# [R] problem of interpretation using mediation package

kende jan kendejan at yahoo.fr
Wed Jan 20 13:31:33 CET 2016

```Dear all,
I am using the package mediation in order to perform a parametric mediation
analysis on survival data. I have 8 variables:

- Mediator
- Treat
- time (days)
- death (event)
- X1-X4 (confounding variables)

I ran the following code to estimate the causal mediation effects.

med.m = lm(Mediator ~ Treat + X1 + X2 + X3 + X4)
med.y = survreg(Surv(time, death) ~ Treat + X1 + X2 + X3 + Mediator + X4)
med.out <- mediate(med.m, med.y, treat = "Treat", mediator = "Mediator")
summary(med.out)

Here are the output provided by this script:

Causal Mediation Analysis

Quasi-Bayesian Confidence Intervals

Estimate 95% CI Lower 95% CI Upper p-value
ACME (control)           -3.68e+02    -1.27e+03    -3.34e+01    0.01
ACME (treated)           -1.47e+02    -4.46e+02    -1.67e+01    0.01
ADE (control)            -3.76e+03    -1.18e+04    -5.93e+02    0.00
ADE (treated)            -3.54e+03    -1.14e+04    -5.53e+02    0.00
Total Effect             -3.91e+03    -1.20e+04    -6.79e+02    0.00
Prop. Mediated (control)  9.56e-02     1.55e-02     2.36e-01    0.01
Prop. Mediated (treated)  3.82e-02     7.03e-03     1.49e-01    0.01
ACME (average)           -2.57e+02    -8.36e+02    -2.46e+01    0.01
ADE (average)            -3.65e+03    -1.16e+04    -5.78e+02    0.00
Prop. Mediated (average)  6.69e-02     1.17e-02     1.90e-01    0.01

Sample Size Used: 713

Simulations: 1000

My problem is that I do not understand how to interpret the value of the
estimate obtained for the ACME (control) parameter.
I know that when the response variable (Y) is binary, this estimate can be
interpreted as the increase in terms of probability of the event for control
subjects.
What is the good interpretation when the response variable (Y) in the model
is a survival object ?
Does it indicates here a decrease expressed in number of days (368) ?
According to the Prop. Mediated (average) value (i.e last row of the table),
can I conclude that about 6.69% of the total effect of Treat on Y is
explained by the indirect effect of Mediator ?

Thanks for your consideration,

Best regards,

Kendejan
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