Controlling for baseline measures in longitudinal models (random-effects logit model or linear mixed-effects)

[Dan Segal]

A cohort of ~2,000 individuals initiated on treatment for immunosuppressive disease have been followed for 2 years, with weight/BMI assessed every 24 weeks. There is a hypothesis that individuals with lower baseline CD4 counts, indicative of severe disease, may experience uncontrolled weight gain.

A lower baseline CD4 count was highly correlated with a lower baseline weight/BMI. Since these individuals are expected to put on weight (many start underweight), I want to distinguish between healthy and uncontrolled weight gain. I use obesity (BMI>30) as the dependent variable instead of continuous weight or BMI. I don't expect the effect of baseline CD4 to be linear; nor do I think time effects will be linear.

I initially used a Cox model to explore time-to-obesity, but was uncomfortable with this as it necessitated excluding those already obese at baseline.

I am using the following random-effects logistic models:

xtset id week
xtlogit obese i.cd4_cat_j0 i.week age i.sex, vce(robust)
xtlogit obese bmi_j0 i.cd4_cat_j0 i.week age i.sex, vce(robust)

In the first model, none of the CD4 categories (CD4_cat) are significant.
In the second model, where I adjust for baseline BMI, CD4 is highly significant. This model has a better fit.

My question is, how do I interpret these coefficients? Is it appropriate to control for baseline BMI in these models given my research question?

If I were to use a linear mixed model for weight or BMI, what would the interpretation be? Would it be right to say that without baseline BMI in the model, you are looking at absolute BMI, while including baseline BMI, the interpretation is the change in BMI from baseline?

mixed bmi i.cd4_cat_j0 i.week age i.sex || id:, mle
mixed bmi bmi_j0 i.cd4_cat_j0 i.week age i.sex || id:, mle

Thank you for any help you can provide!


Results from xtlogit models:

obese    Coefficient    Std. err.    z    P>z    [95% conf.    interval]
                        
bmi_j0    1.643538    .0788033    20.86    0.000    1.489086    1.797989
    
cd4_cat_j0    
<100    3.428602    .4571158    7.50    0.000    2.532672    4.324533
100-200    1.4032    .3915591    3.58    0.000    .6357582    2.170642
200-350    .8467031    .3493983    2.42    0.015    .1618951    1.531511

obese    Coefficient    Std. err.    z    P>z    [95% conf.    interval]
                        
cd4_cat_j0    
<100    -.3677383    .5492342    -0.67    0.503    -1.444218    .7087409
100-200    -.4421264    .4927452    -0.90    0.370    -1.407889    .5236365
200-350    -.1903435    .4341114    -0.44    0.661    -1.041186    .6604991

[Erik Ruzek]

You say,

There is a hypothesis that individuals with lower baseline CD4 counts, indicative of severe disease, may experience uncontrolled weight gain.

Is this the hypothesis you want to test? If so, it suggests you want to model change in weight somehow. The approach you use, sometimes called the ANCOVA approach or change from baseline model is one of many ways you could model change, especially if treating BMI as continuous. Treating it as categorical, you are a little more limited.

I would suggest you check out Dave Kenny's work on models for change. Specifically, look at the introduction PowerPoint as it deals directly with the situation you report of a high correlation between the baseline outcome and the predictor of interest.

Would it be right to say that without baseline BMI in the model, you are looking at absolute BMI, while including baseline BMI, the interpretation is the change in BMI from baseline?

Without baseline BMI in the model, you are looking at the association between CD4 and weight at time 2. With baseline BMI in the model, you are looking at the association between CD4 and weight at time 2, comparing individuals with the same weight at time 1.

For more context on the causal implications of the ANCOVA approach you utilize, see this article by Lüdtke and Robitzsch.