Selection of mediators and dependence structure for high-dimensional mediation analysis

Commentary: Mediation Analyses in the Real World.

Using a sequential conditional independence assumption, this paper discusses fully nonparametric estimation of natural direct and indirect causal effects in causal mediation analysis based on inverse probability weighting. We propose estimators of the average indirect effect of a binary treatment, which operates through intermediate variables (or mediators) on the causal path between the treatment and the outcome, as well as the unmediated direct effect. In a first step, treatment propensity scores given the mediator and observed covariates or given covariates alone are estimated by nonparametric series logit estimation. In a second step, they are used to reweigh observations in order to estimate the effects of interest. We establish root-n consistency and asymptotic normality of this approach as well as a weighted version thereof. The latter allows evaluating effects on specific subgroups like the treated, for which we derive the asymptotic properties under estimated propensity scores. We also provide a simulation study and an application to an information intervention about male circumcisions.

High-dimensional mediation analysis is an extension of unidimensional mediation analysis that includes multiple mediators, and increasingly it is being used to evaluate the indirect omics-layer effects of environmental exposures on health outcomes. Analyses involving high-dimensional mediators raise several statistical issues. Although many methods have recently been developed, no consensus has been reached about the optimal combination of approaches to high-dimensional mediation analyses. We developed and validated a method for high-dimensional mediation analysis (HDMAX2) and applied it to evaluate the causal role of placental DNA methylation in the pathway between exposure to maternal smoking (MS) during pregnancy and gestational age (GA) and birth weight of the baby at birth. HDMAX2 combines latent factor regression models for epigenome-wide association studies with tests for mediation and considers CpGs and aggregated mediator regions (AMRs). HDMAX2 was carefully evaluated using simulated data and compared to state-of-the-art multidimensional epigenetic mediation methods. Then, HDMAX2 was applied to data from 470 women of the Etude des Déterminants pré et postnatals du développement de la santé de l'Enfant (EDEN) cohort. HDMAX2 demonstrated increased power in comparison with state-of-the-art multidimensional mediation methods and identified several AMRs not identified in previous mediation analyses of exposure to MS on birth weight and GA. The results provided evidence for a polygenic architecture of the mediation pathway with a posterior estimate of the overall indirect effect of CpGs and AMRs equal to lower birth weight representing 32.1% of the total effect [standard deviation ]. HDMAX2 also identified AMRs having simultaneous effects both on GA and on birth weight. Among the top hits of both GA and birth weight analyses, regions located in COASY, BLCAP, and ESRP2 also mediated the relationship between GA and birth weight, suggesting reverse causality in the relationship between GA and the methylome. HDMAX2 outperformed existing approaches and revealed an unsuspected complexity of the potential causal relationships between exposure to MS and birth weight at the epigenome-wide level. HDMAX2 is applicable to a wide range of tissues and omic layers. https://doi.org/10.1289/EHP11559.

Mediation analysis is an important statistical method in prevention research, as it can be used to determine effective intervention components. Traditional mediation analysis defines direct and indirect effects in terms of linear regression coefficients. It is unclear how these traditional effects are estimated in settings with binary variables. An important recent methodological advancement in the mediation analysis literature is the development of the causal mediation analysis framework. Causal mediation analysis defines causal effects as the difference between two potential outcomes. These definitions can be applied to any mediation model to estimate natural direct and indirect effects, including models with binary variables and an exposure–mediator interaction. This paper aims to clarify the similarities and differences between the causal and traditional effect estimates for mediation models with a binary mediator and a binary outcome. Causal and traditional mediation analyses were applied to an empirical example to demonstrate these similarities and differences. Causal and traditional mediation analysis provided similar controlled direct effect estimates, but different estimates of the natural direct effects, natural indirect effects, and total effect. Traditional mediation analysis methods do not generalize well to mediation models with binary variables, while the natural effect definitions can be applied to any mediation model. Causal mediation analysis is therefore the preferred method for the analysis of mediation models with binary variables.

