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Longitudinal & Mixed Models

GEE vs. Mixed Models: When to Use Each

A practical guide to choosing between generalized estimating equations and mixed-effects models for longitudinal and clustered clinical data, including population-averaged versus subject-specific effects, correlation structures, missing data, interpretation, R and SAS implementation, and a worked clinical trial example.

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What You'll Learn

  • The fundamental difference between GEE and mixed-effects models
  • Population-averaged versus subject-specific treatment effects
  • How working correlation and random-effects structures differ
  • How missing data affect the choice between the methods
  • When GEE is preferable and when mixed models are preferable
  • How to implement and interpret both approaches in R and SAS

Introduction

Longitudinal clinical studies rarely produce independent observations. A patient may contribute measurements at baseline, Week 4, Week 8, Week 12, and several later visits. Patients treated at the same clinical center may also be correlated, and subjects within the same cluster may share common characteristics.

The statistical challenge is therefore not simply to estimate a treatment effect. We must also account for the dependence among repeated observations.

Two of the most important frameworks for doing this are generalized estimating equations (GEE) and mixed-effects models.

Key idea: GEE and mixed models can both handle correlated longitudinal observations, but they answer somewhat different scientific questions. GEE primarily targets population-averaged effects, whereas mixed models naturally produce subject-specific effects through their random-effects structure.

The First Question: What Is the Scientific Target?

Before choosing a model, ask what the treatment effect is supposed to mean. This is often more important than the choice of software procedure.

Suppose \(Y_{ij}\) is the outcome for patient \(i\) at visit \(j\). A treatment indicator \(A_i\) may be used to compare two randomized groups. The investigator might ask:

  • What is the average treatment effect across the population?
  • How does treatment affect an individual patient's expected trajectory?
  • How much do patients differ from one another?
  • How much correlation exists among repeated measurements?

These questions naturally lead toward different modeling frameworks.

What Is GEE?

Generalized estimating equations extend generalized linear models to correlated observations. Instead of explicitly modeling a subject-specific latent random effect, GEE specifies a model for the marginal mean and a working correlation structure for observations within a cluster.

Let:

$$ \mu_{ij}=E(Y_{ij}\mid X_{ij}) $$

and let \(g(\cdot)\) denote the link function. The marginal mean model is:

$$ g(\mu_{ij})=X_{ij}^{T}\beta $$

The parameter vector \(\beta\) describes the relationship between covariates and the population-level mean response.

The GEE estimating equation can be written schematically as:

$$ \sum_i D_i^T V_i^{-1}(Y_i-\mu_i)=0 $$

where \(D_i\) contains derivatives of the mean with respect to the model parameters and \(V_i\) represents the working covariance matrix.

Important: GEE does not require the working correlation matrix to be exactly correct for the regression coefficient estimates to remain consistent under the usual large-sample conditions, provided the mean model is correctly specified and the dependence structure is appropriately handled. The sandwich or robust variance estimator is central to this property.

What Is a Mixed-Effects Model?

A mixed-effects model combines fixed effects, which describe systematic population-level relationships, with random effects, which represent subject- or cluster-specific deviations.

For a continuous outcome, a basic linear mixed model can be written:

$$ Y_{ij}=X_{ij}^{T}\beta+Z_{ij}^{T}b_i+\epsilon_{ij} $$

where:

  • \(\beta\) contains the fixed-effect parameters.
  • \(b_i\) contains subject-specific random effects.
  • \(Z_{ij}\) relates the random effects to observation \(j\).
  • \(\epsilon_{ij}\) represents residual error.

A common random-intercept model is:

$$ Y_{ij}=\beta_0+\beta_1A_i+\beta_2t_{ij}+b_{0i}+\epsilon_{ij} $$

where \(b_{0i}\) allows each patient to have their own baseline deviation from the population intercept.

A random-slope model can additionally allow patients to have different trajectories:

$$ Y_{ij}=\beta_0+\beta_1A_i+\beta_2t_{ij} +b_{0i}+b_{1i}t_{ij}+\epsilon_{ij} $$
Key distinction: A mixed model explicitly represents heterogeneity among subjects through random effects. This makes it especially useful when the individual trajectory itself is scientifically important.

