Longitudinal Models · GEE-2G-S

Sample Size for Two-Group GEE: Difference in Linear Trends

Plan a population-averaged Wald test of the comparison-minus-reference difference in linear rates of change.

1. Planning setup

Include a baseline measurement

Without baseline, a separate group intercept is estimated.

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

Marginal outcome standard deviation

Assumed common across groups and visits.

3. Inputs decided by the researcher for the new study

Smallest clinically important difference in linear trends

Comparison-group minus reference-group outcome units per time unit. Negative values are accepted.

Comparison-to-reference allocation ratio

Type I error, alpha (%)

Alternative hypothesis

Power (%)

Anticipated participant dropout/non-response (%)

4. Results

Enter the longitudinal trend assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized pulmonary-rehabilitation trial measures walking distance at baseline and at 3, 6, 9, and 12 months. Investigators plan a population-average GEE analysis and want to detect a difference between groups in the mean linear rate of change over time.

Formula and methodological note

The marginal model contains time, group when baseline is absent, and group-by-time. Model-based GEE information is X′V⁻¹X for V = A½R(ρ)A½. The target is the group-by-time coefficient. With randomized baseline adjustment, the group main effect is omitted to impose a common baseline mean. Exact allocation units are searched using normal-theory Wald power.

The method assumes linear marginal trends, correctly specified common marginal SD and working correlation, equally spaced visits, independent participants, and randomized groups for a common baseline. Dropout is inflation only. Nonlinear or categorical-visit effects, irregular schedules, visit-specific variance, 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 and NormalIndPower documentation.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Two-Group GEE: Difference in Linear Trends (GEE-2G-S).” Web calculator. NajibMY, 2026. Accessed August 2, 2026. https://najibmy.netlify.app/tools/sample-size/clinical-complex-study-designs/gee-difference-in-linear-trends/.