# Causal mediation analysis interpretation help

The mediation analysis that I have run is as follows ;

   mod.x <- glm(Diversity ~ Gene1 + covariates, data=df, family=binomial)
mod.y <- glm(Disease ~ Diversity + Gene1 + covariates, family=binomial)

mediate(mod.x, mod.y, treat="Gene1", mediator= "Diversity", boot=T, sims=100).


From https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5124624/, it states that "with binary outcome variables, the estimated coefficients from above links to the probability scale, rather than that obtained from logistic regression model that its exponentiation gives the odds ratio (OR)"

From https://www.ncbi.nlm.nih.gov/books/NBK261974/, "ADE and ACME for binary outcomes are produced as standardised estimates, which may not be meaningfully back-transformed to estimates of ORs or similar statistics".

Separate from my mediation analysis, my results show that an increase in gene1 is associated with reduced odds of disease. Similarly, an increase in diversity is associated with a reduced odds of disease.

Would my negative estimates for ADE and ACME be in accordance with this?

I am a little bit confused by the term probabilty stated in the first link ( probabilities usually range from 0 to 1 and aren't negative), and that you cannot take the exponential of these estimates to get a meaningful answer.

Any insight would be helpful.