Population-Averaged vs. Subject-Specific Effects

This is the single most important conceptual distinction between GEE and mixed models.

Question GEE Mixed Model
Primary interpretation Population-averaged Subject-specific
Models subject heterogeneity explicitly? No Yes
Random effects No Yes
Working correlation Yes Implied by covariance structure
Individual trajectories Not directly modeled Can be modeled directly
Robust sandwich variance Commonly used Not the defining feature

The distinction becomes especially important for nonlinear links such as logit and log links. For a continuous identity-link model, the population and subject-specific interpretations can sometimes appear numerically similar, but this should not obscure the conceptual distinction.

A Simple Clinical Example

Suppose a randomized clinical trial compares an active treatment with placebo. Depression severity is measured at baseline and Weeks 2, 4, 8, and 12.

The investigator wants to estimate the treatment difference in mean depression score over follow-up.

There are several reasonable approaches.

1
GEE: estimate the average treatment effect across the trial population while accounting for within-patient correlation.
2
Mixed model: estimate treatment effects while explicitly modeling patient-specific deviations and trajectories.
3
Scientific decision: determine whether the trial primarily needs a marginal population effect or a subject-specific model.

The GEE Working Correlation

GEE requires a working correlation structure describing how observations within a subject or cluster are related.

Common choices include:

Structure Assumption Typical Use
Independent Within-subject correlations treated as zero for working purposes Large clusters or weak dependence
Exchangeable All pairs within a subject have the same correlation Repeated measurements with roughly constant correlation
AR(1) Correlation decreases with increasing time separation Regularly spaced longitudinal visits
Unstructured Each pair can have a different correlation Small number of visits with sufficient data

For an exchangeable structure, the working correlation matrix has the form:

$$ R(\alpha)= \begin{pmatrix} 1 & \alpha & \alpha & \cdots \\ \alpha & 1 & \alpha & \cdots \\ \alpha & \alpha & 1 & \cdots \\ \vdots & \vdots & \vdots & \ddots \end{pmatrix} $$

For an AR(1) structure:

$$ R_{jk}=\alpha^{|j-k|} $$

Thus observations closer together in time are assumed to be more strongly correlated.

Practical point: In GEE, the working correlation is primarily a tool for improving efficiency of the estimating procedure and variance estimation. It is not necessarily a scientific model of the true subject-level covariance process.

Covariance Structures in Mixed Models

Mixed models take a different approach. The covariance among repeated measurements is generated by the random-effects structure and residual covariance specification.

For example, a random-intercept model creates correlation because two observations from the same patient share the same \(b_{0i}\).

If:

$$ Y_{ij}=\beta_0+\beta_1t_{ij}+b_{0i}+\epsilon_{ij} $$

with:

$$ b_{0i}\sim N(0,\sigma_b^2) \qquad\text{and}\qquad \epsilon_{ij}\sim N(0,\sigma^2) $$

then two observations from the same patient have covariance:

$$ \operatorname{Cov}(Y_{ij},Y_{ik})=\sigma_b^2 $$

and therefore correlation:

$$ \operatorname{Corr}(Y_{ij},Y_{ik}) = \frac{\sigma_b^2} {\sigma_b^2+\sigma^2} $$

A random slope produces a more complicated covariance pattern that depends on the timing of the observations.

GEE Does Not Have Random Intercepts

This distinction is worth emphasizing because the two approaches are sometimes described as interchangeable ways of "accounting for repeated measures."

They are not identical models.

A mixed model might explicitly state:

$$ Y_{ij}=\beta_0+b_{0i}+\beta_1t_{ij}+\epsilon_{ij} $$

where the patient-specific random intercept \(b_{0i}\) is an unobserved quantity representing subject heterogeneity.

GEE instead specifies a marginal mean and a working correlation among observations.

Think of the difference this way: Mixed models ask, "How does this patient's outcome evolve, after accounting for patient-specific random effects?" GEE asks, "What is the average relationship between treatment and outcome across the population?"

When GEE Is Often a Good Choice

GEE is often attractive when the primary scientific objective is a population-level treatment effect.

