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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Sample size and power calculations based on generalized linear mixed models with correlated binary outcomes.

Qianyu Dang¹, Sati Mazumdar, Patricia R Houck

¹Department of Medicine, University of Pittsburgh, Pittsburgh, PA 15213, USA. dangq@upmc.edu

Computer Methods and Programs in Biomedicine

|May 9, 2008

Summary

This study presents formulas for calculating power and sample sizes for longitudinal studies with missing data using generalized linear mixed models (GLIMMIX). Sample size depends on within-subject correlation and random effects, with provided tables and a SAS macro for convenience.

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Area of Science:

Statistical modeling
Longitudinal data analysis

Background:

Generalized linear mixed models (GLIMMIX) are effective for correlated outcomes.
SAS PROC GLIMMIX (version 9.1) facilitates implementation.
Penalized quasi-likelihood (PQL) and marginal quasi-likelihood (MQL) offer accurate variance estimates for binary outcomes.

Purpose of the Study:

Derive formulas for power and sample size calculations in longitudinal designs with attrition.
Provide practical tools for researchers conducting such studies.
Address the need for accurate sample size determination in correlated binary outcome research.

Main Methods:

Utilized GLIMMIX with PQL/MQL linearization methods.
Developed formulas for power and sample size.
Conducted a simulation study for validation.
Presented tables of minimum sample sizes.

Main Results:

Power and sample size are influenced by within-subject correlation and random effect magnitudes.
Derived formulas provide a basis for sample size estimation.
Simulation results support the derived formulas.

Conclusions:

The developed formulas and SAS macro enable accurate power and sample size calculations for longitudinal studies with correlated binary outcomes and attrition.
Researchers can use these tools to optimize study design and resource allocation.
Emphasizes the importance of considering within-subject correlation and random effects in sample size determination.