Sample size calculations for clustered binary data

Sin Ho Jung, Seung Ho Kang, Chul Ahn

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


In this paper we propose a sample size calculation method for testing on a binomial proportion when binary observations are dependent within clusters. In estimating the binomial proportion in clustered binary data, two weighting systems have been popular: equal weights to clusters and equal weights to units within clusters. When the number of units varies cluster by cluster, performance of these two weighting systems depends on the extent of correlation among units within each cluster. In addition to them, we will also use an optimal weighting method that minimizes the variance of the estimator. A sample size formula is derived for each of the estimators with different weighting schemes. We apply these methods to the sample size calculation for the sensitivity of a periodontal diagnostic test. Simulation studies are conducted to evaluate a finite sample performance of the three estimators. We also assess the influence of misspecified input parameter values on the calculated sample size. The optimal estimator requires equal or smaller sample sizes and is more robust to the misspecification of an input parameter than those assigning equal weights to units or clusters.

Original languageEnglish (US)
Pages (from-to)1971-1982
Number of pages12
JournalStatistics in Medicine
Issue number13
StatePublished - Jul 15 2001

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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