Typical situations include:

  • The estimand is explicitly population-averaged.
  • The observations are clustered or longitudinal.
  • Subject-specific random effects are not of primary interest.
  • The number of clusters is reasonably large.
  • The analysis focuses on marginal means or risks.
  • Robust inference under a potentially imperfect working correlation is valuable.

For example, suppose a public-health study asks whether an intervention reduces the average probability of hospitalization across a population of patients. A marginal treatment effect may be exactly the desired estimand.

When Mixed Models Are Often a Better Choice

Mixed models are often preferable when individual trajectories or between-subject heterogeneity are central to the scientific question.

  • Patients have meaningful subject-specific trajectories.
  • Random intercepts or slopes are scientifically important.
  • Cluster-level heterogeneity needs to be estimated.
  • Individual-level predictions are required.
  • The outcome is continuous and approximately Gaussian.
  • Irregular measurement times need to be modeled naturally.
  • The covariance structure can be represented through random effects.

For example, in a growth study, investigators may want to know not only whether the treatment changes the average trajectory but also how much patients differ in their baseline values and rates of change.

Longitudinal Clinical Trials: A Practical Comparison

Clinical Situation Often Prefer Reason
Average population treatment effect GEE Direct marginal interpretation
Patient-specific trajectories Mixed model Random effects describe subject heterogeneity
Random intercept and slope Mixed model Explicit trajectory modeling
Binary repeated outcome with marginal risk interpretation GEE Natural population-averaged framework
Continuous repeated outcome with incomplete observations Mixed model often attractive Likelihood-based estimation can use incomplete longitudinal records under appropriate assumptions
Many independent clusters GEE often attractive Robust population inference
Very few clusters Neither automatically solves the problem Small-cluster inference requires special attention

The Importance of the Number of Clusters

A frequently overlooked issue with GEE is that the asymptotic justification for the sandwich variance estimator depends on having a sufficiently large number of independent clusters.

If a study has hundreds of patients, each contributing repeated observations, GEE may have strong large-sample support.

But consider a cluster-randomized trial with only 12 clinics. There may be many patient observations, but only 12 independent clusters. The effective number of independent units for the robust variance calculation is much smaller.

Important: Having thousands of observations does not automatically make GEE a large-sample problem. For clustered data, the number of independent clusters can be more important than the total number of observations.

Missing Data: GEE vs. Mixed Models

Missing longitudinal observations are common in clinical research. Patients may discontinue treatment, miss visits, withdraw consent, or become lost to follow-up.

The handling of missing data can therefore influence the choice of model.

Mixed Models

Likelihood-based mixed models can use incomplete longitudinal records without requiring every patient to have observations at every scheduled visit. Under a correctly specified model and assumptions such as missing at random (MAR), likelihood-based estimation can remain valid.

GEE

Standard GEE is also capable of handling incomplete repeated observations, but the validity of inference depends on the missingness mechanism and the estimating approach used. Standard complete-case-style GEE is not universally robust to informative dropout.

Do not say "mixed models handle missing data" without qualification. Neither method makes missing data disappear. The missingness mechanism, mean model, covariance assumptions, estimation method, and sensitivity analyses still need to be considered.

MAR Does Not Mean "Missing Data Are Ignorable"

A common misunderstanding is that MAR means missing observations are irrelevant.

Instead, MAR is a conditional assumption about the probability of missingness. For example, after conditioning on observed treatment history and observed outcomes, the probability of a missing future measurement may no longer depend on the unobserved value itself.

The credibility of that assumption is a scientific issue, not merely a software setting.

Continuous Outcomes

For a continuous approximately Gaussian outcome, a linear mixed model is often a natural starting point.

For example:

$$ Y_{ij} = \beta_0 +\beta_1A_i +\beta_2t_{ij} +\beta_3(A_i t_{ij}) +b_{0i} +b_{1i}t_{ij} +\epsilon_{ij} $$

Here:

  • \(\beta_1\) describes a treatment difference at the reference time.
  • \(\beta_2\) describes the average time trend in the reference group.
  • \(\beta_3\) describes the difference in trajectories between treatment groups.
  • \(b_{0i}\) allows patient-specific baseline deviations.
  • \(b_{1i}\) allows patient-specific trajectory deviations.

