As a researcher dealing with randomized trial, should I use GEE or a GLMM? I'm sorry, I searched all topics on StackExchange and cannot still get the difference between marginal and conditional model. All answers tell me the same by showing averaged non-linear curves, which agrees in the general linear model (one averaged straight line is a literally average of random intercepts), but doesn't in the GLM (attenuation of the coefficients).
But still - what does it mean to me, a physician?
If I have a randomized longitudinal (repeated-measure) study comparing two drugs, where I measure some binary clinical outcome 5 times and want to compare the % of successes at the last timepoint, but using all the data, I fit a longitudinal model, right? I can run GLMM or GEE.
The regulator asks me to use unstructured covariance with GEE. GLMM with random slopes and intercepts might the concurrent model.
But then I hear that each tells me something different. The overall model coefficients differ between the two.
People tell me, that for the randomized study I need the population-average results that simplify things and force me to think about complicated random effects, introduce any additional assumptions and ensure easier convergence, and is not that much dependent from the chosen covariance.
Others tell me, that mixed model needs additional assumptions about the random effects, I know they hardly converge for random slopes + intercepts, depend on this structure (correlation of the two) and are also conditional to the random effects.
So what does it mean for having just 2 fixed terms - Treatment*Time? I want to check the Treatment : Time, or simpler Treatment at time N.
How do I interpret the result of the 2 methods?
Now I add biological sex and race to the model. This cannot be changed for a patient, it's fixed.
I was told that GEE will treat this as a comparison between sub-populations of men and women, and different races. THIS IS what I want.
At the same time I was told that GLMM will treat a patient as one changes their sex or race(!). This is totally twisted to me.
But most of the people I know tell me GLMM is better. HOW come!?
Statisticians tell me that "you should choose the model". How can I if I don't get it? My research question is: to compare 2 drugs. I want to make it adjusted for sex and race.
Do I need a conditional or population-average model in this case?
I understand, that for inference about comparing I should use GEE, and if I wanted to predict the success, should I then use GLMM?
 A: The difference between GLMM and GEE is indeed primarily in the interpretation of what you are estimating. I.e. effects of treatments on individual patients vs. the average effect for the trial population. There's no reason why one would interpret GLMM results as if patients "changed their covariates", that just seems to be confused mis-information. What comes in with GLMM vs. GEE is also that with repeated assessments you can see whether even beyond explanatory covariates some patients tend to consistently respond badly or well, which one can estimate as a latent patient response. GLMM calculates the patient specific effect taking that into account (in the way discussed below), while GEE averages that out for the population (in the way discussed below).
We don't even need to look at repeated assessments to see the difference between patient specific and population average effects, it's also easier to discuss it with an observed covariates (rather than the latent one). To illustrate this with a hypothetical example of survival 1 year after starting on a new and an old drug for some type of cancer (and you can easily construct even more extreme scenarios, these occur in practice a lot).




Sex
% of the population
Survival at 1 year on new drug
Survival at 1 year on old drug
Conditional odds ratio
Marginal (unconditional) odds ratio
Rate ratio




Female
50%
90%
75%
3
3.00
1.2


Male
50%
50%
25%
3
3.00
2.0


Overall
100%
70%
50%
3
2.33
1.4




We assume the percentages given above are known exactly (e.g. based on an
extremely large RCT, there was no dropouts).
In both male and female patients the odds of survival at 1 year is 3 times
higher with the new drug compared with the old drug, but female patients are
more likely to survive to 1 year. As a result, the overall conditional odds
ratio is also 3. This is the effect any specific patient could expect, but would not be what happens on a population average level when you e.g.
However, the marginal (population average) odds ratio is 2.33,
which we obtain by calculating $(0.7 / 0.3) / (0.5 / 0.5)$.
Thus, the treatment effect is attenuated towards no effect (odds ratio of $1$), if you look at the marginal effect. This - for logistic regression type analyses - is always that way. While this is indeed the average odds ratio for the population given the particular distribution of male and female patients, this effect does not apply to either male or female patients (or any other population where you have a different male/female distribution - perhaps male/female is not the best example, but e.g. split into disease severities could easily be different between trials and clinical practice). I.e. this effect is arguably irrelevant to
any one patient and for any physician that makes a treatment decisions for an
individual patient. The marginal effect also tends to not translate well to different studies or clinical practice. On the other hand, some methods have been discovered to obtain marginal (covariate-adjusted) estimates in ways that have nice
robustness properties, which is one of the main arguments for doing this anyway (and why the recent FDA guidance on covariate adjustment talks a lot about population average effects).
This issue can avoided by effect measures such as the risk ratio that are
collapsible. For example, if in our example, the risk ratio
if 2 for the male patients (calculated as $0.5/0.25$). If the risk ratio
also were 2 for the female patients, the population average risk ratio would
also be 2. However, the risk ratio cannot be constant across all levels
of control group percentages. For example, in our example for the control group
percentage of 75%, we would need an impossible 150% of patients to survive
on the new drug to achieve a risk ratio of 2 in the female patients.
For these reasons, the choice of population-level summary remain controversial.
However, note that the choice between a conditional and a marginal effect is
separate from the choice of whether analyses should be covariate adjusted, in
fact a covariate adjusted analysis is typically more efficient even for
estimating a marginal effect. One can for example obtain a marginal effect
after a covariate adjusted analysis by averaging the model predicted treatment
differences for each patient in a trial.
