Does Imposing a Constrain Make a Method More Powerful?

Suppose we have 100 patients in a randomized trial. 50 of them are in treatment group and the rest are in placebo group. This is a longitudinal study so that we measure the response from each individual at four different periods: baseline, week 1, week 4, and week 6.

Now suppose we have good reason to assume that "the two groups (treatment group and placebo group) have the same mean response at baseline". But one researcher considered the method with the assumption (Method 1) and another researcher considered the method without the assumption (Method 2). Both researchers got equivalent results.

Now my question is while the assumption of equal mean of baseline in different groups hold, then why do not considering the assumption make the method *LESS POWERFUL* while I am getting equivalent results from both the two methods?

The question arose after reading of adjusting for baseline response&f=false

Thank you.


TS Contributor
just my 5 cents: If you are tracking differences between two groups over time and you have to consider that even at time 0 there was a difference between the two groups then, I would think, that you will be less able to see an effect due to a treatment - I mean if at time T there is a a differenec D between the two groups, that can be in part due to the original difference and only in part due to the treatment. If I can assume, that originally there was no difference between the two groups then the whole D is only due to the treatment - hence this is a more powerful method.