A GEE version could instead specify a marginal mean:

$$ E(Y_{ij}\mid X_{ij}) = \beta_0 +\beta_1A_i +\beta_2t_{ij} +\beta_3(A_i t_{ij}) $$

and then use a working correlation for repeated measurements within a patient.

Binary Outcomes

For a repeated binary endpoint, the distinction becomes especially important because odds ratios from marginal and subject-specific logistic models can differ substantially.

A GEE logistic model might be:

$$ \operatorname{logit}\{\Pr(Y_{ij}=1)\} = \beta_0+\beta_1A_i+\beta_2t_{ij} $$

Then:

$$ \exp(\beta_1) $$

is interpreted as a population-averaged odds ratio, subject to the exact model specification and covariate interpretation.

A mixed-effects logistic model could be:

$$ \operatorname{logit}\{\Pr(Y_{ij}=1\mid b_i)\} = \beta_0+\beta_1A_i+\beta_2t_{ij}+b_i $$

where \(\exp(\beta_1)\) has a conditional, subject-specific interpretation.

Important: For nonlinear models such as logistic regression, population-averaged and subject-specific effects are generally not numerically identical. A GEE odds ratio should not automatically be interpreted as the same estimand as the fixed-effect odds ratio from a mixed-effects logistic model.

Why the Two Odds Ratios Differ

Suppose patients differ in an unobserved propensity to experience the event. A mixed model conditions on the random effect, whereas GEE averages over the population distribution of that heterogeneity.

Because the logistic transformation is nonlinear, averaging and transforming do not generally commute.

Conceptually:

$$ \operatorname{logit}\{E(Y\mid X)\} \neq E\{\operatorname{logit}(Y\mid X,b)\} $$

in general.

This is one reason why simply fitting both models and comparing coefficients without identifying the estimand can lead to confusion.

Random Intercept vs. Exchangeable GEE

A random-intercept mixed model and an exchangeable GEE may sometimes produce similar-looking results for a continuous outcome, but they are not the same model.

A random-intercept model implies a particular covariance pattern:

$$ \operatorname{Cov}(Y_{ij},Y_{ik})=\sigma_b^2 $$

for observations from the same subject, assuming independent residual errors.

An exchangeable GEE specifies that all within-subject correlations are equal to a common working parameter \(\alpha\).

The resemblance is therefore useful for intuition, but the inferential framework remains different.

Random Slopes Change the Story

Suppose patients improve at different rates. A random-intercept model alone assumes patients differ in baseline level but share the same population slope, apart from residual noise.

A random-slope model allows:

$$ b_{1i}\neq0 $$

and therefore permits patients to have different rates of change.

This is one of the clearest situations in which a mixed model has a scientifically meaningful advantage over a simple marginal correlation structure.

Rule of thumb: If "patients differ in their trajectories" is part of the scientific story, a mixed model deserves serious consideration.

GEE With Different Outcome Distributions

GEE is not limited to continuous outcomes. It can be used with different distributions and link functions, including:

  • Gaussian outcomes with identity links
  • Binary outcomes with logit links
  • Count outcomes with log links
  • Other generalized estimating-equation settings supported by the software and analysis design

Likewise, mixed-effects models can be generalized beyond Gaussian outcomes. Generalized linear mixed models (GLMMs) introduce random effects into non-Gaussian models.

Therefore, the decision is not simply "GEE for binary data and mixed models for continuous data." The scientific estimand and dependence structure remain central.

GEE vs. GLMM

Feature GEE GLMM
Primary estimand Population-averaged Subject-specific
Random effects No Yes
Correlation Working correlation Generated by random effects and residual structure
Individual predictions Limited Natural application
Robust sandwich inference Central feature Not the defining framework
Interpretation of nonlinear effects Marginal Conditional

R Example: GEE

The geepack package provides a common R implementation of GEE.

library(geepack)

gee_fit <- geeglm(
  outcome ~ treatment * visit + baseline,
  id = patient_id,
  data = dat,
  family = gaussian,
  corstr = "ar1"
)

summary(gee_fit)

For a binary endpoint:

gee_bin <- geeglm(
  response ~ treatment * visit + baseline,
  id = patient_id,
  data = dat,
  family = binomial(link = "logit"),
  corstr = "exchangeable"
)

summary(gee_bin)

The treatment coefficient should be interpreted according to the marginal mean model.

