Mixed Models for Repeated Measures · MMRM-EQ-T

Sample Size for MMRM Equivalence at a Specified Visit

Plan a two-group parallel trial in which the entire confidence interval for the experimental-minus-reference difference at one prespecified visit must lie within lower and upper equivalence margins.

1. Estimand and equivalence hypothesis

Outcome label optional

Outcome unit optional

Number of post-baseline visits

Primary target visit

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

Expected experimental − reference difference

Equivalence margins

Lower Upper

The expected difference must lie strictly between both margins.

2. Repeated-measure and retention assumptions

Enter assumptions for each post-baseline visit. Retention is the proportion of randomized participants expected to remain observed at that visit.

Visit	Outcome SD	Reference retention (%)	Experimental retention (%)

Within-participant covariance structure

Adjacent-visit correlation

3. Operating characteristics

One-sided alpha for each TOST component

Confirm the protocol’s confidence level; “alpha 5%” can be ambiguous in an equivalence trial.

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 dropout twice.

4. Results

Enter the MMRM assumptions and select Calculate sample size.

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

Scope and estimand

For continuous outcomes and a categorical-visit MMRM.

This calculator uses all measurements through the target visit, monotone retention assumptions, REML, Kenward–Roger variance adjustment, and a TOST-compatible confidence-interval criterion. It is not a calculator for change-score proportions, repeated-measures ANOVA, or a treatment-by-time omnibus test.

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

Method

The calculator forms the assumed covariance matrix, applies its modified Cholesky decomposition, and evaluates Tang’s expected REML/Kenward–Roger variance and Satterthwaite degrees of freedom under group-specific monotone retention. Equivalence power uses Tang’s MMRM adaptation of two one-sided tests (Equation 28). Integer group allocations are searched until power first reaches the target, then any additional non-evaluable allowance is applied by arm.

Assumptions and limitations

Two independent randomized parallel groups; continuous approximately normal outcomes.
Common correctly specified covariance matrix in both groups and monotone missingness compatible with the planned likelihood analysis.
REML estimation with Kenward–Roger variance and degrees-of-freedom adjustment.
Equivalence margins, analysis population, missing-data strategy, intercurrent-event strategy, target visit, and confidence level must be prespecified and clinically justified.
Not for cluster trials, more than two groups, binary outcomes, non-monotone pattern-specific planning, average effects across visits, 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 all eight q = 1 sample-size totals in Tang (2018), Table 6, across unstructured, compound-symmetry, AR(1), and Toeplitz covariance examples and both equivalence margins. A separate R validation simulates longitudinal data and fits the models with 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;37:3207–3220. 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 Equivalence at a Specified Visit.” Web calculator. NajibMY, 2026. Accessed August 16, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/mmrm-equivalence-at-specified-visit/.