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

Example clinical scenario

A randomized diabetes-management trial measures HbA1c at baseline and 3, 6, 9, and 12 months. Investigators expect little difference initially and a larger intervention effect later. The primary analysis uses GEE to estimate population-average marginal means and jointly tests whether the intervention and control profiles differ across follow-up visits.

Formula and methodological note

For marginal covariance V = A½R(α)A½, categorical-visit GEE information is D′V⁻¹D. The calculator combines group information at the allocation ratio and extracts covariance Σδ for the comparison-minus-reference difference profile. With baseline adjustment, C is the identity matrix; without baseline, C compares later differences with the first follow-up. Noncentrality per allocation unit is (Cδ)′(CΣδC′)⁻¹(Cδ), and power uses the corresponding noncentral chi-square distribution.

This version uses model-based planning covariance and assumes that the selected working correlation is correct. A subsequent robust-sandwich analysis does not protect planning from incorrect variance or correlation assumptions. It assumes a continuous outcome, common marginal SD, equally spaced visits, independent participants, and randomized groups for common-baseline adjustment. Dropout is recruitment inflation only. Irregular schedules, visit-specific variances, small-sample sandwich corrections, clusters beyond participants, and informative missingness are outside scope. This tool supports research planning and does not replace statistical consultation.

Technical results

Method references

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