R Example: Linear Mixed Model

The lme4 package is widely used for mixed models. A random-intercept model can be fitted as:

library(lme4)

lmm_fit <- lmer(
  outcome ~ treatment * visit + baseline +
    (1 | patient_id),
  data = dat
)

summary(lmm_fit)

A random-intercept and random-slope model is:

lmm_rs <- lmer(
  outcome ~ treatment * visit + baseline +
    (1 + visit | patient_id),
  data = dat
)

summary(lmm_rs)

The second model explicitly allows both baseline levels and trajectories to vary among patients.

R Example: Generalized Linear Mixed Model

For a binary longitudinal outcome:

glmm_fit <- glmer(
  response ~ treatment * visit + baseline +
    (1 | patient_id),
  data = dat,
  family = binomial(link = "logit")
)

summary(glmm_fit)

The treatment effect is conditional on the random effect and therefore has a subject-specific interpretation.

SAS Example: GEE

In SAS, GEE analyses are commonly implemented with PROC GENMOD using a repeated statement.

proc genmod data=dat;
    class patient_id treatment visit;
    
    model outcome =
        treatment
        visit
        treatment*visit
        baseline
        / dist=normal link=identity;

    repeated subject=patient_id
        / type=ar(1)
          corrw;
run;

For a binary outcome:

proc genmod data=dat;
    class patient_id treatment visit;

    model response =
        treatment
        visit
        treatment*visit
        baseline
        / dist=binomial link=logit;

    repeated subject=patient_id
        / type=exch
          corrw;
run;

SAS Example: Mixed Model

For a continuous outcome, PROC MIXED is a standard choice:

proc mixed data=dat method=reml;
    class patient_id treatment visit;

    model outcome =
        treatment
        visit
        treatment*visit
        baseline
        / solution;

    random intercept
        / subject=patient_id;

    repeated visit
        / subject=patient_id
          type=ar(1);
run;

A random-slope model can be specified as:

proc mixed data=dat method=reml;
    class patient_id treatment visit;

    model outcome =
        treatment
        visit
        treatment*visit
        baseline
        / solution;

    random intercept visit
        / subject=patient_id
          type=un;
run;
Do not choose the SAS procedure first. First identify the estimand, outcome distribution, clustering structure, missing-data assumptions, and desired interpretation. Then choose the procedure that implements the statistical model.

A Worked Clinical Trial Example

Consider a randomized trial with 200 patients. Each patient has a continuous outcome measured at baseline, Week 4, Week 8, and Week 12.

The scientific objective is to determine whether the active treatment changes the average trajectory compared with placebo.

Design Feature Planning Value
Total patients 200
Treatment groups Active vs. placebo
Outcome Continuous
Post-baseline visits Weeks 4, 8, 12
Primary scientific target Average treatment effect over time
Repeated observations Within patient

Both GEE and a mixed model may be defensible. The question is which one most naturally matches the estimand and assumptions.

GEE Analysis of the Example

Suppose the marginal model is:

$$ E(Y_{ij}) = \beta_0 +\beta_1A_i +\beta_2t_{ij} +\beta_3A_it_{ij} +\beta_4B_i $$

where \(B_i\) is baseline severity.

The treatment-by-time interaction \(\beta_3\) describes the difference in average longitudinal change between treatment groups.

If the primary question is:

"What is the average difference in outcome trajectories between the two treatment groups?"

then GEE is a very natural choice.

Mixed-Model Analysis of the Same Example

Now suppose the investigator believes that patients differ substantially in their baseline levels and rates of change.

A mixed model might be:

$$ Y_{ij} = \beta_0 +\beta_1A_i +\beta_2t_{ij} +\beta_3A_it_{ij} +\beta_4B_i +b_{0i} +b_{1i}t_{ij} +\epsilon_{ij} $$

Now the model explicitly represents two sources of patient heterogeneity:

  • \(b_{0i}\): patient-specific baseline deviation.
  • \(b_{1i}\): patient-specific deviation in rate of change.

The treatment-by-time coefficient still describes the fixed treatment effect under the model, but the framework also provides a model for individual trajectories.