Based on the application of an aggregate reproductive model, this study demonstrates that a small number of intermediate fertility variables are responsible for most of the variation in fertility levels of populations. Four variables--proportion married, contraception, induced abortion, and postpartum infecundability--are generally the most important determinants of fertility; the other intermediate factors are of less interest except in unusual circumstances. These four factors explain 96 percent of the variance in the total fertility rate in a sample of 41 populations that include developing and developed countries as well as historical populations. In the last section, the average fertility effect of the principal intermediate fertility variables is estimated for groups of contemporary populations with different total fertility rates.

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.

SAS Macro for Causal Mediation Analysis with Survival Data

A large institutional literature has been concerned with restructuring the banking system in such a way as to decrease uncontrolled variation in the money supply. Some advocate this restructuring as a means of getting increased control over an target variable; apparently they reason that tighter control of an intermediate target variable will ultimately lead to better control of target variables such as inflation or unemployment. More recently, control theorists have acknowledged the fact that monetary authorities do not exert direct control over the money supply or interest rates, and a number of control engineering studies have been concerned with the optimal control of various intermediate financial variables. Common to all of this literature (and perhaps current FOMC policy making as well) would appear to be the basic premise that the optimal control problem can be divided into two separate control problems that are solved sequentially: First, in the control problem, one pretends that the intermediate variables are set directly and finds the intermediate variable path (called the intermediate target path) that will make the final variables track their target path as well as possible. Then, in the control problem, one finds the path for the actual instruments of monetary policy that will make the intermediate variables track the intermediate target path as well as possible. The purpose of this note is to show that this basic premise is not generally valid, that the second step in the procedure constitutes an improper specification of the intermediate control problem, and that the intermediate control problem, properly specified, is fundamentally different from the standard control problem. Two examples will illustrate situations in which the two-step procedure described above leads to an incorrect solution, and the difference between standard and properly specified intermediate control problems will be characterized. Both examples will be constructed within a very simple setting: The relationships between the true instruments of monetary policy and the intermediate variable, which is taken to be the money supply M, will be viewed as a black box generating the random variable M. The monetary authority will be assumed to be able to control both the mean and the variance of the random variable emanating from the black box by judicious setting of its true instruments. That is, letting M = M + m, where m is a random variable with zero mean and variance 2, the monetary

We provide an overview of regression-based causal mediation analysis in the field of traumatic stress and guidance on how to conduct mediation analysis using our R package regmedint. We discuss the causal interpretations of the quantities that causal mediation analysis estimates, including total, direct, and indirect effects, especially when the interaction between exposure and mediator is permitted. We discuss the assumptions that must be fulfilled for mediation analyses to validly estimate these causal quantities, discuss suitable study designs for assessing mediation, and describe how causal mediation analysis differs from traditional methods of mediation. To illustrate how to conduct and interpret mediation analysis using our R package regmedint, we use data from a published longitudinal study to assess the extent to which children's externalizing behavior mediates changes in parental negative feelings during the COVID-19 lockdown. We compare the results to those obtained using traditional methods, thus illustrating the importance of accounting for exposure-mediator interaction when an interaction may be present. When the exposure and the mediator interact, traditional methods can provide estimates of direct and indirect effects that differ from those provided by more flexible causal mediation methods. When the exposure and the mediator do not interact, traditional methods and causal mediation method may estimate similar direct and indirect effects depending on the model specification. In contrast to traditional methods of mediation analysis, regression-based causal mediation methods seek to estimate specific interventional quantities, not mere associations, and the causal methods explicitly allow for exposure-mediator interactions. We recommend using these methods by default rather than using more restrictive traditional methods. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Background High-dimensional mediation analysis is an extension of unidimensional mediation analysis that includes multiple mediators, and is increasingly used in environmental epidemiology to evaluate the indirect epigenetic effects of environmental exposures on health outcomes. However, analyses involving high-dimensional mediators raise several statistical issues. While many methods have recently been developed to tackle those issues, no consensus has been reached about the optimal combination of approaches. Methods We developed HDMAX2, a new multi-step approach to mediation that combines latent factor regression models for epigenome-wide association studies with max-squared tests for mediation, and considers CpGs and aggregated mediator regions (AMR). HDMAX2 was carefully evaluated on simulated data, and compared to state-of-the- art multi-dimensional epigenetic mediation methods. Then it was applied to assess the indirect effects of exposure to maternal smoking (MS) on term birth weight (BW) and gestational age (GA) at delivery in a study of 470 women from the EDEN cohort. Results HDMAX2 resulted in increased power compared to state-of-the-art multi-dimensional mediation methods, and identified several AMRs not identified in previous mediation analyses of exposure to MS on BW and GA. The results provided evidence for a polygenic architecture of the causal pathway with an overall indirect effect of CpGs and AMRs of 44.5g lower BW (32.1% of the total effect size). HDMAX2 also identified AMRs having simultaneous effects both on GA and BW. Among the top hits of both GA and BW analyses, regions located in COASY, BLCAP and ESRP2 also mediated the relationship between GA on BW, suggesting a reverse causality in the relationship between GA and the methylome. Discussion This study brought up several statistical improvements of high-dimensional mediation analyses, which revealed an unsuspected complexity of the causal relationships between exposure to MS and BW at the epigenome-wide level. Mediation; high dimension; causal inference; epigenetics; DNA methylation; pregnancy

