Longitudinal Models · GEE-2G-BI

Sample Size for Two-Group GEE: Binary Omnibus Group-by-Time Interaction

Plan an omnibus logistic-GEE Wald test of whether the population-averaged treatment odds-ratio profile changes across follow-up visits.

1. Planning setup

Include a baseline measurement

With baseline, the joint null sets every follow-up odds ratio to 1. Without baseline, it tests whether odds ratios vary across follow-ups.

Working correlation structure

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

Common baseline event probability (%)

3. Inputs decided by the researcher for the new study

Enter the anticipated comparison-versus-reference population-averaged odds ratio at every follow-up.

Comparison-to-reference allocation ratio

Type I error, alpha (%)

Power (%)

Anticipated participant dropout/non-response (%)

4. Results

Enter the binary-outcome profiles and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized infection-prevention trial records whether infection occurred during four successive follow-up periods. Investigators expect little early effect and a stronger later effect, and plan an omnibus logistic-GEE test of whether the population-average odds-ratio profile changes over time.

Formula and methodological note

A saturated categorical-visit logistic GEE estimates a treatment log odds ratio at every follow-up. Model-based information is D′V⁻¹D. With baseline, the joint null sets all follow-up log odds ratios to zero; without baseline, later log odds ratios are contrasted with the first. Power uses a noncentral chi-square Wald distribution and exact allocation search.

Pairwise Bernoulli feasibility is checked using Fréchet bounds. The method assumes correctly specified probability profiles and working correlation, common visits, independent participants, and randomized groups for baseline adjustment. Dropout is inflation only. Informative missingness, extra clustering, robust planning under misspecification, and small-sample corrections are outside scope. This tool supports research planning and does not replace statistical consultation.

Technical results

Method references

Rochon J. Application of GEE procedures for sample size calculations in repeated measures experiments. Stat Med. 1998;17:1643–1658.
Liang KY, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika. 1986;73:13–22.
Statsmodels developers. Generalized Estimating Equations documentation.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Two-Group GEE: Binary Omnibus Group-by-Time Interaction (GEE-2G-BI).” Web calculator. NajibMY, 2026. Accessed August 2, 2026. https://najibmy.netlify.app/tools/sample-size/clinical-complex-study-designs/gee-binary-group-by-time-interaction/.