Penalized models for analysis of multiple mediators

Mediation analysis attempts to determine whether the relationship between an independent variable (e.g., exposure) and an outcome variable can be explained, at least partially, by an intermediate variable, called a mediator. Most methods for mediation analysis focus on one mediator at a time, although multiple mediators can be jointly analyzed by structural equation models (SEMs) that account for correlations among the mediators. We extend the use of SEMs for the analysis of multiple mediators by creating a sparse group lasso penalized model such that the penalty considers the natural groupings of parameters that determine mediation, as well as encourages sparseness of the model parameters. This provides a way to simultaneously evaluate many mediators and select those that have the most impact, a feature of modern penalized models. Simulations are used to illustrate the benefits and limitations of our approach, and application to a study of DNA methylation and reactive cortisol stress following childhood trauma discovered two novel methylation loci that mediate the association of childhood trauma scores with reactive cortisol stress levels. Our new methods are incorporated into R software called regmed.     

New proposal to address mediation analysis interrogations by using genetic variants as instrumental variables

The application of causal mediation analysis (CMA) considering the mediation effect of a third variable is increasing in epidemiological studies; however, this requires fitting strong assumptions on confounding bias. To address this limitation, we propose an extension of CMA combining it with Mendelian randomization (MRinCMA). We applied the new approach to analyse the causal effect of obesity and diabetes on pancreatic cancer, considering each factor as potential mediator. To check the performance of MRinCMA under several conditions/scenarios, we used it in different simulated data sets and compared it with structural equation models. For continuous variables, MRinCMA and structural equation models performed similarly, suggesting that both approaches are valid to obtain unbiased estimates. When noncontinuous variables were considered, MRinCMA presented, overall, lower bias than structural equation models. By applying MRinCMA, we did not find any evidence of causality of obesity or diabetes on pancreatic cancer. With this new methodology, researchers would be able to address CMA hypotheses by appropriately accounting for the confounding bias assumption regardless of the conditions used in their studies in different settings.     

Estimation of causal mediation effects for a dichotomous outcome in multiple‐mediator models using the mediation formula

Mediators are intermediate variables in the causal pathway between an exposure and an outcome. Mediation analysis investigates the extent to which exposure effects occur through these variables, thus revealing causal mechanisms. In this paper, we consider the estimation of the mediation effect when the outcome is binary and multiple mediators of different types exist. We give a precise definition of the total mediation effect as well as decomposed mediation effects through individual or sets of mediators using the potential outcomes framework. We formulate a model of joint distribution (probit‐normal) using continuous latent variables for any binary mediators to account for correlations among multiple mediators. A mediation formula approach is proposed to estimate the total mediation effect and decomposed mediation effects based on this parametric model. Estimation of mediation effects through individual or subsets of mediators requires an assumption involving the joint distribution of multiple counterfactuals. We conduct a simulation study that demonstrates low bias of mediation effect estimators for two‐mediator models with various combinations of mediator types. The results also show that the power to detect a nonzero total mediation effect increases as the correlation coefficient between two mediators increases, whereas power for individual mediation effects reaches a maximum when the mediators are uncorrelated. We illustrate our approach by applying it to a retrospective cohort study of dental caries in adolescents with low and high socioeconomic status. Sensitivity analysis is performed to assess the robustness of conclusions regarding mediation effects when the assumption of no unmeasured mediator‐outcome confounders is violated. Copyright © 2013 John Wiley & Sons, Ltd.     

Boosting the precision of mediation analyses of randomised experiments through covariate adjustment

Analyses of randomised experiments frequently include attempts to decompose the intention‐to‐treat effect into a direct and indirect effect, mediated by given intermediaries, with the aim to shed light onto the treatment mechanism. Methods from causal mediation analysis have facilitated this by allowing for arbitrary models for the outcome and the mediator. They thereby generalise the traditional approach to direct and indirect effects, which is essentially limited to linear models. The default maximum likelihood methods make use of a model for the conditional distribution of the mediator, given treatment and baseline covariates, but are prone to bias when that model is misspecified. In randomised experiments, specification of such model can be easily avoided, but at the expense of a sometimes major efficiency loss when those baseline covariates are predictive of the mediator. In this article, we develop a compromise approach: it makes use of a model for the mediator to optimally extract information from the baseline covariate data but is insulated from the impact of misspecification of that model; it achieves this by exploiting the known randomisation probabilities. Simulation studies and the analysis of a randomised study show major efficiency gains and confirm our theoretical findings that the default methods from causal mediation analysis are sometimes, although not always, reasonably robust to model misspecification. Copyright © 2017 John Wiley & Sons, Ltd.     

