[Mediation-information] Casual Mediation Analysis using R

[Kosuke Imai]

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

On Nov 3, 2011, at 12:14 PM, Samson Gebreab wrote:

> 
> Dear Drs Imai, Keele, Tingley, and Teppei
> 
> I have enjoyed your recent papers on causal mediation and sensitivity
> analysis. I am conducting casual mediation and sensitivity analyses using
> “Mediation R package” you created, which I can implement easily with my
> dataset (results given below). But, I have few questions regarding the
> interpretation of the results. 
> 
> As you can see below I have a common outcome, so I used long-linear model
> (Poisson) to estimate risk ratio (RR), with mediator continuous and
> exposure binary.  Is there a way I can translate the results of causal
> mediation analysis to RR by exponentiating the results (e.g., Mediation
> Effect: exp (0.01457) = 1.014677, etc.) or these results are simply
> proportions.
> 
> 
> A second questions could you shed some insight into the interpretation of
> the sensitivity analysis, especially how do you interpret the following
> values?
> 
> Rho at which Delta = 0: 0.0438 
> 
> R^2_M*R^2_Y* at which ACME = 0: 0.0019 
> 
> 
> R^2_M~R^2_Y~ at which ACME = 0: 0.0015
> 
> Any insights on the interpretation of these results would be much
> appreciated.
> 
> Thank you
> Samson 
> 
> ###### Here is the full results 
> 
> model.m <- lm(m ~ age + exp + c1 + c2 + c3, data=dsn)
> model.y <- glm(y ~ age + exp + c1 + c2 + c3 + m, family=poisson (),
> data=dsn)
> med.exp <- mediate (model.m, model.y, boot=TRUE, INT = false, treat="exp",
> mediator="m")
> 
> summary(med.exp)
> 
> Causal Mediation Analysis 
> 
> Confidence Intervals Based on Nonparametric Bootstrap
> 
> Mediation Effect:  0.01457 95% CI  0.004999 0.024552 
> Direct Effect:  0.07113 95% CI  0.01001 0.13884 
> Total Effect:  0.0857 95% CI  0.02329 0.15345 
> Proportion of Total Effect via Mediation:  0.162 95% CI  0.08676 0.56001
> 
> 
> sens.exp <- medsens(med.exp, rho.by = 0.05)
> 
> Mediation Sensitivity Analysis
> 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    0.0065      -0.0005       0.0136 1.232595e-32       
> 0.000
> [2,] 5.000000e-02   -0.0009      -0.0081       0.0053 2.500000e-03       
> 0.002
> 
> Rho at which Delta = 0: 0.0438 
> 
> R^2_M*R^2_Y* at which ACME = 0: 0.0019 
> 
> R^2_M~R^2_Y~ at which ACME = 0: 0.0015
>