute effects to interactions and methods that assess mediation. We introduce the Stata command med4way to estimate the causal contrasts that arise in this decomposition. Med4way is implemented as a Stata stand-alone command requiring Stata version 10 or higher (StataCorp, College Station, TX, USA), and allows estimating the four-way decomposition using parametric regression models. Med4way can be used when the outcome is continuous, dichotomous, count or survival time, and the mediator is continuous or binary. The command accommodates cohort and case-control designs. We present two examples of application of the command to gain insight on important public health problems. In the first application, we employ med4way to investigate the role of birth outcomes in explaining the effect of maternal exposure to manganese on child neurodevelopment. In the second application, we investigate the role of stage at diagnosis in explaining income disparities in colorectal cancer survival. The command is freely available on GitHub [https://github.com/anddis/med4way] and has been published under General Public License (GPL) version 3.

Mediation analysis for common binary outcomes

Mediation analysis provides an attractive causal inference framework to decompose the total effect of an exposure on an outcome into natural direct effects and natural indirect effects acting through a mediator. For binary outcomes, mediation analysis methods have been developed using logistic regression when the binary outcome is rare. These methods will not hold in practice when a disease is common. In this paper, we develop mediation analysis methods that relax the rare disease assumption when using logistic regression. We calculate the natural direct and indirect effects for common diseases by exploiting the relationship between logit and probit models. Specifically, we derive closed-form expressions for the natural direct and indirect effects on the odds ratio scale. Mediation models for both continuous and binary mediators are considered. We demonstrate through simulation that the proposed method performs well for common binary outcomes. We apply the proposed methods to analyze the Normative Aging Study to identify DNA methylation sites that are mediators of smoking behavior on the outcome of obstructed airway function.

The mediating role of the venules between smoking and ischemic stroke

A potential mechanism by which smoking affects ischemic stroke is through wider venules, but this mediating role of wider venules has never been quantified. Here, we aimed to estimate to what extent the effect of smoking on ischemic stroke is possibly mediated by the venules via the recently developed four-way effect decomposition. This study was part of a population-based study including 9109 stroke-free persons participated in the study in 1990, 2004, or 2006 (mean age: 63.7 years; 58% women). Smoking behavior (smoking versus non-smoking) was identified by interview. Retinal venular calibers were measured semi-automatically on retinal photographs. Incident strokes were assessed until January 2016. A regression-based approach was used with venular calibers as mediator to decompose the total effect of smoking compared to non-smoking into four components: controlled direct effect (neither mediation nor interaction), pure indirect effect (mediation only), reference interaction effect (interaction only) and mediated interaction effect (both mediation and interaction). During a mean follow-up of 12.5 years, 665 persons suffered an ischemic stroke. Smoking increased the risk of developing ischemic stroke compared to non-smoking with an excess risk of 0.41 (95% confidence interval 0.10; 0.67). With retinal venules as a potential mediator, the excess relative risk could be decomposed into 77% controlled direct effect, 4% mediation only, 4% interaction only, and 15% mediated interaction. To conclude, in the pathophysiology of ischemic stroke, the effect of smoking on ischemic stroke may partly explained by changes in the venules, where there is both pure mediation and mediated interaction.

Efficiency and robustness of causal effect estimators when noncompliance is measured with error

Estimating causal effects from randomized controlled trials is often complicated due to participant noncompliance to randomized treatment. Although there are a variety of methods to estimate causal effects in the presence of noncompliance, they generally make the assumption that noncompliance is measured without error. This is frequently an untenable assumption, particularly when noncompliance is based on participant self-report. To overcome this issue, we treat compliance as an unobserved variable and show how to estimate the probability of compliance given a biomarker of treatment and the other observed data. We present inverse probability weighted estimators, regression-based estimators, and a doubly-robust augmented estimator that rely on the estimated probability of compliance rather than an indicator of compliance. We investigate the finite-sample properties of the estimators and their efficiency and robustness under correctly specified or misspecified models, and we apply the estimators to a recently completed trial of very low nicotine content cigarettes.

Quantifying an Adherence Path-Specific Effect of Antiretroviral Therapy in the Nigeria PEPFAR Program

Since the early 2000s, evidence has accumulated for a significant differential effect of first-line antiretroviral therapy (ART) regimens on human immunodeficiency virus (HIV) viral load suppression. This finding was replicated in our data from the Harvard President's Emergency Plan for AIDS Relief (PEPFAR) program in Nigeria. Investigators were interested in finding the source of these differences, i.e., understanding the mechanisms through which one regimen outperforms another, particularly via adherence. This question can be naturally formulated via mediation analysis with adherence playing the role of a mediator. Existing mediation analysis results, however, have relied on an assumption of no exposure-induced confounding of the intermediate variable, and generally require an assumption of no unmeasured confounding for nonparametric identification. Both assumptions are violated by the presence of drug toxicity. In this paper, we relax these assumptions and show that certain path-specific effects remain identified under weaker conditions. We focus on the path-specific effect solely mediated by adherence and not by toxicity and propose an estimator for this effect. We illustrate with simulations and present results from a study applying the methodology to the Harvard PEPFAR data. Supplementary materials are available online.

