Longitudinal Models · LMM-2G-I

Sample Size for Two-Group Linear Mixed Model: Omnibus Group-by-Time Interaction

Plan an omnibus Wald test of whether the comparison-minus-reference mean profile differs over categorical follow-up visits.

1. Planning setup

Random-effects structure

Residual structure

Include a baseline measurement

With baseline, the joint test compares every follow-up group difference with zero. Without baseline, it tests whether group differences vary across follow-ups.

Follow-up measurements per participant

Time from baseline to final follow-up

Follow-ups are equally spaced.

2. Information obtained from previous studies or pilot data

Random-intercept standard deviation

Residual standard deviation

3. Inputs decided by the researcher for the new study

Enter anticipated comparison-group minus reference-group mean differences. Negative and positive values are accepted.

Comparison-to-reference allocation ratio

Type I error, alpha (%)

Power (%)

Anticipated participant dropout/non-response (%)

4. Results

Enter the longitudinal design assumptions and anticipated group-difference profile, then select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized rehabilitation trial measures mobility at baseline and at 1, 3, 6, and 12 months. Investigators want an omnibus test of whether the intervention and control mean profiles differ across follow-up visits, allowing the treatment effect to emerge and change over time.

Formula and methodological note

The calculator fits categorical visit means. It forms the generalized least-squares covariance of the vector of comparison-minus-reference follow-up differences from V = ZGZ′ + R. With baseline adjustment, A is the identity matrix and the null hypothesis sets every follow-up difference to zero. Without baseline, A contains differences from the first follow-up, so the null hypothesis is a constant group difference across follow-ups. The Wald statistic has degrees of freedom equal to the rank of A and noncentrality k(Aδ)′(AΣδA′)⁻¹(Aδ). Exact allocation multiples are searched using the noncentral chi-square distribution.

The calculation assumes a continuous outcome, equally spaced common visits, independent participants, a correctly specified covariance model, and randomized groups when a common baseline mean is used. Recruitment is inflated separately by group and rounded upward. Dropout is not a missing-data model. The tool excludes irregular visit schedules, cluster designs, informative missingness, nonlinear random effects, and non-Gaussian outcomes. It supports research planning and does not replace statistical consultation.

Technical results

Method references

Diggle PJ, Heagerty P, Liang KY, Zeger SL. Analysis of Longitudinal Data. 2nd ed. Oxford University Press; 2002.
Statsmodels developers. NormalIndPower documentation.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Two-Group Linear Mixed Model: Omnibus Group-by-Time Interaction (LMM-2G-I).” Web calculator. NajibMY, 2026. Accessed August 1, 2026. https://najibmy.netlify.app/tools/sample-size/clinical-complex-study-designs/linear-mixed-model-group-by-time-interaction/.