Sample size and 2x2 factorial randomised control trial with interaction

[Jen Ward]

I am looking to estimate the necessary sample size for a 2x2 factorial randomised control trial, where the primary outcome is hospital discharge (yes/no) at 3 months. We are interested is in the 2 main effects as well as the interaction. For the two main effects, I plan to use the -power- command but I am not sure this command can help with the interaction.

Can anyone suggest how to do it?

[Ken Chui]

Chuck Huber posted a very cool and detailed blog post on how to solve this with simulation: https://blog.stata.com/2019/08/13/ca...ic-regression/

[Jen Ward]

Amazing, thanks for the link!

[Jen Ward]

Ken Chui thanks again for the link.

I have two follow-up questions based on the code; I am assuming I can use the same approach when the two predictors are binary - is that correct? I my case, I don't have such rich dataset to get estimates of the parameters, I can use previous studies but I am not sure what the value for the intercept should be...

In my case, I have 2x2 factorial RCT where each factors consist of a new treatment (vs. control), so I am assuming the intercept reflects the the likelihood of discharge in those in the control condition of both factors/variables, is that correct? and if so, would assuming 50% be OK? or is there anything else I should consider...

[Ken Chui]

Yes, the intercept is the logit(y=1) when factor 1 and factor 2 both equal 0. So, you can look at this imaginary 2x2 table, and make a best guess.

By the way, if you or your colleagues have access to a software called PASS, it can also compute 2x2 factor + interaction as well.

[Jen Ward]

Thanks Ken Chui for such a quick response. I suppose the the probability for groups receiving control interventions could be estimated from usual care data...

Unfortunately, we don't have access to PASS