# Explaining a Mixed Effect Model to a Non Statistician/Mathematician

I'm not a statistician, but I do have a basic understanding of biostatistics in the context of medicine and clinical trials. However, recently I came across a trial that is using a statistical method that I am very unfamiliar with and was hoping someone could help.

Here is the study. It's in the "Statistical Analysis" of Clark, D., et al., (2021). Clinically relevant activity of the novel rasp inhibitor reproxalap in allergic conjunctivitis: the Phase 3 ALLEVIATE trial. American Journal of Ophthalmology, 230, 60-67.

Where I'm getting very confused is with this sentence: "Reproxalap was compared to vehicle via a MIXED EFFECT MODEL for Repeated Measures with baseline area under the curve as a covariate and treatment group and minutes post-challenge as factors. A generalized estimating equation procedure, with baseline area under the curve as a covariate and treatment group and minutes post-challenge as factors, was used to compare responder proportions for the key secondary endpoint."

I'm trying to understand what the terms in this entire paragraph actually mean and why this would be a valid statistical method to use for this given trial.

If someone could explain, non-mathematically, the actual intuition and reasoning behind what a "mixed effect model for repeated measures" is(and what the significance of the covariate and factors are in this model) with some examples or point to some sources that explain it well to someone with a basic understanding of stats, and even perhaps then proceed to explain it mathematically, I'd be very grateful.

Mixed Effect Model for Repeated Measures (MMRM)

What is it?

An MMRM is a statistical technique used to analyse data collected from the same subjects at multiple time points. It is commonly used in clinical trials where each participant's response is measured several times throughout the study. The software will estimate "random effects" (which you won't typically care about in a clinical trial) in addition to the fixed effects of covariates and factors (which will be your primary interest), hence the name "mixed effects"

Why Use MMRM?

In clinical trials, measurements are often taken on the same subjects over time, leading to correlated data within subjects. Traditional methods like simple ANOVA are not appropriate because they assume measurements are independent. MMRMs handles this by accounting for the within-subject correlation (by estimating a variance for the random effect of subjects), providing a more accurate and reliable analysis of the data.

Covariate and Factors

Covariate: This is a variable that's (usually) not of primary interest but may influence the outcome, such as a confounder or baseline measurements. In your case, 'baseline area under the curve' is used as a covariate, meaning the analysis adjusts for this variable to isolate the effect of the treatment.

Factors: These are usually the primary variables of interest. Treatment group and minutes post-challenge are the factors here, indicating that the analysis is investigating how these variables affect the outcome.

Note that this distinction between covariates and factors is not universally used. They are both simply variables in a model.

Generalized Estimating Equation (GEE) Procedure

What is GEE?

GEE is another statistical method for analyzing correlated data, like in longitudinal studies where responses are measured over time. It's particularly useful for comparing groups (e.g., treatment vs. control) in terms of response proportions or other outcomes.

Application in the Study

The study uses GEE to compare responder proportions (how many patients responded to treatment) between different treatment groups over time. Like MMRM, GEE accounts for the fact that data from the same subject are correlated.

Why Use GEE?

GEE is robust and provides valid results even if the correlation structure is not perfectly known. It's effective for analyzing binary outcomes (like responder/non-responder) or counts, which seem to be the case in the study.

Intuition Behind Using These Methods

Correlated Data: Both MMRM and GEE are chosen because data from the same subjects over time are correlated. Traditional methods assuming independent observations would be inadequate and potentially misleading.

Adjustment for Covariates: Adjusting for covariates like baseline measurements ensures that the analysis accounts for individual differences that could affect the response to the treatment.

Comparing Groups Over Time: Both methods allow for the comparison of treatment effects over time, which is crucial in assessing the effectiveness of a medical treatment in clinical trials.

How to choose between MMRM and GEE ?

Broadly speaking, GEE is indicated when our interest lies in uncovering the population average effect of a factor rather than the individual specific effect, which is what mixed models estimate. Note that in the case of linear models (where we typically have a numeric outcome variable), both MMRM and GEE should produce the same results, whereas in nonlinear models (such as a logistic model where the outcome is binary), the results will differ, so which model to use will be determined by whether you want to estimate the population average effect, or the individual effect.

• Hi Robert. Appreciate you taking the time to answer my question. Sorry I took so long respond. I've been away from stats for a bit. I actually recently created a new thread on mixed effects models. Perhaps you could share your expertise there as well? stats.stackexchange.com/questions/636829/… All the best and thanks again. Commented Jan 14 at 13:10