[Mediation-information] Questions about R mediation package

[Kosuke Imai]

Dear Jessica,

  My responses are below but I’m ccing my collaborators who are much more informed about the software.  Also, you should look at the accompanying paper: http://imai.princeton.edu/research/files/mediationR2.pdf  This paper details the software in terms of both implementation and interpretation.

Best,
Kosuke

---------------------------------------------------------
Kosuke Imai               Office: Corwin Hall 036
Professor                 Phone: 609-258-6601
Department of Politics    Fax: 609-258-1110
Princeton University      Email: kimai at Princeton.Edu
Princeton, NJ 08544-1012  http://imai.princeton.edu
---------------------------------------------------------

On Oct 30, 2013, at 11:17 AM, Jessica Dennis <jessica.dennis at mail.utoronto.ca> wrote:

> Dear Dr. Imai,
> 
> I am a PhD student in genetic epidemiology at the University of Toronto, and as part of my thesis work, I have been using your mediation package in R to do some mediation analyses.
> 
> I'm having a little bit of trouble, however, with implementation and interpretation, and I was hoping you could help clarify a few things:
> 
> 	• Testing for interaction between the treatment and the mediator.  I don't quite understand the output of the Test.TMint function.  On the example on page 9 of the mediation documentation:
> Test of ACME(1) - ACME(0) = 0
> 
> data: estimates from med.out
> 
> ACME(1) - ACME(0) = 0.015, p-value = 0.42
> 
> alternative hypothesis: true ACME(1) - ACME(0) is not equal to 0
> 
> 95 percent confidence interval:
> 
> -0.03865720 0.05212853
> 
> 
> 
> Since the 95% CI includes 0, does this mean that we fail to reject the null hypothesis?  The wording in the output is a little ambiguous.

You fail to reject the null hypothesis of no interaction in this case. 

> 
> 
> 
> Also, I had wanted to test the interaction between the treatment and mediator in an lmer model.  When I apply the Test.TMint function, however, I get: Error in test.TMint.default(med.out.2, conf.level = 0.95) : currently no test.TMint method exists for the input object.
> 
> 
> Does this mean that the Test.TMint function is unable to handle output from the lmer object?
> 

We are currently working to add several functionalities to lmer models.  We will put this on our to-do list.


> 
> 	• Sensitivity analysis for sequential ignorability.  Can sensitivity analysis be useful when the ACME is non-significant?  In all the examples I've seen online, sensitivity analysis is used to determine when an ACME becomes non-significant.

Most commonly, sensitivity analysis is used to assess the robustness of empirical findings.  So, if you have null findings, it may not make much sense to do this. 

> In my mediation analysis, I estimated the ACME to be (my treatment variable is continuous, with values 0, 1, and 2):
> 
>                Estimate 95% CI Lower 95% CI Upper p-value
> ACME            -0.0196      -0.0662       0.0201    0.31
> 
> I have the following output table from the sens.out function:
> Sensitivity Region
> 
>        Rho    ACME 95% CI Lower 95% CI Upper R^2_M*R^2_Y* R^2_M~R^2_Y~
>  [1,] -0.9  0.1750      -0.1765       0.5266         0.81       0.4807
>  [2,] -0.8  0.1061      -0.1072       0.3194         0.64       0.3798
>  [3,] -0.7  0.0728      -0.0738       0.2195         0.49       0.2908
>  [4,] -0.6  0.0511      -0.0522       0.1544         0.36       0.2136
>  [5,] -0.5  0.0348      -0.0361       0.1058         0.25       0.1484
>  [6,] -0.4  0.0216      -0.0233       0.0665         0.16       0.0949
>  [7,] -0.3  0.0101      -0.0134       0.0336         0.09       0.0534
>  [8,] -0.2 -0.0003      -0.0123       0.0117         0.04       0.0237
>  [9,] -0.1 -0.0101      -0.0337       0.0134         0.01       0.0059
> [10,]  0.0 -0.0196      -0.0607       0.0215         0.00       0.0000
> [11,]  0.1 -0.0291      -0.0886       0.0305         0.01       0.0059
> [12,]  0.2 -0.0388      -0.1177       0.0400         0.04       0.0237
> [13,]  0.3 -0.0492      -0.1487       0.0503         0.09       0.0534
> [14,]  0.4 -0.0607      -0.1832       0.0617         0.16       0.0949
> [15,]  0.5 -0.0740      -0.2230       0.0750         0.25       0.1484
> [16,]  0.6 -0.0903      -0.2719       0.0913         0.36       0.2136
> [17,]  0.7 -0.1120      -0.3370       0.1131         0.49       0.2908
> [18,]  0.8 -0.1453      -0.4371       0.1465         0.64       0.3798
> [19,]  0.9 -0.2142      -0.6443       0.2159         0.81       0.4807
> 
> 
> Since the value of the ACME doesn't change appreciably across different values of rho (i.e., the 95% CI always includes 0), do I conclude that there are no unmeasured confounders of the mediator-outcome relationship?
> 
> 
> Thank you very much for your input.
> Jessica
> 
> 
> Jessica Dennis
> CIHR Vanier Scholar, CIHR STAGE Fellow
> PhD Candidate in Epidemiology
> Dalla Lana School of Public Health University of Toronto
> 155 College St, Suite 734
> Toronto, ON M5T 3M7