Dear All,
I would be grateful if someone can help me for the following puzzling problem.
I have a longitudinal data about n = 300 Alzeihmer's patients. Each patient "i" has a number of visits "n_i" say.
For each patient "i" and at each visit "j" some measures have been taken such that: Y_ij, Age_ij and X_i1 where Y_ij is the dependent variable
Age_ij is the age of the patient "i" at visit "j" and X_i1 is a baseline covariate observed at visit 1 only (X_i1 may be a time-varying covariate but for some technical reasons we observe it at visit1 only). Furthermore, the number of visits are not the same for all patients. However, the interval between two consecutive visits is constant and is equal to 6 months.
The main objective is to test whether the baseline value "X_i1" has a significant effect on "Y_ij" or not. To do that, I used a linear mixed effect model (longitudinal data) but with two different parameterizations:
1- I used the linear mixed effects model: Y_ij = beta0 + beta0i + beta1*Age_ij + beta2*X_i1 + epsilon_ij
Results: beta2 > 0 and the corresponding p-value < 0.05.
2- I used the linear mixed effects model: Y_ij = alpha0 + alpha0i + alpha1*j + alpha2*X_i1 + alpha3*Age_i1 + epsilon_ij
where Age_i1 is the age of patient "i" at the first visit, i.e. at visit "1".
Results: alpha2 < 0 and the corresponding p-value < 0.05.
Thus, the conclusison drawn from the two models are not the same. The first one says that "X_i1 " has a positif effect on "Y_ij" and the second one says the converse even if the two models seems to be identical from the parameters interpretation point of view.
Many thanks,
A.O
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