Mediated Effects
David Judkins writes:
I just saw Dylan Small give a very interesting talk in Salt Lake City on mediation analysis using random assignment interacted with baseline covariates as instrumental variables. He mentioned that Albert (2007) just established a formal definition for mediated effects with Neyman-Rubin causal language. Anyone know which Albert? Is it James Albert at Bowling Green? Any rival formal definitions for mediated effects? Page 165 of Pearl's 2000 text has a definition of indirect effects, but I didn't find it quite as satisfying as the version that Small put on the screen last week.
Formal definitions of direct and indirect effects are given in Pearl (2001) [click here to view] and I cannot imagine a more satisfactory rival. I am curious therefore to see how Dylan Small and Albert define mediated effects. See also Peterson et al., (Epidemiology vol 17 no 3, May 2006, p 276.) which uses the same definitions and same graphical technique of interpreting counter factual dependencies. Can anyone invite Small or Albert to participate?
Comment by judea — August 7, 2007 @ 3:39 pm
Hello, The paper by Jeff Albert at Case Western (jaml3@case.edu) presents the same "natural" effect definition of an indirect effect as does Pearl (2001). However, he fails to cite Pearl, given he wasn't aware of Pearl's work. Jeff's paper is to appear in Statistics in Medicine. I will email the paper to David. Dylan Small focuses on IV estimation of direct effects and then baseline*randomized intervention interactions but all are "prescribed" effects. Nonetheless, he does favor the natural effects of Pearl. Dylan just didn't have time in his presentation to address this issue.
Comment by Tom Tenhave — August 8, 2007 @ 11:00 am
Thanks David and Judea for the insightful comments. The work I referred to in my talk is a forthcoming Statistics in Medicine paper by Jeff Albert of Case Western Reserve University. Albert's definition that I referred to is consistent with Pearl (2001)'s definition — Albert defines the "proportion of the treatment effect that is mediated" as the natural indirect effect when treatment is set to the control level divided by the average effect of treatment (i.e., expected potential outcome under treatment, letting the mediating variable take its natural value under treatment minus expected potential outcome under control), letting the mediating variable take its natural value under control). My work is focused on issues that arise in estimating prescribed and natural direct effects and natural indirect effects when one is concerned that sequential ignorability of the mediating variable might not hold. Dylan
Comment by Dylan Small — August 8, 2007 @ 5:31 pm
I see a related article in issue #18 of 2007 Statistics in Medicine, in which Yan Li, Julie Schneider, and David Bennett also advance a definition for a mediated effect without reference to Pearl. I haven't studied it carefully, but it doesn't look consistent with Pearl or Albert.
Comment by David Judkins — August 16, 2007 @ 10:14 am