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I'm reading a paper which reports a multilevel model with random intercepts and slopes in which individual people's score on a scale of anxiety is assessed at five different timepoints. So the timepoints are nested inside people.

There is a single fixed person-level variable Treatment, representing the particular type of treatment each person was randomly assigned to (Control, Treatment Type 1, Treatment Type 2). The main aim of the study is to assess whether the treatments work.

The T1 measurement occurs right after the study commences, then all participants view some materials that are likely to provoke anxiety, and then the T2 measurement is made. Then the people are randomly sorted into treatment groups and the treatment is applied, after which the T3 measurement is made. Then T4 is a week after that, and T5 is a few weeks after that.

However, I notice that in their analysis the T1 measurement is omitted. The authors don't give any rationale for omitting T1 other than saying it was done to reduce noise. So they delete the original T1 baseline before running the multilevel model, but leave in the T2 'baseline' which was raised by their manipulation common to all participants but had not yet been affected by their Treatment manipulation.

Does this analysis with the deleted T1 make sense, given their goal of assessing whether the treatments work? Does the answer depend on whether the goal is understanding whether the treatments work with respect to a regular baseline (i.e. timepoint 1), or whether their goal is understanding whether the treatments work with respect to a baseline temporarily increased by circumstantial factors (i.e. timepoint 2?

Note that as I mentioned there is only one predictor variable, and therefore neither the T1 nor T2 baselines are covariates in the study. Would it have made more sense to instead delete both T1 and T2 but then include them instead as covariates?

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A couple of thoughts:

  • If originally in the protocol they planned to take the T1 measurement, it seems a bit strange/fishy that they decided afterward to exclude it. E.g., perhaps the results are not that nice/significant with this measurement in the analysis.
  • From the analysis viewpoint, I don't see any reason for excluding the measurement. You could fit the model with the main effects of treatment and the categorical/factor time variable and their interaction, and then only test if the coefficients of interaction terms between treatment and the T3-T5 measurements are different from zero. Also, if there is a sufficient number of participants, you could fit directly a marginal model with an unstructured covariance matrix for the error terms.
  • If there are any missing data, especially of the missing at random type, it is even more important to not exclude any measurements.
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  • $\begingroup$ Exclusion of T1 increases rather than decreases noise. Adjusting for easily explainable variation in outcomes through baseline covariate adjustment is necessary. Otherwise your effect sample size has just taken a hit. This is discussed in detail in the longitudinal modeling chapter in RMS. $\endgroup$ Nov 17, 2021 at 13:25

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