Reporting guideline for bayesian using pd and ROPE

Question

In the bayestestR articles, I came across the reporting guidelines that they recommend

“the effect of X has a probability of pd of being negative (Median = median, 89% CI [ HDI_low , HDI_high ] and can be considered as significant (ROPE% in ROPE).”

Is this applicable for Bayesian logistic regression? Since in logistic regression, we are more interested in the odds ratio.

For instance: If we are looking at whether vintage transplant (<5 years vs >=5 years) has an association with being vaccine-acceptance.

Based on my results, “the effect of transplant vintage of >=5 years has a probability of 96.47% of being positive (Median = 2.26, 89% CI [0.25, 4.52] and can be considered as significant (2.45% in ROPE).”

How do I write it in terms of OR? "Patients with transplant vintage of >=5 years have 9.58 times (pd = 96.47%, 2.45% in ROPE) higher odds as compared to those with <5 years."

Answer 1

Just as you exponentiate the point estimate (the posterior median), you can exponentiate the credible intervals (CIs) to get CIs for odds ratio as well, but the CIs must be 'equal tailed intervals', also called 'central intervals', rather than 'highest density intervals' - from here, the important part

"...the ETI range does not change when transformations are applied to the distribution (for instance, for log-odds to probabilities transformation)..."

Also see here. I don't think the pd or ROPE reporting would change as they're derived from the model coefficients not odds ratio.

You can get the ETI for the CIs using the ci() function with method="ETI" from bayestestR or posterior_interval() from rstanarm (I'm sure other packages have the same).

For your example, something like:

"Patients with transplant vintage of >=5 years have 9.58 times (89% CI [...], pd = 96.47%, 2.45% in ROPE) higher odds as compared to those with <5 years."

where 89% CI [...] are the exponential of ETIs (i.e. odds ratio CIs) seems reasonable.