[Mediation-information] Interpreting the ACME

[Elizabeth Pasipanodya]

Hello All,

I am a doctoral student working on data from a project focusing on couples coping with breast cancer. I have a mediation model with two simultaneous predictors, X1 (a positive relationship event) and  X2 (a relationship conflict), a mediator, M (a measure of intimacy), and an outcome Y (a measure of anxiety). X1 and X2 are both binary while M is continuous. Additionally, Y follows a count distribution. These variables are repeatedly measured for each individual across a number of days and, thus, I used the R packages lme4 and mediation to conduct my analyses.

I would like to double-check the meaning of the ACME. My understanding is that it represents the expected difference in the potential outcome when the mediator takes the value that it would have under the treatment condition compared to the control condition, while the treatment condition is held constant. Since I have a count outcome, should I report and interpret my ACME in the same units as my count outcome, as one would a rate ratio? That is, the ACME shall represent, in the logs of expected counts, the estimated average change in Y among the treatment group (those with a relationship event) as a result of M (intimacy) rather than directly from X1 (positive relationship event) and X2 (negative relationship event)?

For instance, based on the mediation output below, could I say something like the following --- on a day in which participants reported experiencing at least one negative relationship event, their estimated average change in anxiety due to changes in intimacy was 1.08 times (e^0.07485) that of those without a relationship conflict, controlling for the occurrence of positive relationship events?

> med2 <- mediate(apath, bpath, treat = "X2", mediator = "M", sims=5000, control.value = -0.5, treat.value = 0.5, dropobs=TRUE, method = "boot", boot.type = "bca")
> summary(med2)

Causal Mediation Analysis

Quasi-Bayesian Confidence Intervals

Mediator Groups: ID

Outcome Groups: ID

Output Based on Overall Averages Across Groups

                          Estimate 95% CI Lower 95% CI Upper p-value
ACME (control)             0.07890      0.02639      0.15107    0.00
ACME (treated)             0.07080      0.02354      0.13856    0.00
ADE (control)             -0.06645     -0.32283      0.17712    0.50
ADE (treated)             -0.07455     -0.35353      0.19218    0.50
Total Effect               0.00435     -0.25810      0.26892    0.97
Prop. Mediated (control)   0.16404    -11.47515     12.32893    0.97
Prop. Mediated (treated)   0.20262     -9.82740     10.87888    0.97
ACME (average)             0.07485      0.02583      0.14364    0.00
ADE (average)             -0.07050     -0.33728      0.18478    0.50
Prop. Mediated (average)   0.18333    -10.80037     11.56373    0.97

Sample Size Used: 602


Simulations: 5000

Best,

Elizabeth Pasipanodya


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