Estimation and Inference for the Mediation Proportion

In epidemiology, public health and social science, mediation analysis is often undertaken to investigate the extent to which the effect of a risk factor on an outcome of interest is mediated by other covariates. A pivotal quantity of interest in such an analysis is the mediation proportion. A common method for estimating it, termed the "difference method", compares estimates from models with and without the hypothesized mediator. However, rigorous methodology for estimation and statistical inference for this quantity has not previously been available. We formulated the problem for the Cox model and generalized linear models, and utilize a data duplication algorithm together with a generalized estimation equations approach for estimating the mediation proportion and its variance. We further considered the assumption that the same link function hold for the marginal and conditional models, a property which we term "g-linkability". We show that our approach is valid whenever g-linkability holds, exactly or approximately, and present results from an extensive simulation study to explore finite sample properties. The methodology is illustrated by an analysis of pre-menopausal breast cancer incidence in the Nurses' Health Study. User-friendly publicly available software implementing those methods can be downloaded from the last author's website (SAS) or from CRAN (R).

Misclassified exposure in epigenetic mediation analyses. Does DNA methylation mediate effects of smoking on birthweight?

AIMS

Assessing whether epigenetic alterations mediate associations between environmental exposures and health outcomes is increasingly popular. We investigate the impact of exposure misclassification in such investigations.

MATERIALS & METHODS

We quantify bias and false-positive rates due to exposure misclassification in mediation analysis and assess the performance of the simulation extrapolation method (SIMEX). We evaluate whether DNA-methylation mediates smoking-birth weight relationship in the Norwegian Mother and Child Study birth cohort.

RESULTS

Ignoring exposure misclassification increases type I error in mediation analysis. The direct effect is underestimated and, when the mediator is a biomarker of the exposure, as is true for smoking, the indirect effect is overestimated.

CONCLUSION

Misclassification correction plus cautious interpretation are recommended for mediation analyses in the presence of exposure misclassification.

Measurement error, time lag, unmeasured confounding: Considerations for longitudinal estimation of the effect of a mediator in randomised clinical trials

Clinical trials are expensive and time-consuming and so should also be used to study how treatments work, allowing for the evaluation of theoretical treatment models and refinement and improvement of treatments. These treatment processes can be studied using mediation analysis. Randomised treatment makes some of the assumptions of mediation models plausible, but the mediator–outcome relationship could remain subject to bias. In addition, mediation is assumed to be a temporally ordered longitudinal process, but estimation in most mediation studies to date has been cross-sectional and unable to explore this assumption. This study used longitudinal structural equation modelling of mediator and outcome measurements from the PACE trial of rehabilitative treatments for chronic fatigue syndrome (ISRCTN 54285094) to address these issues. In particular, autoregressive and simplex models were used to study measurement error in the mediator, different time lags in the mediator–outcome relationship, unmeasured confounding of the mediator and outcome, and the assumption of a constant mediator–outcome relationship over time. Results showed that allowing for measurement error and unmeasured confounding were important. Contemporaneous rather than lagged mediator–outcome effects were more consistent with the data, possibly due to the wide spacing of measurements. Assuming a constant mediator–outcome relationship over time increased precision.

Implementation and reporting of causal mediation analysis in 2015: a systematic review in epidemiological studies

Background

Causal mediation analysis is often used to understand the impact of variables along the causal pathway of an occurrence relation. How well studies apply and report the elements of causal mediation analysis remains unknown.

Methods

We systematically reviewed epidemiological studies published in 2015 that employed causal mediation analysis to estimate direct and indirect effects of observed associations between an exposure on an outcome. We identified potential epidemiological studies through conducting a citation search within Web of Science and a keyword search within PubMed. Two reviewers independently screened studies for eligibility. For eligible studies, one reviewer performed data extraction, and a senior epidemiologist confirmed the extracted information. Empirical application and methodological details of the technique were extracted and summarized.

Results

Thirteen studies were eligible for data extraction. While the majority of studies reported and identified the effects of measures, most studies lacked sufficient details on the extent to which identifiability assumptions were satisfied. Although most studies addressed issues of unmeasured confounders either from empirical approaches or sensitivity analyses, the majority did not examine the potential bias arising from the measurement error of the mediator. Some studies allowed for exposure-mediator interaction and only a few presented results from models both with and without interactions. Power calculations were scarce.

