interpreting logistic regression coefficients when reversing the reference group

Question

I applied logistic regression to check the relationship between a binary variable that is called FG and few independent variables

the reference group for the variable SSE is SSE1. The OR is 0.48 meaning that the chances for those in SSE2 (from the same age group and the same physiological status) decrease by 52% to be in FG group 1 compared to those from SSE1.

However now when considering SSE2 as the reference group :

now OR for SSE1 is 2.08 meaning the chances for SSE1 are 108% higher to be in FG group 1 compared to those from SSE2. Is it logical this way or am I making some interpretation error (because I thought that the resulted OR must indicate 52% more of chances) ? Thanks.

Answer 1

I strongly recommend that you don't try to interpret such results in terms of percentage changes. That too often leads to confusion like this. See Frank Harrell post on "Why I Don't Like Percents."

If you just stay in the odds ratio (OR) scale, everything makes sense. The OR for SSE2 versus SSE1 is 0.48 in the first model. The OR for SSE1 versus SSE2 in the second model is exactly the inverse, 1/0.48 = 2.08, as expected. The problems arise when you try to convert to percentage changes as the baseline for comparison changes. There's no need to do that. As Harrell says:

Many quantities reported in the scientific literature are naturally ratios. For example, odds ratios and hazard ratios are commonly used. If the ratio of stroke hazard rates [in] treatment B compared to treatment A is 0.75, I prefer to report “the B:A stroke hazard ratio was 0.75.” There’s no need to say that there was a 25% reduction in stroke hazard rate.