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Rudolph KE, Williams N, Díaz I. Using instrumental variables to address unmeasured confounding in causal mediation analysis. Biometrics 2024; 80:ujad037. [PMID: 38412300 PMCID: PMC11057970 DOI: 10.1093/biomtc/ujad037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Revised: 10/24/2023] [Accepted: 12/21/2023] [Indexed: 02/29/2024]
Abstract
Mediation analysis is a strategy for understanding the mechanisms by which interventions affect later outcomes. However, unobserved confounding concerns may be compounded in mediation analyses, as there may be unobserved exposure-outcome, exposure-mediator, and mediator-outcome confounders. Instrumental variables (IVs) are a popular identification strategy in the presence of unobserved confounding. However, in contrast to the rich literature on the use of IV methods to identify and estimate a total effect of a non-randomized exposure, there has been almost no research into using IV as an identification strategy to identify mediational indirect effects. In response, we define and nonparametrically identify novel estimands-double complier interventional direct and indirect effects-when 2, possibly related, IVs are available, one for the exposure and another for the mediator. We propose nonparametric, robust, efficient estimators for these effects and apply them to a housing voucher experiment.
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Affiliation(s)
- Kara E Rudolph
- Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, New York 10032, USA
| | - Nicholas Williams
- Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, New York 10032, USA
| | - Iván Díaz
- Division of Biostatistics, New York University Grossman School of Medicine, New York, New York 10016, USA
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Cheng C, Spiegelman D, Li F. Mediation analysis in the presence of continuous exposure measurement error. Stat Med 2023; 42:1669-1686. [PMID: 36869626 DOI: 10.1002/sim.9693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Revised: 01/06/2023] [Accepted: 02/16/2023] [Indexed: 03/05/2023]
Abstract
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.
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Affiliation(s)
- Chao Cheng
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, USA.,Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, Connecticut, USA
| | - Donna Spiegelman
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, USA.,Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, Connecticut, USA
| | - Fan Li
- Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut, USA.,Center for Methods in Implementation and Prevention Science, Yale School of Public Health, New Haven, Connecticut, USA
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Syriopoulou E, Rutherford MJ, Lambert PC. Understanding disparities in cancer prognosis: An extension of mediation analysis to the relative survival framework. Biom J 2021; 63:341-353. [PMID: 33314292 PMCID: PMC7898837 DOI: 10.1002/bimj.201900355] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2019] [Revised: 08/07/2020] [Accepted: 09/21/2020] [Indexed: 02/06/2023]
Abstract
Mediation analysis can be applied to investigate the effect of a third variable on the pathway between an exposure and the outcome. Such applications include investigating the determinants that drive differences in cancer survival across subgroups. However, cancer disparities may be the result of complex mechanisms that involve both cancer-related and other-cause mortality differences making it difficult to identify the causing factors. Relative survival, a commonly used measure in cancer epidemiology, can be used to focus on cancer-related differences. We extended mediation analysis to the relative survival framework for exploring cancer inequalities. The marginal effects were obtained using regression standardization, after fitting a relative survival model. Contrasts of interests included both marginal relative survival and marginal all-cause survival differences between exposure groups. Such contrasts include the indirect effect due to a mediator that is identifiable under certain assumptions. A separate model was fitted for the mediator and uncertainty was estimated using parametric bootstrapping. The avoidable deaths under interventions can also be estimated to quantify the impact of eliminating differences. The methods are illustrated using data for individuals diagnosed with colon cancer. Mediation analysis within relative survival allows focus on factors that account for cancer-related differences instead of all-cause differences and helps improve our understanding on cancer inequalities.
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Affiliation(s)
- Elisavet Syriopoulou
- Biostatistics Research GroupDepartment of Health SciencesUniversity of LeicesterLeicesterUK
| | - Mark J. Rutherford
- Biostatistics Research GroupDepartment of Health SciencesUniversity of LeicesterLeicesterUK
| | - Paul C. Lambert
- Biostatistics Research GroupDepartment of Health SciencesUniversity of LeicesterLeicesterUK
- Department of Medical Epidemiology and BiostatisticsKarolinska InstitutetStockholmSweden
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Abstract
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.
