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I am using the mediation package in R and would appreciate assistance with several questions.

One path (let's call this the first model) involves a dichotomous predictor -> continuous mediator -> dichotomous outcome, like:

med.fit <- svyglm(numhealthcare ~ epi, data = dat2,design=wgt2)
out.fit <- svyglm(htnaware ~ numhealthcare + epi,data=dat2, family=binomial(link="logit"),design=wgt2)
set.seed(123)
med.out <- mediate(med.fit, out.fit, treat = "epi", mediator = "numhealthcare",robustSE = TRUE, sims = 1000)
summary(med.out)
                       Estimate 95% CI Lower 95% CI Upper p-value   
ACME (control)            0.02115     -0.24876         0.15   0.626   
ACME (treated)            0.00367     -0.12051         0.07   0.626   
ADE (control)             0.10990      0.03529         0.16   0.010 
ADE (treated)             0.09242      0.00723         0.27   0.010 
Total Effect              0.11357     -0.03820         0.18   0.088  
Prop. Mediated (control)  0.41118     -4.20367         2.90   0.542   
Prop. Mediated (treated)  0.09624     -1.65612         1.83   0.542   
ACME (average)            0.01241     -0.17915         0.10   0.626   
ADE (average)             0.10116      0.02972         0.20   0.010 
Prop. Mediated (average)  0.25371     -2.87898         2.33   0.542

Another path (let's call this the second model) involves a dichotomous predictor -> continuous mediator -> log of a continuous outcome, like:

med.fit <- svyglm(incpovratio~epi, data = dat3,design=wgt3)
out.fit <- svyglm(logascvd~epi+incpovratio,data = dat3,design=wgt3)
set.seed(123)
med.out <- mediate(med.fit, out.fit, treat = "epi", mediator = "incpovratio",robustSE = TRUE, sims = 1000)
summary(med.out)
               Estimate 95% CI Lower 95% CI Upper p-value
ACME            -0.0487      -0.2579         0.10    0.53
ADE              0.7268      -0.1784         1.63    0.12
Total Effect     0.6781      -0.2667         1.58    0.13
Prop. Mediated  -0.0345      -1.3529         0.68    0.61

Here are my questions:

  1. Proportion mediated: What does it mean that the second path has a negative proportion mediated (-0.0345), and that confidence intervals likewise can be less than 0 or greater than 1 (the first model's CI spans -289% to 233%)? Does that mean I just don't have enough power to adequately assess proportion mediated and shouldn't report this value given terrible precision? Or should I somewhat ignore the boostrapped CI's and report proportion mediated anyways, with or without the CI's? Or is it better to just report ACME and ADE which look like they have better precision? Someone asked a question like this but it was never answered: Seemingly impossible CIs for proportion mediated (package 'mediation')

  2. How does one interpret ACME and ADE in above models where the outcome is either dichotomous (first model) or log of a continuous variable (second model)?
    -For the dichotomous outcome (first model): I know it isn't significant, but can the average ACME (0.01241) be interpreted as: "When the predictor goes from 0 to 1, there is a 0.01241 absolute increase in the log(odds) of the dichotomous outcome related to the path through the mediator"? And if so would I just exponentiate the point estimate and confidence intervals then to put this into a more interpretable odds ratio? Or is it "When the predictor goes from 0 to 1, there is a 0.01241 absolute increase in the predicted probability of the dichotomous outcome related to the path through the mediator"? I see another post Comprehending output from mediation analysis in R which seems to indicate the latter which would be great if the ACME was already somehow on the probability scale rather than the log(odds) scale, but I wasn't clear.
    -For the continuous outcome (second model): For a typical model, I know to interpret a coefficient when the outcome is logged, one can say for a 1-unit change in X, there is a [e^coefficient - 1]*100% relative change in Y. So should this be interpreted as "When the predictor goes from 0 to 1, there is a [e^-0.0487 - 1]*100% relative change in the original non-logged outcome related to the path through the mediator"?

  3. For mediation analysis like above when variables exist on different scales and some are dichotomous, some continuous, some logged, do I need to standardize each variable before running the above models and how would that change interpretation of ACME? Or is it better for interpretability to keep all variables on their original scale? I'd rather keep everything on their original scale if it was valid to do so, for interpretability.

Thank you greatly to anyone who can assist.

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If anyone looks at this post in the future, I have collected answers from experts, so I'm all set.

  1. The proportion mediated is negative if the direct and indirect effects have opposite directions. It makes more sense to discuss the proportion mediated if the direct is the same for both.
  2. If the outcome is binary, the ACME and ADE are absolute percent changes, not log(odds) change. Above interpretation for log(continuous outcome) is correct.
  3. No need to standardize.
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