Estimation and Inference for the Mediation Effect in a Time-varying Mediation Model

TL;DR

This paper extends traditional mediation analysis to account for time-varying effects using a two-step estimation approach and confidence bands, demonstrated through simulations and real data from a smoking cessation study.

Contribution

It introduces a novel method for estimating and inferring time-varying mediation effects in longitudinal data, addressing a gap in existing analysis techniques.

Findings

Proposed procedures perform well in simulation studies.

Confidence bands accurately capture the true mediation effect.

Applied method successfully to real-world smoking cessation data.

Abstract

Traditional mediation analysis typically examines the relations among an intervention, a time-invariant mediator, and a time-invariant outcome variable. Although there may be a direct effect of the intervention on the outcome, there is a need to understand the process by which the intervention affects the outcome (i.e. the indirect effect through the mediator). This indirect effect is frequently assumed to be time-invariant. With improvements in data collection technology, it is possible to obtain repeated assessments over time resulting in intensive longitudinal data. This calls for an extension of traditional mediation analysis to incorporate time-varying variables as well as time-varying effects. In this paper, we focus on estimation and inference for the time-varying mediation model, which allows mediation effects to vary as a function of time. We propose a two-step approach to estimate the time-varying mediation effect. Moreover, we use a simulation based approach to derive the corresponding point-wise confidence band for the time-varying mediation effect. Simulation studies show that the proposed procedures perform well when comparing the confidence band and the true underlying model. We further apply the proposed model and the statistical inference procedure to real-world data collected from a smoking cessation study.