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I have a dataset with protein measured twice from the same individual at three different timepoints. The data also includes the mean protein measure (the mean of the two repeated measures) for each timepoint.

The data looks like this:

    ID  Timepoint   ProteinMeasure1   ProteinMeasure2   MeanProtein
    1          1               2,47              5,94           4,2
    1          2               3,89              4,16             4
    1          3               2,12              2,29           2,2
    2          1               6,44              6,57           6,5
    2          2                 20             21,24          20,6
    2          3               9,81              9,97           9,9

The researchers originally wanted to see the effect of time on the change in MeanProtein. I am asking: Would it be better/more accurate to test for the effect of time on protein change in a mixed model, using the repeated measures (subject) as a random effect, rather than performing a model on just the mean measures? If this is the case, why would it be better?

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    $\begingroup$ One difference will occur, if you have some missing values for one of the measurements. The mean would look like its more variable, while repeated measures would "correctly" assume it is not more variable, but rather that one of the repeated observation is missing and implicitly impute it under missing at random (rather than by the mean of the other observations with no uncertainty around it, as using the mean of two or 1 available observations would). $\endgroup$ – Björn Jan 15 '16 at 10:56
  • $\begingroup$ Thanks! There is some missing data for the repeated measures, so that's definitely something I should think about. $\endgroup$ – Ederi Jan 15 '16 at 11:25
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I found the answer to my question. It depends on the reason behind sampling repeated measures.

If the repeated measures represent measurement error, then the mean of the two repeated measures is a more accurate value. In this case, it is feasible to use the mean values.

However, if the reason for sampling the repeated measures was because the variable fluctuates naturally from one moment to another, it would be better to use the repeated measures in a mixed model, as these represent the real values.

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