Related Experiment Video
Updated: Jun 16, 2026

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model
Published on: April 18, 2025
Sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with
Math J J M Candel1, Gerard J P Van Breukelen
1Department of Methodology and Statistics, Maastricht University, Maastricht, The Netherlands. math.candel@stat.unimaas.nl
Adjusting sample size formulas for cluster randomized trials with varying cluster sizes is crucial. This study provides accurate methods for mixed-effects logistic regression, suggesting a 14% increase in clusters can often compensate for efficiency loss.
Area of Science:
- Biostatistics
- Clinical Trials Methodology
- Statistical Modeling
Background:
- Cluster randomized trials (CRTs) with binary outcomes often have unequal cluster sizes.
- Standard sample size formulas may not accurately reflect efficiency when cluster sizes vary.
- Mixed-effects logistic regression with second-order penalized quasi-likelihood (PQL) is a common analysis method.
Purpose of the Study:
- To provide adjusted sample size formulas for CRTs with binary outcomes and varying cluster sizes.
- To evaluate the accuracy of asymptotic relative efficiency for unequal versus equal cluster sizes using second-order PQL.
- To develop a simpler formula for estimating efficiency loss due to varying cluster sizes during trial planning.
Main Methods:
- Derivation of asymptotic relative efficiency for unequal versus equal cluster sizes, starting from first-order marginal quasi-likelihood (MQL) estimation.
- Monte Carlo simulation studies to assess the accuracy of the derived efficiency and to determine a conversion factor for second-order PQL variance estimation.
- Development of an approximate formula for estimating efficiency loss.
Main Results:
- The asymptotic relative efficiency derived from MQL is accurate for realistic sample sizes when using second-order PQL.
- An approximate formula effectively estimates efficiency loss from varying cluster sizes.
- In many scenarios, increasing the number of clusters by 14% can mitigate efficiency loss.
- A conversion factor of at most 1.25 is needed to adjust for the variance of the second-order PQL estimator compared to first-order MQL.
Conclusions:
- Adjusted sample size calculations are necessary for CRTs with binary outcomes and varying cluster sizes.
- The proposed methods and formulas provide accurate adjustments for trial planning.
- Understanding and accounting for efficiency loss due to varying cluster sizes improves the reliability of sample size estimations in CRTs.
Related Concept Videos
Cluster Sampling Method
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Sampling Plans
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
Randomized Experiments
Simple randomization
Simple...
Comparing the Survival Analysis of Two or More Groups
One-Way ANOVA: Equal Sample Sizes
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
One-Way ANOVA: Unequal Sample Sizes
