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  • Help interpreting longitudinal mixed model interaction term

    Hi all

    I have data from a randomized trial that measures the effect of an intervention group (0/1) on a biomarker outcome measured at 3 time points (0hr, 12hr, 24hr). I have constructed the below model to assess whether there is any difference in change in the biomarker outcome over time by group. The biomarker is log transformed as it is not normally distributed.

    mixed log_biomarker group##i.time || StudyID: studysite, cov(exch)

    The output gives me a significant interaction effect at the 24 hour time point with a coefficient of 0.3 and p-value of 0.04.

    I understand this means that there is a difference in the trajectory of the biomarker between group with respect to time. What I'm not clear on is how to report this coefficient. Is it fair to exponentiate it ~1.4 and say that a change in group results in a 40% difference in slope over time? Is there a way to use margins here?

    Thanks in advance for any suggestions!








  • #2
    First, your -mixed- model is mis-specified unless you plan to constrain the mean slope for studysite to zero. Also, the variable name studysite evokes, in my mind, a discrete, not a continuous variable. If that's the case, the specification StudyID: studysite is completely off-base, because it treats studysite as a continuous variable. In fact, if your design is the fairly common one were observations are nested in StudyID and StudyIDs are nested in study sites, then you actually need a three level model (or, if the number of study sites is small, a two level model with studysite as one of the fixed effects.) So I think you are trying to interpret coefficients that are coming from an invalid model.

    That said, assuming that your base catgegory for the time variable is 0 hr, this means that at time 24 hr, the difference between the expected log_biomarker in the intervention group and in the control group is 0.3 greater than it is at time 0 hr. It is a difference in differences. If you exponentiate it you will have the corresponding ratio of ratios. Both of these are fairly difficult for most people to grasp intuitively, and I think the ratio of ratios is, for most people more difficult.

    Non-normal distribution is not a good reason to log-transform a variable. If you are interested in framing the results in the original non-transformed metric, then just do the regression in the non-transformed metric in the first place--the non-normality isn't an issue unless your sample size is small. Log-transforming would be appropriate if the model fits poorly and the fit is improved by log-transforming, or if the log-transformed results gave homoscedastic residuals where the untransformed results do not. But non-normality is simply not a reason to log-transform.

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    • #3
      Thanks Clyde. Appreciate the help! The number of sites is only 5 and the total N is 80. We can change the site ID to a fixed effect as you suggest. For now, based on prespecified analysis plans, the biomarker will need to remain log-transformed (and the distribution is highly skewed with only 40 patients per group).

      When I exponentiate the interaction coefficient I get 1.35 (exp^0.3). Would it then be fair to say that there is a 35% geometric mean difference in the slope of the biomarker over time?

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      • #4
        When I exponentiate the interaction coefficient I get 1.35 (exp^0.3). Would it then be fair to say that there is a 35% geometric mean difference in the slope of the biomarker over time?
        No. What you can say is that the ratio of the geometric mean biomarker in the treatment group to the geometric mean biomarker in the control group at time 24 hours is 35% higher than the same ratio of geometric means at time 0.

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        • #5
          Got it. This is very helpful. Agree not the easiest for a reader to understand. Thanks!

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