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

Mediation analysis is a popular approach to examine the extent to which the effect of an exposure on an outcome is through an intermediate variable (mediator) and the extent to which the effect is direct. When the mediator is mis‐measured, the validity of mediation analysis can be severely undermined. In this paper, we first study the bias of classical, non‐differential measurement error on a continuous mediator in the estimation of direct and indirect causal effects in generalized linear models when the outcome is either continuous or discrete and exposure–mediator interaction may be present. Our theoretical results as well as a numerical study demonstrate that in the presence of non‐linearities, the bias of naive estimators for direct and indirect effects that ignore measurement error can take unintuitive directions. We then develop methods to correct for measurement error. Three correction approaches using method of moments, regression calibration, and SIMEX are compared. We apply the proposed method to the Massachusetts General Hospital lung cancer study to evaluate the effect of genetic variants mediated through smoking on lung cancer risk. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference,with application to clinical trials

To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two‐phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (Y) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y | W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. Copyright © 2013 John Wiley & Sons, Ltd.     

Centile estimation for a proportion response variable

This paper introduces two general models for computing centiles when the response variable Y can take values between 0 and 1, inclusive of 0 or 1. The models developed are more flexible alternatives to the beta inflated distribution. The first proposed model employs a flexible four parameter logit skew Student t ( logitSST ) distribution to model the response variable Y on the unit interval (0, 1), excluding 0 and 1. This model is then extended to the inflated logitSST distribution for Y on the unit interval, including 1. The second model developed in this paper is a generalised Tobit model for Y on the unit interval, including 1. Applying these two models to (1‐Y) rather than Y enables modelling of Y on the unit interval including 0 rather than 1. An application of the new models to real data shows that they can provide superior fits. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantile causal mediation analysis allowing longitudinal data

Mediation analysis has mostly been conducted with mean regression models. With this approach modeling means, formulae for direct and indirect effects are based on changes in means, which may not capture effects that occur in units at the tails of mediator and outcome distributions. Individuals with extreme values of medical endpoints are often more susceptible to disease and can be missed if one investigates mean changes only. We derive the controlled direct and indirect effects of an exposure along percentiles of the mediator and outcome using quantile regression models and a causal framework. The quantile regression models can accommodate an exposure‐mediator interaction and random intercepts to allow for longitudinal mediator and outcome. Because DNA methylation acts as a complex “switch” to control gene expression and fibrinogen is a cardiovascular factor, individuals with extreme levels of these markers may be more susceptible to air pollution. We therefore apply this methodology to environmental data to estimate the effect of air pollution, as measured by particle number, on fibrinogen levels through a change in interferon‐gamma (IFN‐γ) methylation. We estimate the controlled direct effect of air pollution on the qth percentile of fibrinogen and its indirect effect through a change in the pth percentile of IFN‐γ methylation. We found evidence of a direct effect of particle number on the upper tail of the fibrinogen distribution. We observed a suggestive indirect effect of particle number on the upper tail of the fibrinogen distribution through a change in the lower percentiles of the IFN‐γ methylation distribution.     

Sharp bounds on causal effects using a surrogate endpoint

This paper considers a problem of evaluating the causal effect of a treatment X on a true endpoint Y using a surrogate endpoint S, in the presence of unmeasured confounders between S and Y. Such confounders render the causal effect of X on Y unidentifiable from the causal effect of X on S and the joint probability of S and Y. To evaluate the causal effect of X on Y in such a situation, this paper derives closed‐form formulas for the sharp bounds on the causal effect of X on Y based on both the causal effect of X on S and the joint probability of S and Y under various assumptions. In addition, we show that it is not always necessary to observe Y to test the null causal effect of X on Y under the monotonicity assumption between X and S. These bounds enable clinical practitioners and researchers to assess the causal effect of a treatment on a true endpoint using a surrogate endpoint with minimum computational effort. Copyright © 2013 John Wiley & Sons, Ltd.     

