Functional mediation analysis with an application to functional magnetic resonance imaging data

Yi Zhao, Xi Luo, Martin Lindquist, Brian Caffo

Research output: Contribution to journalArticlepeer-review


Causal mediation analysis is widely utilized to separate the causal effect of treatment into its direct effect on the outcome and its indirect effect through an intermediate variable (the mediator). In this study we introduce a functional mediation analysis framework in which the three key variables, the treatment, mediator, and outcome, are all continuous functions. With functional measures, causal assumptions and interpretations are not immediately well-defined. Motivated by a functional magnetic resonance imaging (fMRI) study, we propose two functional mediation models based on the influence of the mediator: (1) a concurrent mediation model and (2) a historical mediation model. We further discuss causal assumptions, and elucidate causal interpretations. Our proposed models enable the estimation of individual causal effect curves, where both the direct and indirect effects vary across time. Applied to a task-based fMRI study, we illustrate how our functional mediation framework provides a new perspective for studying dynamic brain connectivity. The R package cfma is available on CRAN.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - May 17 2018


  • Dynamic brain connectivity
  • Functional data analysis
  • Structural equation model
  • Time-varying causal trajectory

ASJC Scopus subject areas

  • General

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