[Mediation-information] Sensitivity Analysis

[Kosuke Imai]

I agree with Dustin.  It's important to think about what is the possible omitted variable is.  Ideally, you measure that.  But if you weren't able to, then sensitivity analysis can help you figure out the robustness of your results. 

Kosuke

On Nov 22, 2011, at 11:22 AM, dustin tingley wrote:

> Hi
> I prefer to think about SI violations with respect to a particular hypothesized confounder. Depending on the direction of the effect on M and Y (by the confounder), you should think about whether the violation of SI would actually give you stronger results. IF there is a clear confounder that you think most people will be worried about, then you should think through these directional issues as part of the sensitivity process.
> best,
> Dustin
> 
> Dustin Tingley
> Government Department
> Harvard University
> http://scholar.harvard.edu/dtingley
> 
> 
> 
> On Tue, Nov 22, 2011 at 11:07 AM, Keele Luke <ljk20 at psu.edu> wrote:
> Yes.
> 
> 
> Luke Keele
> Associate Professor
> Dept. of Political Science
> Penn State University
> 
> 
> 
> On Nov 22, 2011, at 11:06 AM, Samson Gebreab wrote:
> 
> >
> >
> > Hi Luke,
> >
> > Thank you for help on this and quick response.  Yes, the mediation effect
> > is not
> > statistically significant although we think that there is modest (~8%)
> > mediation effects in this case.
> >
> > So, our sensitivity analysis is suggesting that unmeasured confounder would
> > need to explain only small portion of the remaining variance in the
> > mediator and outcome models  for the average mediation effects to lose its
> > importance or significance ( although it is not significant in this case).
> > Correct ?
> >
> > In other words, our results is not robust to potential violation of the
> > sequential ignorability assumption.
> >
> >
> > Thank you for help
> > Samson
> >
> >
> >
> > On Mon, 21 Nov 2011 14:53:25 -0500, Luke Keele <ljk20 at psu.edu> wrote:
> >> Samson
> >>
> >> A couple of things about your results.  First, your estimate of the
> >> mediation effect is not statistically significant.
> >>
> >> That is the CI brackets zero.  This means in the sensitivity analysis
> > that
> >> rho could be nonzero under any
> >> situation.  You can seen this as the value from rho is very small.
> >>
> >> Actually you prefer the R^2 values to be larger.  That is the bigger the
> >> better.
> >>
> >> Luke
> >>
> >>
> >> On Nov 21, 2011, at 2:44 PM, Samson Gebreab wrote:
> >>
> >>>
> >>> Hi Kosuke
> >>>
> >>> Thank you for your help and pointers. Currently, we are working on a
> >>> revise
> >>> and submit paper that implement your method on  casual mediation and
> >>> sensitive analysis method ( which we would be citing).
> >>>
> >>> Although, I understood reasonably well the estimates of the mediation
> >>> results based on your papers (Stat Science, Psych Methods or APSR).
> >>>
> >>> I am not quite sure if understood the interpenetration of the
> > sensitivity
> >>> analysis estimates. I thought I would check with you on the
> >>> interpenetration our sensitivity analysis before we resubmit our paper.
> >
> >>>
> >>> Following the results below and given that Rho and R^2_M*R^2_Y &
> >>> R^2_M~R^2_Y~ extremely small, is it fair to say that the assumption of
> >>> ignorability held reasonably well in this case?  Any help to shed light
> >>> on
> >>> the the sensitivity estimates would be greatly appreciated.
> >>>
> >>>
> >>> Thanks again for all your help on this.
> >>> Happy Thanks giving
> >>> Samson
> >>>
> >>> Quasi-Bayesian Confidence Intervals
> >>> Mediation Effect:  -0.007546 95% CI  -0.018562  0.002709
> >>> Direct Effect:  -0.08922 95% CI  -0.1868219  0.0008452
> >>> Total Effect:  -0.09677 95% CI  -0.19628 -0.00875
> >>> Proportion of Total Effect via Mediation:  0.08109 95% CI  0.03769
> >>> 0.51936
> >>>
> >>> Sensitivity Region
> >>>             Rho Med. Eff. 95% CI Lower 95% CI Upper R^2_M*R^2_Y*
> >>> R^2_M~R^2_Y~
> >>> [1,] 1.110223e-16   -0.0043      -0.0103       0.0012 1.232595e-32
> >
> >>> 0.000
> >>> [2,] 5.000000e-02    0.0013      -0.0046       0.0076 2.500000e-03
> >
> >>> 0.002
> >>>
> >>> Rho at which Delta = 0: 0.0387
> >>> R^2_M*R^2_Y* at which ACME = 0: 0.0015
> >>> R^2_M~R^2_Y~ at which ACME = 0: 0.0012
> >>>
> >>>
> >>>
> >>> Thank you!!!
> >>> Samson
> >>>
> >>>
> >>> On Fri, 4 Nov 2011 23:22:21 -0400, Kosuke Imai <kimai at princeton.edu>
> >>> wrote:
> >>>> Samson,
> >>>>
> >>>> In general, I would avoid using Risk Ratio as the result can become
> >>>> sensitive when the denominator is small.  Those numbers indicate the
> >>>> values of sensitivity parameters when the ACME is zero.  But, please
> >>> see
> >>>> our papers (either Stat Science, Psych Methods or APSR) for the
> >>> details.
> >>>>
> >>>> Kosuke
> >>>>
> >>>> Department of Politics
> >>>> Princeton University
> >>>> http://imai.princeton.edu
> >>>>
> >>>
> >>>
> >>
> >> Luke Keele
> >> Associate Professor
> >> Dept of Political Science
> >> Penn State University
> 
>