Mediation Analyses and Causal Inferences

Mediation analysis has been comprehensively studied for independent data but relatively little work has been done for correlated data, especially for the increasingly adopted stepped wedge cluster randomized trials (SW-CRTs). Motivated by challenges in underlying the effect mechanisms in pragmatic and implementation science clinical trials, we develop new methods for mediation analysis in SW-CRTs. Specifically, based on a linear and generalized linear mixed models, we demonstrate how to estimate the natural indirect effect and mediation proportion in typical SW-CRTs with four data types, including both continuous and binary mediators and outcomes. Furthermore, to address the emerging challenges in exposure-time treatment effect heterogeneity, we derive the mediation expressions in SW-CRTs when the total effect varies as a function of the exposure time. The cluster jackknife approach is considered for inference across all data types and treatment effect structures. We conduct extensive simulations to evaluate the finite-sample performances of proposed mediation estimators and demonstrate the proposed approach in a real data example. A R package mediateSWCRT has been developed. 

Causal mediation analysis is a popular tool for studying complicated causal dependence between multiple variables. We investigate the extent to which the effect of an exposure, X, on a response, Y, is mediated by a third variable, M. One common approach involves fitting regression models and identifying mediation effects with functions of the regression parameters. Unfortunately, uncertainty quantification for these mediation effects is often non-trivial in even simple settings. Existing methods in the literature tend to rely on intensive computation, and are thus slow.
We propose an analytical method for obtaining standard errors of estimated mediation effects using the δ-method. We compare the performance of our method with its main competitor using Monte Carlo studies and analysis of a dataset on adherence to pandemic lockdown measures across 11 countries. 

Mediation analysis is increasingly used to identify omics molecules that mediate the relationship between an exposure and an outcome. Since high-dimensional omics data often exhibit clustered structures and biologically defined sets, group selection may improve detection power and interpretability. We propose a group-guided approach that leverages biologically informed omics groups, followed by sparse group lasso for mediator selection, allowing selection within and between groups. We adapted and implemented de-biased beta coefficients and variance estimates for inference. In simulations, de-biased sparse group lasso provided more accurate mediation effect estimates than sparse group lasso, lasso, and one-by-one regression. Our method also performed well under reasonable group misspecification, particularly when mediation effects were small. We will apply this approach to Framingham Heart Study data to demonstrate its utility. 

Treatment interference occurs when the treatment status of one unit affects the response of another unit. Substantial work has investigated various methods for modeling treatment interference and the impact of interference on units' responses.
The efficacy of these methods depends largely on the plausibility of the assumptions used for these methods. However, there has been little work at developing rigorous tests for these assumptions.
In this talk, we review various models of response for interference models under the Neyman-Rubin potential outcomes framework. We then outline certain assumptions that may be made on responses and the impact of these assumptions when estimating causal quantities. We then develop a framework for testing assumptions related to the weak interaction between direct and indirect effects. These assumptions require that the change of response due to a unit receiving treatment does not depend on which of that units' neighbors receive treatment. We evaluate the efficacy of these tests through a thorough simulation study. 

Scientists regularly pose questions about treatment effects on outcomes conditional on a post-treatment event. However, defining, identifying, and estimating causal effects conditional on post-treatment events requires care, even in perfectly executed randomized experiments. Recently, the conditional separable effect (CSE) was proposed as an interventionist estimand that corresponds to scientifically meaningful questions in these settings. However, while being a single-world estimand, which can be queried experimentally, existing identification results for the CSE require no unmeasured confounding between the outcome and post-treatment event. This assumption can be violated in many applications. In this work, we address this concern by developing new identification and estimation results for the CSE in the presence of unmeasured confounding. We establish nonparametric identification of the CSE in observational and experimental settings when time-varying confounders are present, and certain proxy variables are available for hidden common causes of the post-treatment event and outcome. For inference, we characterize an influence function for the CSE under a semiparametric model in which nuisance functions are a priori unrestricted. Moreover, we develop a consistent, asymptotically linear, and locally semiparametric efficient estimator of the CSE using modern machine learning theory. We illustrate our framework with simulation studies and a real-world cancer therapy trial.  

Understanding how an exposure influences an outcome through mediators is essential in medical and epidemiological research, especially when mediators vary over time and influence each other reciprocally. This complex condition, termed causally ordered multiple time-varying mediation, frequently appears in chronic diseases. For instance, in COPD, low lung capacity initiates a vicious cycle where dyspnea and physical inactivity reinforce each other, progressively worsening patients' quality of life. However, existing mediation methods often focus on single time-varying mediators or fail to fully decompose the total effect, making them inadequate for capturing such feedback dynamics. To address these limitations, we propose a novel framework that decomposes the total effect into path-specific effects (PSEs) for each mediator, offering a precise and clinically relevant analysis. Our approach ensures that the sum of these PSEs equals the total effect, resolving interpretative issues in prior methods. For estimation, we derive efficient influence function and employ targeted maximum likelihood estimation, which combines flexibility with strong statistical properties, including multiple robustness, asymptotic normality and efficiency. Our framework offers powerful solutions for analyzing complex mediation mechanisms in longitudinal data, with substantial applications in clinical research.