[R-sig-ME] Advice for modelling a crossover RCT

[Chris Howden]

Thanks Jorge,

Generally I believe one doesn’t include a factor as both fixed and random, as my understanding of that is that it effectively means you’re trying to estimate its effect 2 different ways so its effect has to be split somehow between the fixed effect parameter and the random effects BLUP. But there is no objective way to do this, and it doesn’t really make sense to do that either. So you need to pick a way i.e. is the effect of each person being captured as a fixed effect parameter or in their random effects BLUP. So I don’t think this ones appropriate M2 -> Y ~ GROUP + CONDITION + SEQUENCE + PERIOD +  (1 | ID / SEQUENCE /
PERIOD)


As for this one  M2 -> Y ~ GROUP + CONDITION + SEQUENCE +  (1 | ID / SEQUENCE /
PERIOD)

I’m not sure you have enough data to fit all those random effects!! I’m also not entirely clear if period makes sense in that context – although it might. I’d suggest you start simple and get complex if you think it does. So maybe fit the model with (1 | ID) then (1 | ID / SEQUENCE)  then (1 | ID / SEQUENCE / PERIOD) to see how they go.

Chris Howden B.Sc. (Hons)
Founding Partner
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Evidence Based Strategy/Policy Development, IP Commercialisation and Innovation
(mobile) +61 (0) 410 689 945 | (skype) chris using trickysolutions.com.au<mailto:chris using trickysolutions.com.au>

From: Jorge Teixeira <jorgemmtteixeira using gmail.com>
Sent: Thursday, 13 February 2025 10:58 PM
To: Chris Howden <chris using trickysolutions.com.au>
Cc: R-mixed models mailing list <r-sig-mixed-models using r-project.org>
Subject: Re: [R-sig-ME] Advice for modelling a crossover RCT

Thank you, Chris.

By period I mean the order of the exercise condition within each sequence (aka cycle).

Maybe cycle/ period resonates better for you. See fig 1 of Individual responses to topical ibuprofen gel or capsaicin cream for painful knee osteoarthritis: a series of n-of-1 trials - PubMed<https://pubmed.ncbi.nlm.nih.gov/33197270/>  https://pubmed.ncbi.nlm.nih.gov/33197270/  .

Carryover effects are irrelevant for the study, imo

A quarta, 12/02/2025, 22:26, Chris Howden <chris using trickysolutions.com.au<mailto:chris using trickysolutions.com.au>> escreveu:
Hi Jorge,

I'm not sure you are going to have enough sample to fit complex mixed models, so I would build them up from a simple one and see how they go. The more complex ones may have a hard time converging.

Looks to me like M1 -> Y ~ GROUP + CONDITION + (1 | ID/Sequence) might fit and make sense. I would interpret yr notation to mean that each person is getting their own random intercept, and then each person's sequence is also getting their own random intercept (after accounting for the persons random intercept), is that what you are aiming for? If the exercises aren't particularly onerous or difficult than I would suspect Sequence will come back explaining very little variance and could be dropped - but if onerous you might find they do the 2nd one worse, and if difficult the 2nd one better as they have time to learn.

But what is PERIOD? (I may be missing something, but I can't see where you explain that?)


Chris Howden B.Sc. (Hons)
Founding Partner
Data Analysis, Modelling and Training
Evidence Based Strategy/Policy Development, IP Commercialisation and Innovation
(mobile) +61 (0) 410 689 945 | (skype) chris using trickysolutions.com.au<mailto:chris using trickysolutions.com.au>

-----Original Message-----
From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org<mailto:r-sig-mixed-models-bounces using r-project.org>> On Behalf Of Jorge Teixeira
Sent: Thursday, 13 February 2025 2:00 AM
To: R-mixed models mailing list <r-sig-mixed-models using r-project.org<mailto:r-sig-mixed-models using r-project.org>>
Subject: [R-sig-ME] Advice for modelling a crossover RCT

Dear everyone,

I am going to conduct a randomized crossover study where participants (about 20) are divided into 2 groups due to logistics constraints. The study involves participants performing 4 different exercise modalities (i.e., 4 conditions) in a randomized order, in two SEQUENCEs. So, there are a total of 8 sessions (2 for each exercise modality), per participant.



Given this setup, I am unsure about what is the correct mixed-effects model to use in this case, and also any further insights or considerations you believe I should need... I'll be more than happy to listen!



Some suggestions:

M1 -> Y ~ GROUP + CONDITION + (1 | ID)

M2 -> Y ~ GROUP + CONDITION + SEQUENCE + PERIOD +  (1 | ID / SEQUENCE /
PERIOD)

 M3 -> Y ~ GROUP + CONDITION + (1 | ID / SEQUENCE / PERIOD)



Thank you in advance for the help

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