Longitudinal Models · GEE-2G-B

Sample Size for Two-Group GEE: Repeated Binary Outcomes

Plan a logistic GEE Wald test of one common population-averaged treatment odds ratio across repeated binary-outcome follow-ups.

1. Planning setup

Include a baseline measurement

The treatment indicator is zero at baseline.

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 (%)

Enter the anticipated event probability in the reference group at every follow-up.

3. Inputs decided by the researcher for the new study

Anticipated common population-averaged odds ratio

Comparison-group versus reference-group event odds. Values below and above 1 are accepted.

Comparison-to-reference allocation ratio

Type I error, alpha (%)

Alternative hypothesis

Power (%)

Anticipated participant dropout/non-response (%)

4. Results

Enter the repeated-binary design assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized asthma trial records whether each participant experienced an exacerbation during four successive follow-up periods. Investigators plan a logistic GEE analysis with categorical visit effects and one common population-averaged treatment odds ratio across periods.

Formula and methodological note

The marginal logit model contains categorical visit intercepts and one common treatment coefficient. Reference probabilities and the anticipated odds ratio determine group-specific marginal probabilities. Model-based GEE information is D′V⁻¹D, where Bernoulli variances form the diagonal scale and the chosen working correlation forms V. Exact allocation units are searched using normal-theory Wald power for the common log odds ratio.

Pairwise Bernoulli feasibility is checked using Fréchet bounds. The method assumes a common odds ratio, correctly specified probabilities and working correlation, equally spaced visits, independent participants, and randomized groups for common-baseline adjustment. Dropout is inflation only. Visit-specific treatment effects, robust misspecification protection at planning, informative missingness, extra clustering, small-sample corrections, and nonbinary outcomes 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: Repeated Binary Outcomes (GEE-2G-B).” Web calculator. NajibMY, 2026. Accessed August 2, 2026. https://najibmy.netlify.app/tools/sample-size/clinical-complex-study-designs/gee-repeated-binary-outcomes/.