How to interpret the results of 'mediate' in Stata 18

[Hongjiang Zhai]

Dear all,

Recently, I have been utilizing the ‘mediate’ command in Stata 18 to conduct mediation analysis. In my analysis, I have found that the NIE value is significant, the NDE value is not significant, and the TE value is significant. According to conventional regression methods, the proportion of mediation effect should be 100%. However, when I use the ‘estat proportion’ command, it yields a result of 27% and not significant. I am confused about these results and do not know how to explain them.

My question are:

1.Is the mediating effect 100% or 27%.
2. Why is the NIE value significant and the proportion generated by the "estate promotion" command not significant? What method is used for significance testing?
3.How do I report this result in the paper.

Thank you

[Hongjiang Zhai]

Who can answer?

[Wei Hai Deng]

I think part of the challenge to answer is not being sure where to start in answering.
First, I recommend getting hold of VanderWeele's book "Explanation in Causal Inference". The chapters are nicely organized and should be able to answer all your questions. There are chapters for describing the counterfactual approach to mediation analysis and also one on calculating and interpreting the proportion mediated.

I mention reading the book or other papers by VanderWeele, Judea Pearl, Aidan Cashin.. to name a few, because counterfactual mediation is extremely dependent on correctly specifying its causal assumptions and relationships to produce interpretable results. Especially its assumptions on unmeasured confounding.

1. VanderWeele TJ: Mediation Analysis: A Practitioner’s Guide. Annual Review of Public Health 37:17–32, 2016
2. VanderWeele TJ: Explanation in causal inference: developments in mediation and interaction. International Journal of Epidemiology 45:1904–1908, 2016
3. Cashin AG, Lee H: An introduction to mediation analyses of randomized controlled trials. Journal of Clinical Epidemiology 133:161–164, 2021
4. MacKinnon DP, Fairchild AJ, Fritz MS: Mediation Analysis. Annual Review of Psychology 58:593–614, 2007

Referencing the "Methods and formulas" in the help mediate is also useful.
I apologize if I am wrong in assuming you are new to causal mediation.

As for your questions. The Natural indirect effect (NIE) is a coefficient for the mediating effect of your mediator on the outcome as a causal effect of your treatment. ie. if you remove the purely (natural) direct effect (NDE) of your treatment on the outcome, what is left. This we assume is mediated through your mediator variable. The total effect (TE) is just the effect of everything, including your treatment and mediators on the outcome. ie. what would the effect of your treatment have been if everyone in your sample received the treatment, vs. everyone did not, irrespective of how/through what causal pathway.

Proportion mediated is how much of your total effect was through your mediator (the NIE) as a proportion and is rarely 100%. Using and interpreting this proportion is however not always useful, even more uncertain the use of its confidence intervals. I would not rely on any significance measure for this, rather 95% CIs. MacKinnon 2007 explains some of its limitations. CIs can be unstable and sometimes dubious to interpret depending on the direction of your causal effects. Basing your variance estimators on the NIE's CIs is often a better bet. But again, this is dependent on your model, outcome, results, assumptions, etc.

Hope the above information gives you a little start to figuring out your questions.

Best,
Wei

[Hongjiang Zhai]

Thank you for the help,wei.

I will diligently study the literature you have recommended.