一种新的针对多个中介变量的中介分析方法

中介分析主要用于探究自变量X与因变量Y之间的因果关系机制,将自变量X与因变量Y之间的因果路径进行分解,判断中介变量M是否在其因果路径中起作用及其作用大小。经典的中介分析方法一般仅针对单一中介变量。本文介绍了一种新的针对多个中介变量的中介分析方法。     

A sufficient cause based approach to the assessment of mediation

The minimal sufficient cause (MSC) model, also known as the sufficient component cause model, has been used to facilitate understanding of several key concepts in epidemiology. To improve the understanding of mediation, we introduce a causal model for mediation that is grounded in the MSC approach. First, we describe an unbiased model for mediation, to clarify the causal meaning of previously described indirect effects. Through the use of potential outcomes and response types, we express each indirect (and direct) effect in terms of component causes within the MSC model. Second, we use an MSC-based model to illustrate a common cause of the mediator and outcome, i.e. a confounder of the mediator–outcome relationship. By describing this potential source of bias within the MSC-based model, important complexities are noted that impact the magnitude of plausible confounding. In conclusion, an MSC-based approach leads to several important insights concerning the interpretation of indirect and direct effects, as well as the potential sources of bias in mediation analysis.     

Multilevel modeling versus cross‐sectional analysis for assessing the longitudinal tracking of cardiovascular risk factors over time

Correlated data are obtained in longitudinal epidemiological studies, where repeated measurements are taken on individuals or groups over time. Such longitudinal data are ideally analyzed using multilevel modeling approaches, which appropriately account for the correlations in repeated responses in the same individual. Commonly used regression models are inappropriate as they assume that measurements are independent. In this tutorial, we use multilevel modeling to demonstrate its use for analysis of correlated data obtained from serial examinations on individuals. We focus on cardiovascular epidemiological research where investigators are often interested in quantifying the relations between clinical risk factors and outcome measures (X and Y, respectively), where X and Y are measured repeatedly over time, for example, using serial observations on participants attending multiple examinations in a longitudinal cohort study. For instance, it may be of interest to evaluate the relations between serial measures of left ventricular mass (outcome) and of its potential determinants (i.e., body mass index and blood pressure), both of which are measured over time. In this tutorial, we describe the application of multilevel modeling to cardiovascular risk factors and outcome data (using serial echocardiographic data as an example of an outcome). We suggest an analytical approach that can be implemented to evaluate relations between any potential outcome of interest and risk factors, including assessment of random effects and nonlinear relations. We illustrate these steps using echocardiographic data from the Framingham Heart Study with SAS PROC MIXED. Copyright © 2013 John Wiley & Sons, Ltd.     

Who really gets strep sore throat? Confounding and effect modification of a time‐varying exposure on recurrent events

Unmeasured confounding is the fundamental obstacle to drawing causal conclusions about the impact of an intervention from observational data. Typically, covariates are measured to eliminate or ameliorate confounding, but they may be insufficient or unavailable. In the special setting where a transient intervention or exposure varies over time within each individual and confounding is time constant, a different tack is possible. The key idea is to condition on either the overall outcome or the proportion of time in the intervention. These measures can eliminate the unmeasured confounding either by conditioning or by use of a proxy covariate. We evaluate existing methods and develop new models from which causal conclusions can be drawn from such observational data even if no baseline covariates are measured. Our motivation for this work was to determine the causal effect of Streptococcus bacteria in the throat on pharyngitis (sore throat) in Indian schoolchildren. Using our models, we show that existing methods can be badly biased and that sick children who are rarely colonized have a high probability that the Streptococcus bacteria are causing their disease. Published 2016. This article is a U.S. Government work and is in the public domain in the USA     

Mediation analysis in a case-control study when the mediator is a censored variable

