Mixed Models for Repeated Measures · MMRM-SUP-T

Sample Size for MMRM Superiority at a Specified Visit

Plan a two-group parallel trial powered for an experimental-minus-reference adjusted mean difference at one prespecified visit using a categorical-visit MMRM.

1. Estimand and superiority hypothesis

Outcome label optional

Outcome unit optional

Number of post-baseline visits

Primary target visit

Measurements after this visit are not used to size this target-visit estimand.

Expected experimental − reference difference

Use a negative value when lower outcomes are better and a positive value when higher outcomes are better.

Superiority alternative

The null target-visit difference is zero. Use the separate MMRM non-inferiority or equivalence tools for margin-based hypotheses.

2. Repeated-measure and retention assumptions

Enter conditional residual SDs after covariate adjustment and the expected proportion observed at each visit. Retention must not increase over time.

Visit	Conditional outcome SD	Reference retention (%)	Experimental retention (%)

Within-participant covariance structure

Adjacent-visit correlation

3. Operating characteristics

Two-sided Type I error

The selected alpha is split equally between both tails.

Power (%)

Experimental-to-reference allocation ratio

Enter 1 for 1:1, 2 for 2:1, and so on. Exact whole-number allocation is preserved.

Baseline covariate columns

Baseline outcome only = 1. A k-level factor contributes k − 1 columns.

Additional non-evaluable participants (%)

Applied after MMRM retention has already been modelled; do not count the same missingness twice.

4. Results

Enter the MMRM assumptions and select Calculate sample size.

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

Scope and estimand

For a continuous outcome analyzed using a categorical-visit MMRM.

The estimand is the experimental-minus-reference adjusted mean difference at one prespecified post-baseline visit. The mean model includes categorical visit, treatment-by-visit, and visit-specific baseline-covariate effects. Measurements after the target visit are excluded from planning.

Method

The calculator forms the assumed covariance matrix, uses a modified Cholesky decomposition, and evaluates Tang’s expected REML/Kenward–Roger variance and Satterthwaite degrees of freedom under group-specific monotone retention. Exact noncentral-t power is evaluated for the selected two-sided or directional superiority test. Complete allocation blocks are searched until corrected power first reaches the target.

Assumptions and limitations

Two independent randomized parallel groups and continuous approximately Gaussian outcomes.
A common, correctly specified covariance matrix and a monotone missing-at-random planning pattern conditional on observed model variables.
REML estimation with Kenward–Roger variance and degrees-of-freedom adjustment.
The endpoint, target visit, expected difference, sidedness, analysis population, intercurrent-event strategy, and missing-data sensitivity analyses must be prespecified.
Not for non-inferiority, equivalence, clusters, more than two groups, non-Gaussian outcomes, average-across-visit effects, or omnibus treatment-by-time tests.

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

Independent validation

The numerical engine reproduces the q = 1 superiority scenarios in Tang (2018), Table 3, across unstructured, compound-symmetry, AR(1), and Toeplitz covariance matrices and three target effects. The public result advances odd near-balanced published totals to the next complete 1:1 block. A separate R validation simulates longitudinal trials and fits MMRMs using the independently maintained mmrm package.

Technical results

Privacy

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

References

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.
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.
ICH E9(R1). Addendum on estimands and sensitivity analysis in clinical trials. 2019.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for MMRM Superiority at a Specified Visit.” Web calculator. NajibMY, 2026. Accessed August 18, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/mmrm-superiority-at-specified-visit/.