Mixed effect model and baseline dependent variable as covariate
I would like to determine which predictors are associated with the rate of change in a continuous dependent variable repeatedly/longitudinally measured over time in each patient. The analysis will use a mixed effect model. The model will therefore include an interaction term between the predictor and time (c.time in STATA) and the coefficient for the interaction term will give what is essentially a difference in slopes. So, if the predictor is gender, and males (coded 0) have a c.time coefficient of 1.5 (slope) then the interaction term could give a coefficient of say 0.5 and tell you that females (coded 1) have a slope of 2.0.
This will be tough since I have many variables which will involve many interaction terms (one for each variable) and the interpretation may get complicated. I recently came across an article that states the following where FEV1 (lung function) is the outcome that is being repeatedly measured and mixed effect model is also used:
" All models include baseline lung function as a covariate; therefore, the regression coefficients express the influence of predictor variables upon the annual rate of decline of lung function. " (PMC2078677)
However, is this correct? I tried this with sample data to see if the answers match and they do not. I am not sure if I am doing it right.
I did the following in STATA:
1) xtmixed y gender##c.time || id:, var
and compared this to
2) xtmixed y gender time baseline_y || id:, var
I guess I was expecting the gender coefficient from 2) to match the gender##c.time coefficient from 1) which seems very silly now.
My only other option would be to group individual slopes of the dependent variable into high and low slope patients to use in a logistic regression model which doesn't adjust for covariance. I am wondering what you all think of this as well.
I did something like this some time ago. I just did multiple linear regression of rate of FEV1 loss ( FEV1 at time x - initial FEV1) / time between measurements) (dependent variable) vs age, height, dust., smoking,alcohol etc (indep variables). you could easily add sex.
see attached paper
Thank you for your answer James.
If I am understanding this right, your study had two measurements? The data I have include patients with 0 to 8 measurements and using only two of these measurements would result in loss of data. Also the change seems to be non-linear for many patients.
Hi Spencer,
There are several different issues you raise in your post; I will only give an answer to one.
The example you give in the first paragraph suggests you understand the point of the interaction. However, take care that the coefficient you get for gender represents the difference between genders AT THE INTERCEPT. Thus, in model 1 this is the difference between genders at c.time = 0 (assuming you did not center time), whereas in model 2 - since you have constant slopes per gender (no interaction) it is the average difference over the whole time range. It would then come as no surprise to have different effect sizes if the effect of gender changes along time (equivalent to saying the effect = slope of time changes according to gender). This is why it is recommended to center continuous variables on their mean/median/relevant-value especially when interactions exist in the model (take a look at Schielzeth 2010, Methods is Ecology and Evolution, "Simple means to improve the interpretability of regression coefficients").
Hope that helps.
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