Sample size for a comparison of means based on rates In a clinical trial, I want to demonstrate an effect following an intervention between two groups.
The outcome variable is the rate of improvement. That is, the patient may experience an improvement (e.g., 1.2) or, on the other hand, a worsening (e.g., 0.9) after the intervention. And a value of 1 would indicate no change.
So my question is how we should look at this contrast as a difference or mean (continuous) or as a difference of proportions.
The scale seems to be standardised, but it is not really a proportion.

The answer depends on what real world property is being measured.
This question might give a clue: can the measured value be negative? If not, then a proportion is probably more natural.
If the value reported is the contents of a bank account, overdrafts are possible, so changes should be modelled as amounts in currency. If the value reported is mass of adipose tissue, then proportional change is more natural. If the value reported is percentage of body mass that is fat, then neither is great.