Mediation analysis is an approach for assessing the direct and indirect effects of an initial variable on an outcome through a mediator. In practice, mediation models can involve a censored mediator (eg, a woman's age at menopause). The current research for mediation analysis with a censored mediator focuses on scenarios where outcomes are continuous. However, the outcomes can be binary (eg, type 2 diabetes). Another challenge when analyzing such a mediation model is to use data from a case-control study, which results in biased estimations for the initial variable-mediator association if a standard approach is directly applied. In this study, we propose an approach (denoted as MAC-CC) to analyze the mediation model with a censored mediator given data from a case-control study, based on the semiparametric accelerated failure time model along with a pseudo-likelihood function. We adapted the measures for assessing the indirect and direct effects using counterfactual definitions. We conducted simulation studies to investigate the performance of MAC-CC and compared it to those of the naïve approach and the complete-case approach. MAC-CC accurately estimates the coefficients of different paths, the indirect effects, and the proportions of the total effects mediated. We applied the proposed and existing approaches to the mediation study of genetic variants, a woman's age at menopause, and type 2 diabetes based on a case-control study of type 2 diabetes. Our results indicate that there is no mediating effect from the age at menopause on the association between the genetic variants and type 2 diabetes.     

Inverse odds ratio‐weighted estimation for causal mediation analysis

An important scientific goal of studies in the health and social sciences is increasingly to determine to what extent the total effect of a point exposure is mediated by an intermediate variable on the causal pathway between the exposure and the outcome. A causal framework has recently been proposed for mediation analysis, which gives rise to new definitions, formal identification results and novel estimators of direct and indirect effects. In the present paper, the author describes a new inverse odds ratio‐weighted approach to estimate so‐called natural direct and indirect effects. The approach, which uses as a weight the inverse of an estimate of the odds ratio function relating the exposure and the mediator, is universal in that it can be used to decompose total effects in a number of regression models commonly used in practice. Specifically, the approach may be used for effect decomposition in generalized linear models with a nonlinear link function, and in a number of other commonly used models such as the Cox proportional hazards regression for a survival outcome. The approach is simple and can be implemented in standard software provided a weight can be specified for each observation. An additional advantage of the method is that it easily incorporates multiple mediators of a categorical, discrete or continuous nature. Copyright © 2013 John Wiley & Sons, Ltd.     

Invited commentary: pushing the mediation envelope

The very insightful and clear paper by VanderWeele and Vansteelandt in this issue of the Journal (Am J Epidemiol. 2010;172(12):1339-1348) bridges the gap between biostatistics methodologists focusing on causal methods for mediation analyses and the practitioners of mediational analyses to the benefit of both groups. In an effort to continue the bridging of this gap, this invited commentary relates the important issue of "natural direct effects" to the well-known epidemiologic method of direct standardization. Additionally, attention is paid to the importance of temporal sequencing to help substantiate the mediation relations among the exposure, mediation, and outcome. A crucial mathematical distortion under the logistics model, called "absence of collapsibility," is noted in motivating VanderWeele and Vansteelandt's use of the log-linear model for comparing the effect of exposure adjusted for the mediator with the effect of exposure unadjusted for the mediator. It is also noted that this issue applies to one approach to assessing confounding. Finally, some issues are raised for consideration when testing the interaction between the exposure and mediator before assessing mediation.     

The mediating effect of work–life interference on the relationship between work-time control and depressive and musculoskeletal symptoms

Objectives:Evidence shows that work-time control (WTC) affects health but underlying mechanisms are still unclear. Work–life interference (WLI) might be a step on the causal pathway. The present study examined whether WLI mediates effects on mental and physical health and contrasted these to other causal pathways.Methods:Four biennial waves from the Swedish Longitudinal Occupational Survey of Health (SLOSH, N=26 804) were used. Cross-lagged analyses were conducted to estimate if WLI mediated effects from WTC (differentiating between control over daily hours and time off) to subsequent depressive and musculoskeletal symptoms. Other causal directions (reversed mediation, direct and reversed direct effects) and robustness of mediation (by including covariates) were examined.Results:WLI partially mediated the relationship of WTC (control over daily hours/time off) with both health outcomes. Indirect effect estimates were small for depressive symptoms (-0.053 for control over time off and -0.018 for control over daily hours) and very small for musculoskeletal symptoms (-0.007 and -0.003, respectively). While other causal directions were generally weaker than causal mediational pathways, they played a larger role for musculoskeletal compared to depressive symptoms. Estimates relating to control over time off were in general larger than for control over daily hours.Conclusions:Our results suggest that WLI mediates part of the effect from WTC to mental/musculoskeletal symptoms, but small estimates suggest that (i) WTC plays a small but consistent role in effects on health and (ii) particularly regarding musculoskeletal disorders, other causal directions and mediators need to be further examined.     

