Week 6, Day 4
Met with the Causality team to discuss implementation progress and blockers. Roger requested that I give a PPT presentation to the team next week to explain the theory grounding my implementation; after our meeting I began working on this.
Also looked into the concept of a "controlled indirect effect", as there's no mention of a CIE throughout the referenced Pearl literature. Found that the total effect (TE) can be decomposed into various ways including (1):
- controlled direct effect and eliminated effect
- natural direct effect and natural indirect effect
- 4-way decomposition: controlled direct effect, reference interaction, mediated interaction, and pure indirect effect
As such, the controlled indirect effect is "usually not estimated", as "its sum with the direct effect does not equal the total effect", and is "notably difficult to conceptualize" (2, 3). Source 1 proposes a means of estimating the CIE, defined as "the total effect of mediator on outcome"; this is likely beyond the scope of my implementation, but may be useful for further research. For now, I'll include a calculation for the so-called "eliminated effect": TE-CDE, as used by Source 3.