To the Editor: Previous work on measurement error in mediation analysis has focused on mismeasured mediators.1–4 Here, we consider mediation analysis with a mismeasured outcome. Let A denote an exposure, M denote a mediator, Y denote an outcome of interest, and C denote a vector of covariates. Let and denote the value of the outcome and mediator that would have been observed if the exposure A had been set to level a. Let denote the value of the outcome that would have been observed if the treatment and the mediator had been set to levels a and m, respectively. The average total effect, conditional on , comparing exposure levels a with , is defined by . The controlled direct effect (CDE), conditional on , comparing the effect of the exposure levels a and a' while fixing the mediator at level m, is defined by . The natural direct effect (NDE), conditional on c, comparing the effect of the exposure levels a and a' while fixing the mediator to the level it would have naturally been under some reference condition for the exposure, , is defined by . The natural indirect effect (NIE), conditional on C = c, comparing the effect of the mediator at levels and while fixing the exposure at level a, is defined by . 5,6 Let (A B|C) denote that A is independent of B conditional on C. The following 4 confounding assumptions suffice to identify the NDE and NIE: conditioning on covariates C, there is no unmeasured confounding of (1) the exposure–outcome relationship (Ya A|C), (2) the mediator–outcome relationship (Yam M|C,A), (3) the exposure–mediator relationship (Ma A|C), and (4) there are no mediator–outcome confounders affected by the exposure (Yam Ma'|C). Under these assumptions, we can obtain the formulae for the CDE, NDE, and NIE as follows. Now suppose Y is subject to misclassification and let Y* denote the observed outcome. Suppose We assume that the misclassification is nondifferential, ie, . We then have that U is independent of A, M, and C. The naive estimators use the observed outcome instead of the true outcome to calculate the direct and indirect effects, denoted by , , and , respectively. We can obtain that The estimates thus depend on the form of E(U|Y). Under classical measurement error = 0, which means that the misclassification is completely random, the naive estimators give consistent estimates of the direct and indirect effects. However, we can do correction under other forms of measurement error when is specified. For a binary outcome, the probability of misclassification can be characterized by sensitivity and specificity . We assume that , which is plausible since the observed outcome is more likely to be 1 (or 0) if the true outcome is 1 (or 0). We again assume nondifferential measurement error so that and we can obtain that Substituting the above formula in (1) to (3), we can obtain the following Because we have that the naive estimators estimate both the direct and indirect effects toward the null. We can furthermore get corrected estimates and confidence intervals by dividing the estimate and both limits of the confidence interval of the naive estimator by for the CDE, the NDE, and the NIE. Also because the correction factor is the same for the NDE and the NIE, the proportion-mediated measures will not be biased by nondifferential misclassification of the outcome. This conclusion enables us to draw qualitative conclusions in practice, even when we cannot observe the true outcome. For example, if our estimate of the indirect effect is positive using the observed outcome, we can conclude that our estimate of the true natural indirect effect is positive, ie, mediation is present. On the other hand, if the naive estimator is zero, the estimate of the true natural indirect effect will also be zero, indicating the absence of mediation. Similar results hold with parametric models and it is straightforward to implement an expectation maximization correction algorithm. See eAppendix (https://links.lww.com/EDE/A850) for details. Zhichao Jiang School of Mathematical Sciences Peking University Beijing, China [email protected] Tyler J. VanderWeele Departments of Epidemiology and Biostatistics Harvard School of Public Health Boston, MA

