Sample size and power calculations based on generalized linear mixed models with correlated binary outcomes
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Updated: Jul 5, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Qianyu Dang1, Sati Mazumdar, Patricia R Houck
1Department of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA. dangq@upmc.edu
Abstract:
The generalized linear mixed model (GLIMMIX) provides a powerful technique to model correlated outcomes with different types of distributions. The model can now be easily implemented with SAS PROC GLIMMIX in version 9.1. For binary outcomes, linearization methods of penalized quasi-likelihood (PQL) or marginal quasi-likelihood (MQL) provide relatively accurate variance estimates for fixed effects. Using GLIMMIX based on these linearization methods, we derived formulas for power and sample size calculations for longitudinal designs with attrition over time. We found that the power and sample size estimates depend on the within-subject correlation and the size of random effects. In this article, we present tables of minimum sample sizes commonly used to test hypotheses for longitudinal studies. A simulation study was used to compare the results. We also provide a Web link to the SAS macro that we developed to compute power and sample sizes for correlated binary outcomes.
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