I'm having a mixed model with 5 repeated measurements (time is categorical because the timepoints represent discrete events).

Edit: I have 5 meaningful timepoints: t0 baseline (neutral timepoint); t1 invitation to intervention; t2 shortly before intervention; t3 shortly after intervention; t4 participants receive the result (good or bad news).

I also have 2 treatment groups (randomized trial).The outcome variable is self-reported quality of life (e.g. mental health measured by questionnaire). My plan is to first build a mixed model to test for the significance of the interaction between treatment and time, and then look at specific contrasts (e.g. difference in change in QoL between groups at t0 vs t1)

While the measurement points are equally spaced between the last 4 measurement points for both groups, the average time elapsed between baseline (t0) and the intervention appointment (and thus also t1, t2, t3, t4) differs considerably between the two treatment groups (around 43 days), see image below for illustration.

The reason for this difference is not random sampling error, but a a logistical one, i.e. it was easier to plan in the treatment appointment for treatment group 1 than treatment group 2, as less technologically advanced equipment was used.

I do think that this time difference could impact the outcome variable (e.g. the longer the time elapsed, the more likely it is that a significant event has happened that impacts quality of life). Therefore I would like to control for it, for example when comparing the change in QoL between the two treatment groups for t0 vs. t1.

Does it make sense to use the time between baseline and intervention as a covariate in the model?

So, for example the R code for the model would be:

lmerFitQoL <- lmer(QoL ~ time * treatmentgroup+ timedifference + 
                   (1| id), data = datQoL)

where timedifference= difference in time between baseline and treatment appointment

Would that be a suitable solution in your opinion? I'm unsure if I'm on the right path here or if there is a better way.

enter image description here

  • $\begingroup$ Please edit your question to say more about why the 2 treatment groups differ in their timing between $t_0$ and the time of the intervention. It's one thing if that was just an unlucky result of sampling; it could be another if there is something systematically different between the 2 treatment groups. Also, what is the nature of your QoL measure? The more details you can provide about those aspects of your study, the better the potential answer. Please provide that information by editing the question, as comments are easy to overlook and can get deleted. $\endgroup$
    – EdM
    Mar 1, 2022 at 18:43
  • $\begingroup$ Thanks for the pointers! I edited my original post and I hope it's more clear now. $\endgroup$
    – Dilara
    Mar 1, 2022 at 19:09

1 Answer 1


It would seem most important to ensure that the groups had similar QoL outcome measures at t1 or t2, as those time points are fixed with respect to the intervention time. Your question says that you might include a t1 versus t0 comparison. That doesn't seem to make much sense in terms of evaluating the intervention, however, as the intervention doesn't happen until after t2.

You might want to examine changes from t0 to t1 in a separate analysis with a continuous measure of time in days. That would help you evaluate whether the two treatment groups were adequately well matched both at enrollment into the study and at the time point t1 that (unlike t0) occurs at a fixed time prior to the intervention. It would also let you see if there is any systematic change over time in the outcome measure absent the intervention.

If the groups are adequately well matched at t1, however, I don't see any need to use values at t0 as part of evaluating the intervention itself. You might, however, need to evaluate them as part of your quality control.

In response to comments

I think it's important to distinguish the direct effects of the intervention from possible changes in QoL values associated with the treatment-group assignment, presumably done at t0, which might lead to systematic differences between t0 and t1.

With similar distributions of QoL values between the 2 treatment groups at t1, the specific effects of interventions per se can probably be described as differences between pre-intervention (t1, t2) and post-intervention (t3, t4) QoL values. Think carefully how you want to do that, as the more coefficients you have to estimate the lower power you might have.

For example, might the QoL values at t1 and t2 be considered replicates rather than separate values? Might it make sense to model QoL differences between t1 and t2 against corresponding differences between t3 and t4, both representing 13-day periods? You need to apply your knowledge of the subject matter to make those decisions.

