Functional Causal Mediation Analysis With an Application to Brain Connectivity

Abstract

Mediation analysis is often used in the behavioral sciences to investigate the role of intermediate variables that lie on the causal path between a randomized treatment and an outcome variable. Typically, mediation is assessed using structural equation models (SEMs), with model coefficients interpreted as causal effects. In this article, we present an extension of SEMs to the functional data analysis (FDA) setting that allows the mediating variable to be a continuous function rather than a single scalar measure, thus providing the opportunity to study the functional effects of the mediator on the outcome. We provide sufficient conditions for identifying the average causal effects of the functional mediators using the extended SEM, as well as weaker conditions under which an instrumental variable estimand may be interpreted as an effect. The method is applied to data from a functional magnetic resonance imaging (fMRI) study of thermal pain that sought to determine whether activation in certain brain regions mediated the effect of applied temperature on self-reported pain. Our approach provides valuable information about the timing of the mediating effect that is not readily available when using the standard nonfunctional approach. To the best of our knowledge, this work provides the first application of causal inference to the FDA framework.

Keywords:

• Brain connectivity
• Causal inference
• fMRI
• Functional data analysis
• Instrumental variable
• Mediation
• Structural equation models

Acknowledgments

The author thanks Michael Sobel for all his help with the preparation of this article, Niall Bolger for helpful comments, and Tor Wager for supplying the data. This work was partially funded by the National Institute on Drug Abuse (NIDA) grant 1RC1DA028608.

Notes

Quotation marks are used in this subsection to differentiate the effects in the lfSEM from their counterparts in the CLFM.