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Is it valid to use change scores, i.e. like change in body weight taken between consecutive time points in longitudinal analysis where I'm using nlme/gee? For example, bodyweight at hour 3 minus bodyweight at hour 2, body weight at hour 4 minus bodweight at hour 3 to predict a binary outcome?

Is logit(odds)=intercept+$\beta_1$*(change in bodyweight between two time points) + $\beta_2$*(change in bodyweight between two other time points) +.... $\beta_n$(change in body weight between $x_{k+1}$ and $x_k$th time) + country effect + time*drug effect valid?

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Apart from the points mentioned already some other issues potential considerations are:

  • The time points need to be the same for all subjects. If you have someone coming at 1.4 hours and someone at 1.6 hours, it could be problematic round these up or down at 1 hour and at 2 hours.
  • Related to the above point, you will potentially have problems with these change scores if some subjects have missing data. You would need to impute first.

An alternative approach could be to fit a mixed model for bodyweight and use the empirical Bayes estimates of the random effects as a summary of the longitudinal profile of each subject.

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You could. The real problem with using change scores (regardless of whether it's an independent or a dependent variable) is issues with regression to the mean. Those with extreme baseline ("pre") scores--in either direction--are more likely to have large change scores. This information is therefore packed into the change score, but may not be what you're targeting when you calculate it; that is, your change score is actually reflecting a mixture between what you're trying to measure (the magnitude of change), and something about the baseline score.

A second, closely related, limitation is that the change score can have different meaning depending what the baseline score was; is the scale you're dealing with an interval scale? In other words, does the different $\delta$ have the same meaning regardless of where you are on the scale?

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