You certainly should examine potential changes between t0 and t1, but such changes would have to do with either the time interval or the group assignment (e.g., due to the potential psychological effects you mention) rather than with the intervention per se. They thus would require a type of explanation other than a direct effect of the intervention.

Don't overthink the t0 to t1 differences. What you presumably want to do is to assure yourself and your audience that any such differences between the 2 assignment groups are small enough not to affect your interpretation of the direct intervention effect. Don't worry so much about whether you have the "best" model for the t0 to t1 difference. Just develop one that's adequate to address that potential concern.

A simple analysis of the paired t1-t0 differences within individuals should be adequate and accomplish more simply what you propose in a comment to do with a mixed model. If you are only examining paired t1-t0 differences you don't need the time*treatmentgroup interaction, just the treatmentgroup assignment itself. Flexible inclusion of timeddifference in the model of the t1-t0 QoL paired differences with a regression spline makes sense. You will need more than the 2 degrees of freedom you propose in the model in your comment, however, as that doesn't allow any knots at all. I prefer to model splines with the rcs() function in the R rms() package, in part because (unlike ns()) it provides reasonable default parameter settings.

  • $\begingroup$ The reason I want to compare t1 to t0, is that t0 would represent a more neutral point of time, while t1 already represents a potentially anxiety-inducing event (invitation to the treatment appointment). I have made the appropriate edit in the original post. So according to you, I should do a separate analysis when I want to compare t0 vs t1 or t0 vs t2 with time as continous measure? It's not possible to incorporate this time difference between t0 and the other timepoints as a control variable in the overall model? Thanks so much for your time, it's much appreciated. $\endgroup$
    – Dilara
    Mar 1, 2022 at 20:21
  • $\begingroup$ @Dilara it's possible to incorporate the time difference from t0 to t1 into your model. The model that you propose in the question could do that; you might also add the QoL score at t0 as a predictor along with a flexibly modeled timedifference and set t1 as 0 time for all cases. Then your random intercepts would represent deviations about the t1 QoL. The question is what that would accomplish if there's good balance in QoL between the 2 groups at t1. Presumably both treatment groups have the same anxiety potential at t1 due to the invitation. $\endgroup$
    – EdM
    Mar 1, 2022 at 21:03
  • $\begingroup$ Thanks @EdM! For my understanding, what do you mean with alongside a "flexibly modeled" timedifference? What does flexibly modelled mean in this context? The reason I want to compare the increase in anxiety between the two groups is that the treatment with the more technologically advanced equipment might provoke even more anxiety, also at invitation. I'm note sure if I understand how I could compare the QoL change at t0 vs t1 between groups with the solution you suggested. Does it mean that the grouping factor for the random intercept should be treatmentgroup (1|treatmentgroup)? $\endgroup$
    – Dilara
    Mar 1, 2022 at 21:42
  • $\begingroup$ @Dilaria the way you included timedifference in your proposed model, you assumed a strictly linear change of QoL with time. That might not be the case. It can be better to use a regression spline (with ns(), or with rcs() in the rms package) to allow for more flexible associations between continuous predictors and outcome. I'll update my answer in a day or so to illustrate, but much depends on something you can evaluate right now: how well balanced are the QoL values between the 2 treatment groups at t1? $\endgroup$
    – EdM
    Mar 1, 2022 at 22:10
  • $\begingroup$ So I could use a non-linear time effect, for example: lmerFitQoL <- lmer(QoL ~ time * treatmentgroup+ ns(timedifference,2) +(1| id), data = datQoL)? Or test with AIC/BIC whether a model with a non-linear term with 2 or 3 splines is better than a model with only linear effect? To answer your question, I just checked and at t1 the means of the groups are pretty similiar and not stat. significant, but that doesn't mean that there could not be a sig. difference in QoL change from t0 to t1, no? If you could indeed elaborate on your thoughts, this would be very helpful! $\endgroup$
    – Dilara
    Mar 2, 2022 at 15:46

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