# Percentages as a continuous variable

#### NN_STAT

##### New Member
Hello all

I have a variable, on a continuous scale, it is some medical value before getting a treatment. After the treatment, this value is being reduced. For some people by 10%, for some by 13%, 15%, 20%, etc,....

I have two of these treatments, and I am comparing them. Is it legal (I can't think of a reason why not) to compare the mean reduction ? By mean reduction my intention is: if in one group there are 3 patients (just for the example), and the first had reduction of 10%, the second 13% and the third 17%, than I can say that the average reduction was 13.33%. Now I want to compare the mean reduction for both groups. I make a mean of percentages, is it legal ?

thanks

#### hlsmith

##### Omega Contributor
Instead of percentages, can't you just use the mean differences. What do you get by converting them?

#### NN_STAT

##### New Member
I can't use the mean difference because the baseline is not the same, not every patient start with the same value
for example:

patient 1 started with 30 and reduced to 18
patient 2 started with 33 and reduced only to 20

I can't ignore that patient 2 started with a higher score

#### BGM

##### TS Contributor
It seems that you assume the the medical value before and after treatment is taking the form $$M$$ and $$M(1 - P)$$ respectively; and similar for the other group. And you are doing a hypothesis test, comparing the expected value/mean of the random variable $$P$$ of the two groups.

It is nothing illegal; you should concern whether such model assumption is justifiable (like you stated the baseline issue), especially if that is not a common practice in your field. And whether such assumption fulfill your ultimate objective.

#### NN_STAT

##### New Member
BGM, you are right, this is what I am trying to do. I have reasons for doing it, for example, if I would say that a 15% reduction is a success (legitimate claim in this case) then I would compare the proportion of patients with a success in each group. Since in the control group the success rate is relatively high (the new treatment is assumed to be non-inferior but safer and easier), the sample size I will need will be extremely high, with no practical value (company can't afford it).
By doing what I asked, I move to a continuous scale, I still have a value to my hypothesis, and the sample size is perhaps not small, but practical. For a company there is a big difference between a sample of 200 patients and 700 patients...