Longitudinal Models · GEE-2G-BT

Sample Size for Two-Group GEE: Binary Outcome Difference at a Specified Follow-Up

Plan a logistic-GEE Wald test of the population-averaged comparison-versus-reference odds ratio at one prespecified follow-up.

1. Planning setup

Include a baseline measurement

Baseline adjustment assumes randomized groups with the same baseline probability.

Working correlation structure

Follow-up measurements per participant

Specified follow-up for the primary comparison

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 population-averaged odds ratio at the specified follow-up

Comparison-group event odds divided by 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 diabetes trial records whether each participant achieves glycaemic control at four follow-ups. The primary estimand is the population-averaged treatment odds ratio at month 12, while earlier visits contribute to the prespecified logistic-GEE covariance model.

Formula and methodological note

A saturated categorical-visit marginal logit model estimates a separate treatment log odds ratio at every follow-up. The target coefficient variance is obtained from the relevant diagonal of the inverse model-based information, (D′V⁻¹D)⁻¹. Exact allocation units are searched using normal-theory Wald power. Pairwise Bernoulli feasibility is checked using Fréchet bounds; group recruitment is inflated and rounded separately.

The method assumes correctly specified marginal probability profiles and working correlation, common scheduled visits, independent participants, randomized groups for baseline adjustment, and a single prespecified target visit. Non-target treatment effects are nuisance parameters and are set to odds ratio 1 only when evaluating planning covariance. Robust misspecification protection, informative or visit-specific missingness, extra clustering, small-sample corrections, and multiple target visits 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 Outcome Difference at a Specified Follow-Up (GEE-2G-BT).” Web calculator. NajibMY, 2026. Accessed August 2, 2026. https://najibmy.netlify.app/tools/sample-size/clinical-complex-study-designs/gee-binary-difference-at-follow-up/.