A cluster-adjusted sample size algorithm for proportions was developed using a beta-binomial model

Area of Science:

• Biostatistics
• Epidemiology
• Computational Statistics

Background:

• Sample size calculations are crucial for accurate estimation of population proportions.
• Ignoring clustered sampling units can lead to underestimation of necessary sample sizes.
• Intraclass correlation information is often unavailable in the initial study design phase.

Purpose of the Study:

• To design a computer algorithm for calculating sample sizes for proportions with clustered sampling units.
• To utilize a beta-binomial model when intraclass correlation information is absent.
• To provide a method for incorporating clustering effects into sample size estimations.

Main Methods:

• A computer algorithm was developed using FORTRAN.
• The algorithm was evaluated using a hypothetical sample size scenario.
• A beta distribution was specified to account for within-cluster correlation.

Main Results:

• The algorithm successfully incorporated clustering into sample size calculations.
• A hypothetical example showed a required sample size of 208 units compared to 107 using the normal approximation method ignoring clustering.
• This highlights the significant impact of clustering on sample size requirements.

Conclusions:

• Cluster adjustment is essential in sample size calculations for epidemiologic studies with correlated data.
• Beta-binomial models offer a viable approach to account for clustering effects when intraclass correlation is unknown.
• The developed algorithm provides a practical tool for estimating design effects and determining appropriate sample sizes in clustered designs.