This is a clinical study. Just have a look in the ethics application, there should be explained what kind of data is obtained, what statistical models are used and which statistical hypothesis are to be tested therein.

As far I understand, you may do 24 factorial experimental design to observe the difference and interaction effects among data.

Yasin Arafat can you explain what you mean by "24 factorial experimental design"?

Rainer Duesing for details please visit the link: 14.2: Design of experiments via factorial designs - Engineering LibreTexts

There is no link @Yasin

https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Book%3A_Chemical_Process_Dynamics_and_Controls_(Woolf)/14%3A_Design_of_Experiments/14.02%3A_Design_of_experiments_via_factorial_designs

Rainer Duesing

Yasin Arafat I understand that, but how do you come to the conclusion that this is a 24 factorial design?? Your reference defines a 2n factorial design for experiments, where each of the n factors has 2 levels, and therefore a 4 factorial design has 2*2*2*2 = 24 = 16 groups/combinations. But what Devendra Kumar Singh Varshney described sounded more like a two-factorial 4 (intervention arms) * 3 (measurement point) design with repeated measures on the second factor. Please correct me, if I am missing something here.

And I totally disagree with the following from your reference:"Typically, when performing factorial design, there will be two levels, and n different factors." I think this special case, that ALL factors have only two levels, are very rare, at least in social and medical sciences.

Rainer Duesing Kindly guide me as to how to proceed. thank you

I guess your dependant variable is not continuous data, in such scenario the Friedman test is most appropriate test.

Kandasamy Ravichandran Thanks for replying sir.. Appreciate your response.

For a simple answer we need to ignore that you took two measures (4 week and 8 week) and pre select which is the most important and use that for the primary analysis. Next we need to account for the multiplicity (3 treatment arms compared to a common control arm) we could do a simple Bonferroni and divide your alpha level by 3 and compare the p-value for each treatment to that one third alpha to see if you have significance. A better (less conservative, more powerful) adjustment would be a Dunnett’s and you’ll need some software to that for you.

Now you could get more ambitious and take into account that one of your experimen arms is the combination of the other two. I don’t know how to do this in a frequentist framework, but abandoning the t-test we could fit a Bayesian model where we estimate T1, T2 and T1+T2 with an interaction term that we can put a prior on to keep it within reasonable bounds.

Not sure what you want to do with the data from 2 time points, there are several options but only you know what’s important here. Perhaps the results at either time is interesting (a ‘quick acting‘ treatment and a ‘sustained’ treatment), perhaps a treatment needs to be effective at both endpoints, perhaps you want the average treatment effect over both timepoints, perhaps you only want to use the 4 week endpoint for patients where you were unable to collect 8 week data.

Tom Parke Sir thanks a lot for your precise guidance. I appreciate your guidance a lot. regards, Devendra