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I have a response variable measured at three time points per individual (week 0, 18, and 36). I am interested in differences in the change of the response over the 36 weeks within some categorical variable X.

I see two ways of modeling this.

  1. One way ANOVA with response = week_36_score - week_0_score (this seems like the simplest option)

  2. Repeated Measures ANCOVA with response = week_18_score and week_36_score. Covariate = Week_0_score.

Question

  • Which would you prefer (if any, maybe there is a better choice)?

I know there has been a lot of articles on this and they seem to say each has its own strengths and weaknesses. I believe the second model would have more power. I am not worried about a ceiling effect here.

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In general, I would go with a repeated measures design.

There is nothing technically wrong with the first option. However, you are essentially throwing away 1/3 of your data (and 1/2 of your non-baseline data!), which may result in a lost of power. Additionally, since you have a measurement in between baseline and 36 weeks, you cannot conclude anything about the shapes of the response profiles (i.e. test for a quadratic/cubic effects over time.)

With that being said, for your repeated measures design, I would define a new variable called response_change. I am assuming that you are interested in testing if X has some effect on changes in the responses. At week 18, this variable would take value week_18_score - week_0_score. At week 36, this would take value week_36_score - week_0_score. Using response_change is more suited to this hypothesis.

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    $\begingroup$ Great suggestions. I like the response change idea. With this approach would I still need the week 0 score as a covariate? Also what would be different if the week 36 value was week_36_score-week_18_score? $\endgroup$ – Glen May 3 '11 at 16:42
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There are difficulties in computing change. This doesn't work on ordinal repsonses, and for continuous responses makes a strong assumption of proper choice of transformations for the variables. I recommend adjusting for baseline and modeling the 2nd and 3rd measurements as longitudinal measurements.

Repeated measures ANOVA is becoming obsolete in favor of generalized least squares or mixed effects models.

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