Percent Portion of Logged DV

hlsmith

Less is more. Stay pure. Stay poor.
#1
Well my brain is not on today. I have a continuous outcome, I was going to run a regression where if a categorical variable's coefficient(X1) was greater than 110% of the reference group (intercept) my hypothesis would not be supported. Since this is a non-inferiority hypothesis and bigger numbers are worse. I was running a Bayesian model so I was going to use the following for the cutoff for each X1 estimate in the posterior:

Non-inferiority: 95% of X1 estimates < ((intercept * 1.10) - Intercept)

However, since the dependent variable is a little skewed, I am logging it. Given this, what do I change the right-hand side of the above equation? Since now it is in percentages. For simplicity, the whole Bayesian thing can be ignored, I just need to figure out what the 110% threshold calculation would be for a natural logged continuous variable.