Which Model Would You Choose?

For the worked trial, the answer depends on the scientific objective.

Primary Objective Preferred Framework
Estimate population-average treatment effect GEE
Estimate individual trajectories Mixed model
Estimate between-patient heterogeneity Mixed model
Focus on marginal means GEE
Need subject-specific predictions Mixed model
Need a random intercept/slope structure Mixed model
There is no universal winner. The correct method is the one whose estimand, assumptions, covariance representation, and inferential properties match the scientific question and study design.

What About Covariance Structure Selection?

Covariance selection is another area where the frameworks differ.

In GEE, candidate working correlations might include:

  • Independent
  • Exchangeable
  • AR(1)
  • Unstructured

In a mixed model, covariance can arise through:

  • Random intercepts
  • Random slopes
  • Random intercept plus random slope
  • Residual covariance structures
  • Combinations of random effects and residual covariance

Therefore, "choose AR(1)" does not mean exactly the same thing in GEE and mixed-model analysis.

What If the Working Correlation Is Wrong?

One of the attractions of GEE is that the regression estimates can remain consistent when the working correlation is misspecified, provided the mean model and regularity conditions are appropriate and robust variance estimation is used.

However, an inefficient or poorly chosen working correlation can affect precision.

For example, if the true correlation declines with time separation but the working structure assumes exchangeability, the treatment estimate may still be useful, but efficiency may not be optimal.

GEE principle: The working correlation does not need to be treated as a literal scientific claim about the true covariance process. It is part of the estimating framework.

What If the Random-Effects Structure Is Wrong?

Mixed models are different because the random-effects structure contributes directly to the implied covariance model and likelihood.

If the model assumes only a random intercept when patients actually have substantially different slopes, the model may fail to represent important heterogeneity.

Likewise, an unnecessarily complicated random-effects structure may produce convergence problems or unstable variance estimates.

This makes covariance and random-effects specification an important modeling decision rather than a purely technical afterthought.

Model Selection Should Follow the Scientific Question

A common mistake is to fit several models and choose the one with the best AIC without first deciding what effect is scientifically meaningful.

A better sequence is:

1
Define the estimand and primary scientific question.
2
Identify the outcome distribution and link function.
3
Identify the source of within-subject or within-cluster dependence.
4
Decide whether subject-specific heterogeneity needs to be modeled explicitly.
5
Select a defensible covariance or working-correlation structure.
6
Specify the missing-data and estimation strategy.
7
Perform diagnostics and sensitivity analyses.

Common Mistakes

  1. Thinking GEE and mixed models are interchangeable. They can address the same broad repeated-measures problem but target different types of effects.
  2. Choosing GEE because the data are longitudinal. Longitudinal structure alone does not determine the appropriate framework.
  3. Choosing mixed models because they are "more sophisticated." A more complicated model is not automatically more appropriate.
  4. Calling every repeated-measures analysis a subject-specific analysis. GEE is fundamentally marginal.
  5. Interpreting a GEE odds ratio as a conditional odds ratio. The estimands differ for nonlinear models.
  6. Ignoring the number of independent clusters. Robust GEE inference can be unreliable when the number of clusters is small.
  7. Assuming mixed models automatically solve missing-data problems. Validity still depends on assumptions about the missingness mechanism and model specification.
  8. Using an unnecessarily complicated random-effects structure. Random slopes and covariance parameters require adequate information.
  9. Choosing covariance structure solely from a data-driven search. Clinical and scientific plausibility should be considered alongside statistical criteria.
  10. Failing to prespecify the primary estimand. The treatment effect cannot be interpreted correctly without knowing what population or conditional quantity it represents.

GEE vs. Mixed Models: Decision Framework

1
Is the primary estimand population-averaged? If yes, GEE is often a strong candidate.
2
Are subject-specific trajectories scientifically important? If yes, consider a mixed model.
3
Are random intercepts or slopes required? If yes, a mixed-effects framework is generally more natural.
4
Is the number of independent clusters small? If yes, investigate small-sample corrections and alternative methods before relying on standard GEE sandwich inference.
5
Is the outcome nonlinear? Pay particular attention to the difference between marginal and subject-specific interpretations.
6
Are incomplete longitudinal records common? Evaluate the missing-data assumptions and estimation method rather than assuming either framework is automatically robust.

