Longitudinal Mediation Analysis with Time-varying Mediators and Exposures, with Application to Survival Outcomes

Abstract

In this paper, we study the effect of a time-varying exposure mediated by a time-varying intermediate variable. We consider general longitudinal settings, including survival outcomes. At a given time point, the exposure and mediator of interest are influenced by past covariates, mediators and exposures, and affect future covariates, mediators and exposures. Right censoring, if present, occurs in response to past history. To address the challenges in mediation analysis that are unique to these settings, we propose a formulation in terms of random interventions based on conditional distributions for the mediator. This formulation, in particular, allows for well-defined natural direct and indirect effects in the survival setting, and natural decomposition of the standard total effect. Upon establishing identifiability and the corresponding statistical estimands, we derive the efficient influence curves and establish their robustness properties. Applying Targeted Maximum Likelihood Estimation, we use these efficient influence curves to construct multiply robust and efficient estimators. We also present an inverse probability weighted estimator and a nested non-targeted substitution estimator for these parameters.

Exploring causality mechanism in the joint analysis of longitudinal and survival data

“…On the other hand, the focus of most existing causal mediation analysis methods is to estimate the natural direct effect (NDE) and natural indirect effect (NIE). Zheng and van der Laan 31 provided flexible nonparametric estimation of the NDE and NIE for the longitudinal exposure/mediator with the survival outcome under the sequential ignorability assumption. In the survival setting with a time-varying exposure or mediator, the interventional direct effect (IDE) and interventional indirect effect (IIE) 19 are used to generalize the definition of the NDE and NIE.…”

“…Although several papers have been published for mediation analysis on longitudinal data [17][18][19][20] and on survival data, [21][22][23][24][25][26] there is limited research on the causality in the joint analysis of longitudinal and survival data. [27][28][29][30] Joffe and Greene 29 considered causal frameworks for surrogate outcomes. However, they did not take into account the longitudinal nature of the biomarker.…”

Unraveling the Role of Nonsteroidal Antiinflammatory Drugs in the Link Between Osteoarthritis and Cardiovascular Disease via Causal Mediation Analysis: A Guide to Interpretation

“…Full utilization of repeatedly measured exposure, mediator, and confounders is an area of ongoing methodologic research . Although utilizing repeatedly measured confounders and mediator likely improves confounding control, it is not without its own challenges . Development of user‐friendly software is awaited.…”

Effect decomposition through multiple causally nonordered mediators in the presence of exposure‐induced mediator‐outcome confounding

“…In further recent work, Albert et al consider arbitrary groups of possibly inter‐related mediators sequential in time, although they prefer particular types of contrasts in estimation (eg, transitions from low to high socio‐economic status) to overcome problems with the identifiability of causal effects. Several other papers have sought to extend these methods for longitudinal mediation analysis to incorporate time‐to‐event in a survival setting …”

“…Several other papers have sought to extend these methods for longitudinal mediation analysis to incorporate time-to-event in a survival setting. [25][26][27][28][29][30][31][32][33] The structure of this paper is as follows. In Section 2, we provide a motivating example from our work in dental epidemiology.…”