Understanding How Treatments Affecting the Brain Work: Functional Rank Preserving Models for Causal Mediation

• Activity Number: 123
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Imaging
• Author(s): Yenny Webb-Vargas*+ and Michael Sobel and Elizabeth A. Stuart and Martin Lindquist
• Companies: Johns Hopkins Bloomberg School of Public Health and Columbia University and Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health
• Keywords: causal inference ; functional data analysis ; causal mediation ; rank preserving models ; instrumental variables ; two-stage least squares

Abstract

We have developed a new method to assess causal mediation when the mediator is a function in time (e.g., brain activity measured in fMRI) and the treatment has a direct effect. We extend a method of instrumental variables, which relaxes the assumption that the treatment has no direct effect on outcome, to accommodate a functional regressor. This method is unbiased even when the mediator is confounded with the outcome. To have a causal interpretation, the treatment must be unconfounded with both the mediator and the outcome. The potential outcomes of a person must share the same error with respect to the population mean (referred as rank preservation). The interaction of a baseline covariate with the treatment must be an adequate instrument. Finally, the direct effect of the treatment on the outcome must not vary among different levels of the mediator. The method uses two stage least squares, with a function-on-scalar regression as the first stage, and a scalar-on-function regression as the second stage. We tested this method using simulations, and applied it to data from a trial analyzing how the brain processes thermal pain.