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Affiliation(s)
- Isabel R. Fulcher
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA
| | - Xu Shi
- Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA
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Wang W, Albert JM. Causal Mediation Analysis for the Cox Proportional Hazards Model with a Smooth Baseline Hazard Estimator. J R Stat Soc Ser C Appl Stat 2016; 66:741-757. [PMID: 28943662 DOI: 10.1111/rssc.12188] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An important problem within the social, behavioral, and health sciences is how to partition an exposure effect (e.g. treatment or risk factor) among specific pathway effects and to quantify the importance of each pathway. Mediation analysis based on the potential outcomes framework is an important tool to address this problem and we consider the estimation of mediation effects for the proportional hazards model in this paper. We give precise definitions of the total effect, natural indirect effect, and natural direct effect in terms of the survival probability, hazard function, and restricted mean survival time within the standard two-stage mediation framework. To estimate the mediation effects on different scales, we propose a mediation formula approach in which simple parametric models (fractional polynomials or restricted cubic splines) are utilized to approximate the baseline log cumulative hazard function. Simulation study results demonstrate low bias of the mediation effect estimators and close-to-nominal coverage probability of the confidence intervals for a wide range of complex hazard shapes. We apply this method to the Jackson Heart Study data and conduct sensitivity analysis to assess the impact on the mediation effects inference when the no unmeasured mediator-outcome confounding assumption is violated.
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Affiliation(s)
- Wei Wang
- Center of Biostatistics and Bioinformatics, New Guyton Research Building G562, University of Mississippi Medical Center, 2500 North State Street, Jackson, MS 39216
| | - Jeffrey M Albert
- Department of Epidemiology and Biostatistics, School of Medicine WG-82S, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106, , ,
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Abstract
Recent advances in the literature on mediation have extended from traditional linear structural equation modeling approach to causal mediation analysis using potential outcomes framework. Pearl proposed a mediation formula to calculate expected potential outcomes used in the natural direct and indirect effects definition under the key sequential ignorability assumptions. Current methods mainly focused on binary exposure variables, and in this article, this approach is further extended to settings in which continuous exposures may be of interest. Focusing on a dichotomous outcome, we give precise definitions of the natural direct and indirect effects on both the risk difference and odds ratio scales utilizing the empirical joint distribution of the exposure and baseline covariates from the whole sample analysis population. A mediation-formula based approach is proposed to estimate the corresponding causal quantities. Simulation study is conducted to assess the statistical properties of the proposed method and we illustrate our approach by applying it to the Jackson Heart Study to estimate the mediation effects of diabetes on the relation between obesity and chronic kidney disease. Sensitivity analysis is performed to assess the impact of violation of no unmeasured mediator-outcome confounder assumption.
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Abstract
In many health studies, researchers are interested in estimating the treatment effects on the outcome around and through an intermediate variable. Such causal mediation analyses aim to understand the mechanisms that explain the treatment effect. Although multiple mediators are often involved in real studies, most of the literature considered mediation analyses with one mediator at a time. In this article, we consider mediation analyses when there are causally non-ordered multiple mediators. Even if the mediators do not affect each other, the sum of two indirect effects through the two mediators considered separately may diverge from the joint natural indirect effect when there are additive interactions between the effects of the two mediators on the outcome. Therefore, we derive an equation for the joint natural indirect effect based on the individual mediation effects and their interactive effect, which helps us understand how the mediation effect works through the two mediators and relative contributions of the mediators and their interaction. We also discuss an extension for three mediators. The proposed method is illustrated using data from a randomized trial on the prevention of dental caries.
