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Mixed Models for Repeated Measures · MMRM-SUP-A

Sample Size for MMRM Average Treatment Effect Across Visits

Plan a two-group trial for one prespecified equal-weight average of experimental-minus-reference adjusted mean differences across two or more categorical post-baseline visits.

Choose the visit window before seeing trial results. This is one linear contrast, not an omnibus interaction or a family of visit-specific tests. Equal categorical-visit weights are not calendar-time or area-under-the-curve weights.

1. Estimand and visit window

2. Repeated-measure, covariance, and retention assumptions

Select at least two visits. Selected visits receive equal weights. Enter the expected signed treatment trajectory, conditional residual SDs after covariate adjustment, and monotone retention.

VisitInclude and weightExpected E−R differenceConditional SDReference retention (%)Experimental retention (%)

3. Operating characteristics

Alpha is split equally between both tails.

Use 1 for 1:1, 2 for 2:1, and so on. Complete allocation blocks are preserved.

Applied after MMRM retention has been modelled. Do not count the same missingness twice.

4. Results

Enter the visit window and MMRM assumptions, then select Calculate sample size.

Formula, assumptions, limitations, validation, privacy, and references

Scope and estimand

The primary estimand is θ = Σ wⱼδⱼ, where δⱼ is the adjusted experimental-minus-reference difference at categorical visit j. Each selected visit receives weight 1/k and every unselected visit receives zero weight. All scheduled visits remain in the MMRM.

This is not an omnibus interaction, AUC, slope, final-visit effect, or adjustment for testing several visit windows. Equal weighting gives the same importance to each selected categorical visit even when calendar spacing differs. Averages can conceal transient, heterogeneous, or crossing effects.

Method

The calculator forms the assumed covariance matrix and expected group-specific monotone dropout patterns. It evaluates a general linear Kenward–Roger expected-design approximation for the prespecified contrast, with unstructured covariance nuisance-parameter estimation, and anchors its finite-sample variance and degrees of freedom to Tang’s closed-form final-visit MMRM result. Exact noncentral-t power is searched over complete allocation blocks.

Assumptions and limitations

  • Two independently randomized groups, continuous approximately Gaussian outcomes, and a categorical-visit MMRM fitted by REML.
  • A common correctly specified covariance matrix and monotone missing-at-random planning mechanism conditional on observed model variables.
  • The visit set, weights, effect trajectory, sidedness, analysis population, intercurrent-event strategy, and sensitivity analyses are prespecified.
  • No multiplicity adjustment is included for trying several visit sets or selecting one after examining data.
  • Intermittent missingness, MNAR sensitivity models, custom unequal weights, clusters, and non-Gaussian outcomes require study-specific methods.

This tool supports research planning and does not replace statistical consultation or regulatory advice.

Independent validation

The implementation is checked against analytic complete-data linear-contrast identities, the released Tang target-visit engine under a one-hot reduction, deterministic R contrasts, and independent simulation using the R mmrm and emmeans packages. Validation evidence and limitations are retained in the project validation record.

Technical results

Privacy

Calculations run entirely in your browser. No study assumptions or results are uploaded or stored by this calculator.

References

  1. Tang Y. Closed-form REML estimators and sample size determination for mixed effects models for repeated measures under monotone missingness. Statistics in Medicine. 2017;36:2135–2147. doi:10.1002/sim.7270.
  2. Tang Y. A noniterative sample size procedure for tests based on t distributions. Statistics in Medicine. 2018;37:3197–3213. doi:10.1002/sim.7807.
  3. Kenward MG, Roger JH. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics. 1997;53:983–997.
  4. Wang G, Xiong C, et al. Harnessing greater statistical power: comprehensive evaluation of disease modifying treatment effects across all or multiple post-baseline visits compared to the last visit for Alzheimer’s disease clinical trials. Journal of Alzheimer’s Disease. 2025;106(4):1272–1287.
  5. ICH E9(R1). Addendum on estimands and sensitivity analysis in clinical trials. 2019.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for MMRM Average Treatment Effect Across Visits.” Web calculator. NajibMY, 2026. Accessed August 18, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/mmrm-average-treatment-effect-across-visits/.