Adjusted risk difference and negative confidence interval

Question

I was reading this article. The authors used mixed effects logistic regression and presented their results as adjusted risk difference. I noticed that some of the confidence interval were negative, I was wondering if it is because risk difference is not ratio like OR. If that is the case, does that mean it fails to reach statistical significance when CI crosses zero, instead of one?

McDonald, E.G., Wu, P.E., Rashidi, B. (2022). The MedSafer Study—Electronic Decision Support for Deprescribing in Hospitalized Older Adults: A Cluster Randomized Clinical Trial. JAMA Internal Medicine. Published online January 18, doi:10.1001/jamainternmed.2021.7429

Answer 1

Let's revisit the risk difference ($\text{RD}$):

$$\text{RD}_{\text{A vs B}} = \text{Risk}_{\text{A}} - \text{Risk}_{\text{B}}$$

So a $\text{RD}$ is an absolute difference in risks. Risks (e.g., incidence rates, whether incidence proportions, or incidence densities) can take values between $0$ and $1$, inclusive. So the lowest value a $\text{RD}$ can have is $\text{Risk}_{\text{A}} - \text{Risk}_{\text{B}} = 0 - 1 = -1$, when $\text{Risk}_{\text{A}} = 0$ and $\text{Risk}_{\text{B}} = 1$). (Likewise, the maximum value an $\text{RD}$ can take is $1$, which you get by switching the risk of $0$ and $1$ for each group.)

Finally, if $\text{Risk}_{\text{A}} = \text{Risk}_{\text{B}}$, then $\text{RD}_{\text{A vs B}} = 0$ since something minus itself equals zero. Values of $\text{RD}$ close to zero, thus correspond to "no significant difference" (where the precise meaning of "close to" will depend on sample size and $\alpha$ :), so your understanding about confidence intervals for a $\text{RD}$ spanning $0$ is correct.