SummaryStatistical aspects of causality are reviewed in simple form and the impact of recent work discussed. Three distinct notions of causality are set out and implications for densities and for linear dependencies explained. The importance of appreciating the possibility of effect modifiers is stressed, be they intermediate variables, background variables or unobserved confounders. In many contexts the issue of unobserved confounders is salient. The difficulties of interpretation when there are joint effects are discussed and possible modifications of analysis explained. The dangers of uncritical conditioning and marginalization over intermediate response variables are set out and some of the problems of generalizing conclusions to populations and individuals explained. In general terms the importance of search for possibly causal variables is stressed but the need for caution is emphasized.

Background: High dimensional mediation analysis is frequently conducted to explore the role of epigenetic modifiers between exposure and health outcome. However, the issue of high dimensional mediation analysis with unmeasured confounders for survival analysis in observational study has not been well solved.Methods: In this study, we proposed an instrumental variable based approach for high dimensional mediation analysis with unmeasured confounders in survival analysis for epigenetic study. We used the Sobel‘s test, the Joint test, and the Bootstrap method to test the mediation effect. A comprehensive simulation study was conducted to decide the best test strategy. An empirical study based on DNA methylation data of lung cancer patients was conducted to illustrate the performance of the proposed method.Results: Simulation study suggested that the proposed method performed well in the identifying mediating factors. The estimation of the mediation effect by the proposed approach is also reliable with less bias compared with the classical approach. In the empirical study, we identified two DNA methylation signatures including cg21926276 and cg26387355 with a mediation effect of 0.226 (95%CI: 0.108-0.344) and 0.158 (95%CI: 0.065-0.251) between smoking and lung cancer using the proposed approach.Conclusion: The proposed method obtained good performance in simulation and empirical studies, it could be an effective statistical tool for high dimensional mediation analysis.

Mendelian randomization (MR) assesses the total effect of exposure on outcome. With the rapidly increasing availability of summary statistics from genome-wide association studies (GWASs), MR leverages existing summary statistics and is widely used to study the causal effects among complex traits and diseases. The total effect in the population is a sum of indirect and direct effects. For complex disease outcomes with complicated etiologies, and/or for modifiable exposure traits, there may exist more than one pathway between exposure and outcome. The direct effect and the indirect effect via a mediator of interest could be of opposite directions, and the total effect estimates may not be informative for treatment and prevention decision-making or may be even misleading for different subgroups of patients. Causal mediation analysis delineates the indirect effect of exposure on outcome operating through the mediator and the direct effect transmitted through other mechanisms. However, causal mediation analysis often requires individual-level data measured on exposure, outcome, mediator and confounding variables, and the power of the mediation analysis is restricted by sample size. In this work, motivated by a study of the effects of atrial fibrillation (AF) on Alzheimer's dementia, we propose a framework for Integrative Mendelian randomization and Mediation Analysis (IMMA). The proposed method integrates the total effect estimates from MR analyses based on large-scale GWASs with the direct and indirect effect estimates from mediation analysis based on individual-level data of a limited sample size. We introduce a series of IMMA models, under the scenarios with or without exposure-mediator interaction and/or study heterogeneity. The proposed IMMA models improve the estimation and the power of inference on the direct and indirect effects in the population, as well as the characterization of the variation of effects. Our analyses showed a significant positive direct effect of AF on Alzheimer's dementia risk not through the use of the oral anticoagulant treatment and a significant indirect effect of AF-induced anticoagulant treatment in reducing Alzheimer's dementia risk. The results suggested potential Alzheimer's dementia risk prediction and prevention strategies for AF patients, and paved the way for future re-evaluation of anticoagulant treatment guidelines for AF patients. A sensitivity analysis was conducted to assess the sensitivity of the conclusions to a key assumption of the IMMA approach.

Understanding mechanisms: opening the “black box” in observational studies