Conclusions

Reporting of causal mediation analysis is varied and suboptimal. Given that the application of causal mediation analysis will likely continue to increase, developing standards of reporting of causal mediation analysis in epidemiological research would be prudent.

Evaluation and validation of social and psychological markers in randomised trials of complex interventions in mental health: a methodological research programme

BACKGROUND

The development of the capability and capacity to evaluate the outcomes of trials of complex interventions is a key priority of the National Institute for Health Research (NIHR) and the Medical Research Council (MRC). The evaluation of complex treatment programmes for mental illness (e.g. cognitive-behavioural therapy for depression or psychosis) not only is a vital component of this research in its own right but also provides a well-established model for the evaluation of complex interventions in other clinical areas. In the context of efficacy and mechanism evaluation (EME) there is a particular need for robust methods for making valid causal inference in explanatory analyses of the mechanisms of treatment-induced change in clinical outcomes in randomised clinical trials.

OBJECTIVES

The key objective was to produce statistical methods to enable trial investigators to make valid causal inferences about the mechanisms of treatment-induced change in these clinical outcomes. The primary objective of this report is to disseminate this methodology, aiming specifically at trial practitioners.

METHODS

The three components of the research were (1) the extension of instrumental variable (IV) methods to latent growth curve models and growth mixture models for repeated-measures data; (2) the development of designs and regression methods for parallel trials; and (3) the evaluation of the sensitivity/robustness of findings to the assumptions necessary for model identifiability. We illustrate our methods with applications from psychological and psychosocial intervention trials, keeping the technical details to a minimum, leaving the reporting of the more theoretical and mathematically demanding results for publication in appropriate specialist journals.

RESULTS

We show how to estimate treatment effects and introduce methods for EME. We explain the use of IV methods and principal stratification to evaluate the role of putative treatment effect mediators and therapeutic process measures. These results are extended to the analysis of longitudinal data structures. We consider the design of EME trials. We focus on designs to create convincing IVs, bearing in mind assumptions needed to attain model identifiability. A key area of application that has become apparent during this work is the potential role of treatment moderators (predictive markers) in the evaluation of treatment effect mechanisms for personalised therapies (stratified medicine). We consider the role of targeted therapies and multiarm trials and the use of parallel trials to help elucidate the evaluation of mediators working in parallel.

CONCLUSIONS

In order to demonstrate both efficacy and mechanism, it is necessary to (1) demonstrate a treatment effect on the primary (clinical) outcome, (2) demonstrate a treatment effect on the putative mediator (mechanism) and (3) demonstrate a causal effect from the mediator to the outcome. Appropriate regression models should be applied for (3) or alternative IV procedures, which account for unmeasured confounding, provided that a valid instrument can be identified. Stratified medicine may provide a setting where such instruments can be designed into the trial. This work could be extended by considering improved trial designs, sample size considerations and measurement properties.

FUNDING

The project presents independent research funded under the MRC-NIHR Methodology Research Programme (grant reference G0900678).

Estimating and testing high-dimensional mediation effects in epigenetic studies

MOTIVATION

High-dimensional DNA methylation markers may mediate pathways linking environmental exposures with health outcomes. However, there is a lack of analytical methods to identify significant mediators for high-dimensional mediation analysis.

RESULTS

Based on sure independent screening and minimax concave penalty techniques, we use a joint significance test for mediation effect. We demonstrate its practical performance using Monte Carlo simulation studies and apply this method to investigate the extent to which DNA methylation markers mediate the causal pathway from smoking to reduced lung function in the Normative Aging Study. We identify 2 CpGs with significant mediation effects.

AVAILABILITY AND IMPLEMENTATION

R package, source code, and simulation study are available at https://github.com/YinanZheng/HIMA CONTACT: lei.liu@northwestern.edu.

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.

A unification of mediation and interaction: a 4-way decomposition

The overall effect of an exposure on an outcome, in the presence of a mediator with which the exposure may interact, can be decomposed into 4 components: (1) the effect of the exposure in the absence of the mediator, (2) the interactive effect when the mediator is left to what it would be in the absence of exposure, (3) a mediated interaction, and (4) a pure mediated effect. These 4 components, respectively, correspond to the portion of the effect that is due to neither mediation nor interaction, to just interaction (but not mediation), to both mediation and interaction, and to just mediation (but not interaction). This 4-way decomposition unites methods that attribute effects to interactions and methods that assess mediation. Certain combinations of these 4 components correspond to measures for mediation, whereas other combinations correspond to measures of interaction previously proposed in the literature. Prior decompositions in the literature are in essence special cases of this 4-way decomposition. The 4-way decomposition can be carried out using standard statistical models, and software is provided to estimate each of the 4 components. The 4-way decomposition provides maximum insight into how much of an effect is mediated, how much is due to interaction, how much is due to both mediation and interaction together, and how much is due to neither.