Reporting GEE Results

A clinical report using GEE should make the marginal nature of the analysis clear.

At minimum, report:

  • The marginal mean model.
  • The outcome distribution and link function.
  • The clustering variable.
  • The working correlation structure.
  • The variance estimator.
  • The treatment effect and confidence interval.
  • The interpretation of the effect as population-averaged.
  • The handling of missing observations.

Reporting Mixed-Model Results

A mixed-model analysis should similarly document:

  • The fixed-effects model.
  • The random-effects structure.
  • The residual covariance structure.
  • The estimation method, such as REML or ML when appropriate.
  • The treatment effect and confidence interval.
  • The interpretation of fixed effects.
  • Convergence and model diagnostics.
  • The handling of missing observations.

Can You Use Both?

Yes.

In some analyses, fitting both a marginal model and a mixed model can be useful as a sensitivity or supplementary analysis, provided the two models are interpreted according to their respective estimands.

For example, a clinical trial might use a mixed model as the primary analysis because subject-level trajectories are scientifically important, while a GEE analysis provides a complementary population-averaged perspective.

But do not compare coefficients blindly. If a GEE coefficient and a mixed-model coefficient differ, that does not automatically mean one model is wrong. They may be estimating different quantities.

A Compact Comparison

Question GEE Mixed Model
What is modeled? Marginal mean Conditional mean with random effects
Main estimand Population-averaged Subject-specific
Random effects? No Yes
Working correlation? Yes Not in the same sense
Individual trajectories? No explicit random trajectories Yes
Population interpretation? Natural Requires marginalization for a population-level interpretation
Nonlinear effects Marginal Conditional
Robust variance Central component Not fundamental
Small number of clusters Potential concern Different issues arise, but not automatically solved
Subject-level prediction Limited Strong use case

The Most Important Practical Rule

Do not begin by asking:

"Should I use GEE or a mixed model?"

Begin with:

"What treatment effect am I trying to estimate?"

If the desired answer is the average treatment effect across the population, GEE may provide the most direct framework.

If the desired answer involves individual trajectories, subject-specific effects, or between-subject heterogeneity, a mixed model may be more natural.

Then consider the outcome distribution, covariance assumptions, number of clusters, missing-data mechanism, and inferential method.

Practical Workflow for Clinical Researchers

1
Define the primary estimand.
2
Determine whether the estimand is population-averaged or subject-specific.
3
Identify the outcome distribution and appropriate link function.
4
Identify the clustering and repeated-measures structure.
5
Decide whether subject-level heterogeneity should be explicitly modeled.
6
Choose a defensible GEE correlation or mixed-model covariance structure.
7
Evaluate the number of independent clusters and the adequacy of asymptotic inference.
8
Specify the missing-data assumptions and analysis strategy.
9
Fit the prespecified model and assess diagnostics.
10
Interpret the treatment effect according to the model's actual estimand.

Bottom Line

GEE vs. mixed models: GEE and mixed-effects models are complementary approaches for correlated longitudinal and clustered data. GEE is primarily a marginal, population-averaged framework, while mixed models explicitly model subject- or cluster-specific heterogeneity through random effects. For nonlinear outcomes, their treatment effects can have meaningfully different interpretations. The choice should therefore be driven first by the scientific estimand, and then by the outcome distribution, clustering structure, covariance assumptions, missing-data mechanism, and inferential requirements.

References

Liang, K.-Y. & Zeger, S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13–22.
Zeger, S.L., Liang, K.-Y. & Albert, P.S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics, 44(4), 1049–1060.
Diggle, P., Heagerty, P., Liang, K.-Y. & Zeger, S. (2002). Analysis of Longitudinal Data. Oxford University Press.
Fitzmaurice, G.M., Laird, N.M. & Ware, J.H. (2011). Applied Longitudinal Analysis. Wiley.
McCulloch, C.E., Searle, S.R. & Neuhaus, J.M. (2008). Generalized, Linear, and Mixed Models. Wiley.
Hedeker, D. & Gibbons, R.D. (2006). Longitudinal Data Analysis. Wiley.