Six-way decomposition of causal effects: Unifying mediation and mechanistic interaction

The sufficient component cause (SCC) model and counterfactual model are two common methods for causal inference, each with their own advantages: the SCC model allows the mechanistic interaction to be detailed, whereas the counterfactual model features a systemic framework for quantifying causal effects. Hence, integrating the SCC and counterfactual models may facilitate the conceptualization of causation. Based on the marginal SCC (mSCC) model, we propose a novel counterfactual mSCC framework that includes the steps of definition, identification, and estimation. We further propose a six-way effect decomposition for assessing mediation and the mechanistic interaction. The results demonstrate that when all variables are binary, the six-way decomposition is an extension of four-way decomposition and that without agonism, the six-way decomposition is reduced to four-way decomposition. To illustrate the utility of the proposed decomposition, we apply it to a Taiwanese cohort to examine the mechanism of hepatitis C virus (HCV)-induced hepatocellular carcinoma (HCC) with liver inflammation measured by alanine aminotransferase (ALT) as a mediator. Among the HCV-induced HCC cases, 62.27% are not explained by either mediation or interaction in relation to ALT; 9.32% are purely mediated by ALT; 16.53% are caused by the synergistic effect of HCV and ALT; and 9.31% are due to the mediated synergistic effect of HCV and ALT. In summary, we introduce an SCC model framework based on counterfactual theory and detail the required identification assumptions and estimation procedures; we also propose a six-way effect decomposition to unify mediation and mechanistic interaction analyses.     

The estimation of average hazard ratios by weighted Cox regression

Often the effect of at least one of the prognostic factors in a Cox regression model changes over time, which violates the proportional hazards assumption of this model. As a consequence, the average hazard ratio for such a prognostic factor is under‐ or overestimated. While there are several methods to appropriately cope with non‐proportional hazards, in particular by including parameters for time‐dependent effects, weighted estimation in Cox regression is a parsimonious alternative without additional parameters. The methodology, which extends the weighted k‐sample logrank tests of the Tarone‐Ware scheme to models with multiple, binary and continuous covariates, has been introduced in the nineties of the last century and is further developed and re‐evaluated in this contribution. The notion of an average hazard ratio is defined and its connection to the effect size measure P(X<Y) is emphasized. The suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference. A Monte Carlo study confirms the satisfactory performance. Advantages of the approach are exemplified by comparing standard and weighted analyses of an international lung cancer study. SAS and R programs facilitate application. Copyright © 2009 John Wiley & Sons, Ltd.     

Mental representation of self in relationships indirectly affects young Black women’s engagement in risky sexual behaviors through psychosocial HIV/STI risk factors

Black females are disproportionately affected by human immunodeficiency virus (HIV)/sexually transmitted infections (STIs), though individual-level sexual risk factors do not appear to explain racial/ethnic HIV incidence rate disparities. The current study examined the roles of attachment representations, working models of self and others, with psychosocial risk factors related to population-level sexual network features in association with risky sexual behaviors. A total of 560 Black emerging adult females (M age = 20.58, SD = 1.89) enrolling in a behavioral HIV prevention intervention trial completed the baseline assessment used in the current analyses. A series of multiple mediator models examined indirect effects of working models of self and others on sexual risk engagement through the following psychosocial HIV/STI risk factors: (a) partner communication self-efficacy, (b) fear of condom negotiation, (c) peer norms for risky sexual behavior, (d) partner trust and (e) sex-related alcohol expectancies. Results indicated an indirect effect of working model of self on the following: condom use with boyfriend/main partner through peer norms for risky sex (ab = .08, 95% CI [.02, .17]), any alcohol use prior to sex through peer norms for risky sex (ab = ?.06, 95% CI [?.12, ?.02]) and alcohol use prior to sex through sex-related alcohol expectancies (ab = ?.13, 95% CI [?.21, ?.05]). Findings provided evidence of a direct association between working model of self and each psychosocial HIV/STI risk factor included in the mediation models. Working model of self may help identify Black females at elevated risk for HIV/STI through these psychosocial risk factors.