How to calculate the weighted mean (when weighting factor is not given) for some groups of respondents using a statistical method?

Question

We have 4 cohorts (15, 10, 5, 20 people) and out of these we got responses from few of them in each cohorts (10, 6, 5,16 ) to measure the weight (gained or lost) in a week (in kg) when having a medicine. We have to calculate a weighting factor for each cohorts to measure the weighted mean so that we can compare relative effect of medicine on these cohorts.

Answer 1

I would first remove non-responders from the analysis - you don't know how their weight changed anyway.

Then I would compare the percent difference in each complete cohort (10,6,5,16) for before and after. That would result in something like: (+20%,-12%,-6%,+31%).

In general, you would ideally want the cohorts to be the same size, but I think you can still look at these percent differences for some directional inferences.