Sample size calculations - when to consider interaction

Hi Everyone,

This is my first post and as I’m a recent M Biostats graduate, there are fairly large gaps in my knowledge, so please go easy on me. I figure this will be a good place to learn…

I have a question about how to handle power/sample size calculations in clinical trials. My understanding (based on what has been taught in the course) of sample size calculations in an RCT context has been about two-group comparisons (treatment vs control) for means, proportion, etc.

But in many RCT’s one is interested in the variation in treatment effect over time - i.e. the group by time interaction. In the longitudinal study then, such sample size calculations as described above really only estimate sample size/power for the hypothesised main effect at the end of the study.

Does this effectively mean that whenever one anticipates testing a group x time interaction in the subsequent modelling, their power calculations should be based on an interaction term (which I understand will result in a larger sample size?) rather than just a main effect?

Apologies if the answer is obvious but as I said, there’s still a lot I have to learn.




This is a deep question deserving of several answers. Here’s a start just to further set up the problem.

Until you mentioned longitudinal, I was ready to say that with parallel group clinical trials we’re lucky to get sample sizes that are adequate for assessing the overall main effect of treatment, let alone interaction. There estimation of interactions requires a minimum of 4 times the sample size to estimate a main effect, or 16 times greater to have adequate power as studied by Andrew Gelman. But in longitudinal studies we are routinely interested in treatment x time interaction, and studies are often sized to be able to do that. The reason for such automatic emphasis on interaction is that we often expect treatment to have a delayed effect, and we sometimes expect a treatment effect to wear off within a participant.

All that being said, I hope that others can point us to excellent references on sizing longitudinal studies, accounting for time x treatment interaction.

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i guess id have to hear a specific example. i’m not sure if drugs/interventions could be characterised by waning effects very often? Time to some event is a typical analysis ie changing disease status. In industry there might be a reluctance to create ambiguity or acknowledge that effects wane or generate added costs or uncertainty, and a desire for a simple study design? We don’t really believe power calculations very much anyway

Have a look at this article by Guo and colleagues from 2013:

Selecting a sample size for studies with repeated measures

This article was published in combination with GLIMMPSE, which can be used for power calculations for studies with repeated measures. Documentation for GLIMMPSE can be found here.

This probably does not answer your question directly but may give some pointers that I (as a non-statistician) have previously found useful.
Here they factor in interaction, variance and correlation structures.

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