How MMRM Handles Missing Data ?

 

1. Assumes MAR (Missing At Random)

This is a key assumption. MAR means:

• The probability that data are missing depends only on observed data, not on the unobserved (missing) values.

📌 Example:
If patients with worse baseline scores are more likely to drop out, but you include baseline scores as a covariate in your model, then the missingness mechanism is MAR.

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2. Uses All Available Data

Unlike methods like LOCF (Last Observation Carried Forward), MMRM does not impute missing values directly. Instead:

• It uses all observed values for each participant

• It models the mean structure and the covariance structure across visits

This allows the model to make informed inferences about the treatment effect at each time point, even if some patients missed visits.

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3. Estimation Method: REML or ML

MMRM typically uses:

• REML (Restricted Maximum Likelihood) for unbiased variance component estimation

• ML (Maximum Likelihood) if comparing nested models

These methods compute the likelihood based on observed data and maximize it without imputing the missing values.

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4. No Need for Imputation

MMRM avoids ad hoc imputation methods like:

• LOCF

• Mean imputation

• Median substitution

Instead, it uses likelihood-based estimation, which is more statistically valid under the MAR assumption.

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5. Covariance Structure Is Critical

The choice of within-subject covariance structure (e.g., unstructured, AR(1), compound symmetry) is important because:

• It affects how the model accounts for the correlation between repeated measures

• A well-specified structure improves efficiency and accuracy of parameter estimates

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🧪 Example in SAS

proc mixed data=mydata;
  class subject visit treatment;
  model change = baseline treatment visit treatment*visit / solution;
  repeated visit / subject=subject type=un;
run;

• This uses UN (unstructured) covariance to allow full flexibility.

• Missing visits are ignored, but all available visits are used per subject.

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📘 Summary Table

Feature	MMRM Approach
Missing data handling	Implicit via ML under MAR
Assumption	MAR (Missing At Random)
Imputation	None
Uses partial data	✅ Yes
Estimation method	REML or ML
Key risk	Violation of MAR can bias results

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⚠️ What If MAR Is Not Plausible?

• Consider sensitivity analyses (e.g., Tipping Point, Pattern-Mixture Models)

• Use multiple imputation if necessary

• Collect more data to justify the MAR assumption

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