Sample Size for MMRM Non-Inferiority at a Specified Visit

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. Measurements after the target visit are excluded from planning.

Method

Let delta be experimental minus reference and M be the positive maximum acceptable loss. For higher-favorable outcomes the null boundary is -M; for lower-favorable outcomes it is +M. The calculator transforms the distance from that boundary to a favorable positive scale, then uses Tang's expected REML/Kenward-Roger variance, Satterthwaite degrees of freedom, and exact one-sided noncentral-t power. Complete allocation blocks are searched until corrected power first reaches the target.

At analysis, non-inferiority corresponds to the lower one-sided confidence bound exceeding -M when higher values are favorable, or the upper one-sided confidence bound falling below +M when lower values are favorable.

Assumptions and limitations

• Two independent randomized parallel groups and continuous approximately Gaussian outcomes.
• A common, correctly specified covariance matrix and monotone missing-at-random planning conditional on observed model variables.
• REML estimation with Kenward-Roger variance and degrees-of-freedom adjustment.
• The margin must be clinically justified independently of the expected effect. Constancy and assay sensitivity remain study-specific.
• Nonadherence and protocol deviations can bias a non-inferiority conclusion. The protocol should prespecify appropriate intention-to-treat and per-protocol analysis strategies and reconcile materially different results.
• The endpoint, target visit, favorable direction, margin, analysis population, intercurrent-event strategy, and missing-data sensitivity analyses must be prespecified.
• Not for equivalence, superiority, 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 non-inferiority transformation and noncentral-t probabilities are checked against independent R calculations. The shared MMRM information engine reproduces Tang (2018) target-visit examples across unstructured, compound-symmetry, AR(1), and Toeplitz covariance matrices. A separate R validation fits simulated longitudinal trials 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

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. FDA. Non-Inferiority Clinical Trials to Establish Effectiveness: Guidance for Industry. 2016.
4. EMA. Guideline on the choice of the non-inferiority margin. 2005.
5. ICH E9(R1). Addendum on estimands and sensitivity analysis in clinical trials. 2019.