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Affiliation(s)
- Masataka Taguri
- 1 Department of Biostatistics, School of Medicine, Yokohama City University, Yokohama, Japan.,2 School of Dentistry, University of California, San Francisco, San Francisco, CA, USA
| | - John Featherstone
- 2 School of Dentistry, University of California, San Francisco, San Francisco, CA, USA
| | - Jing Cheng
- 2 School of Dentistry, University of California, San Francisco, San Francisco, CA, USA
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Jiang Z, VanderWeele TJ. When is the difference method conservative for assessing mediation? Am J Epidemiol 2015; 182:105-8. [PMID: 25944885 DOI: 10.1093/aje/kwv059] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2014] [Accepted: 09/24/2014] [Indexed: 11/14/2022] Open
Abstract
Assessment of indirect effects is useful for epidemiologists interested in understanding the mechanisms of exposure-outcome relationships. A traditional way of estimating indirect effects is to use the "difference method," which is based on regression analysis in which one adds a possible mediator to the regression model and examines whether the coefficient for the exposure changes. The difference method has been criticized for lacking a causal interpretation when it is used with logistic regression. In this article, we use the counterfactual framework to define the natural indirect effect (NIE) and assess the relationship between the NIE and the difference method. We show that under appropriate assumptions, the difference method consistently estimates the NIE for continuous outcomes and is always conservative for binary outcomes. Thus, the difference method can be used to provide evidence for the presence of mediation but not for the absence of mediation.
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Naimi AI, Kaufman JS, MacLehose RF. Mediation misgivings: ambiguous clinical and public health interpretations of natural direct and indirect effects. Int J Epidemiol 2014; 43:1656-61. [PMID: 24860122 DOI: 10.1093/ije/dyu107] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Recent methodological innovation is giving rise to an increasing number of applied papers in medical and epidemiological journals in which natural direct and indirect effects are estimated. However, there is a longstanding debate on whether such effects are relevant targets of inference in population health. In light of the repeated calls for a more pragmatic and consequential epidemiology, we review three issues often raised in this debate: (i) the use of composite cross-world counterfactuals and the need for cross-world independence assumptions; (ii) interventional vs non-interventional identifiability; and (iii) the interpretational ambiguity of natural direct and indirect effect estimates. We use potential outcomes notation and directed acyclic graphs to explain 'cross-world' assumptions, illustrate implications of this assumption via regression models and discuss ensuing issues of interpretation. We argue that the debate on the relevance of natural direct and indirect effects rests on whether one takes as a target of inference the mathematical object per se, or the change in the world that the mathematical object represents. We further note that public health questions may be better served by estimating controlled direct effects.
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Affiliation(s)
- Ashley I Naimi
- Department of Obstetrics and Gynecology and Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, QC, Canada and Division of Epidemiology and Community Health, University of Minnesota, Minneapolis, MN, USA
| | - Jay S Kaufman
- Department of Obstetrics and Gynecology and Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, QC, Canada and Division of Epidemiology and Community Health, University of Minnesota, Minneapolis, MN, USA
| | - Richard F MacLehose
- Department of Obstetrics and Gynecology and Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, QC, Canada and Division of Epidemiology and Community Health, University of Minnesota, Minneapolis, MN, USA
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Abstract
Suppose that having established a marginal total effect of a point exposure on a time-to-event outcome, an investigator wishes to decompose this effect into its direct and indirect pathways, also known as natural direct and indirect effects, mediated by a variable known to occur after the exposure and prior to the outcome. This paper proposes a theory of estimation of natural direct and indirect effects in two important semiparametric models for a failure time outcome. The underlying survival model for the marginal total effect and thus for the direct and indirect effects, can either be a marginal structural Cox proportional hazards model, or a marginal structural additive hazards model. The proposed theory delivers new estimators for mediation analysis in each of these models, with appealing robustness properties. Specifically, in order to guarantee ignorability with respect to the exposure and mediator variables, the approach, which is multiply robust, allows the investigator to use several flexible working models to adjust for confounding by a large number of pre-exposure variables. Multiple robustness is appealing because it only requires a subset of working models to be correct for consistency; furthermore, the analyst need not know which subset of working models is in fact correct to report valid inferences. Finally, a novel semiparametric sensitivity analysis technique is developed for each of these models, to assess the impact on inference, of a violation of the assumption of ignorability of the mediator.
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