ROPE range specification for binary models

Sorry for taking long to respond.

I admit I don’t understand the guidelines and the terms you use either, but I think one can do a lot of stuff from the first principles.

In logistic regression, the model coefficients represent additive changes in log-odds. For binary/categorical predictors the coefficient directly represent change in log-odds from the baseline (which is IMHO easy to grasp) while for continuous predictors it is change in log-odds per each unit from the predictor being zero.

In both cases, one can often make sensible considerations about ROPE just with that. Change in log-odds is the same multiplying the odds, so if say baseline odds are 1:1 and 11:10 is the maximal odds you consider practically equivalent for a treatment, you can compute the relevant value of the ROPE for the coefficient as \log \left(\frac{\frac{11}{10}}{\frac{1}{1}} \right) = \log(\frac{11}{10}) - \log(1) \simeq 0.095. Note however that this requires speaking about relative risk, which is not always the beast target. In other words, you are saying that multiplying the odds by 1.1 is practically equivalent regardless of the baseline odds, so with the same ROPE, if the baseline odds are 1:100 the practically equivalent range would end at 11:1000.

Additionally, you may work with absolute risk by making predictions on the absolute scale (i.e. computing the posterior distribution for the mean of the outcome). You can than compare those absolute risks between the groups.

Does that make sense?

Also it helps if you give links to papers or other sources instead of just citations as those might be ambiguous for people that don’t follow the field closely.

3 Likes