ROPE value in Bayesian Regression

hlsmith

Less is more. Stay pure. Stay poor.
#1
I am fitting a Bayesian regression model. The outcome is continuous (patient length of stay; a little skewed) and the independent variable is binary (treatment; y/n). There are a couple of covariates (continuous) in the model as well. I wanted to test that patients in the treatment group do not have a length of stay (LOS) greater than 110% of the control group. The model kicks out the intercept, which in this case is the control group's length of stay as well as an estimate for the treatment group's LOS beyond the intercept's value.

I am currently using 110% of the intercept estimate (intercept*1.10 - intercept) as the threshold for the ROPE (region of practical equivalence, but non-inferiority here given 95% of posteriors land below it, with smaller values representing a better outcome). Next, I can plot the posterior LOSs for the treatment group and overlay a reference line (ROPE) and also calculate what probability of the time the treatment group has a LOS less than the control group median + 10% (ROPE). I say median here since stanarm kicks out medians.

My question is whether using 110% of the control group estimate is appropriate? Can anyone see an issue in using that 'estimate' for the calculation of the ROPE?
 
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hlsmith

Less is more. Stay pure. Stay poor.
#2
I have been searching the web and have found pharm/trial examples where they compare a treat estimate to the comparison estimate + the delta, which represents the ROPE. My initial concern was with the ROPE coming from the sample.

control treatment - treatment < margin (e.g. Control treatment * 1.1 - control treatment)

P.S this is seen say when dealing with rates, now I am wondering if i should be using something like: treatment / control treatment < margin (e.g. 1.1)
 
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hlsmith

Less is more. Stay pure. Stay poor.
#3
I have log transformed the dependent variable, placing the change in the predictor as a percent change in the outcome. With the predictor being binary, this represents in expected increase in percentages of the dependent variable and I believe should suffice given 95% of the posteriors for the term are to the left of the threshold.