### Abstract

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 language | English |
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Pages (from-to) | 1971-1982 |

Number of pages | 12 |

Journal | Statistics in Medicine |

Volume | 20 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2001 Jul 15 |

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### All Science Journal Classification (ASJC) codes

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*20*(13), 1971-1982. https://doi.org/10.1002/sim.846

}

*Statistics in Medicine*, vol. 20, no. 13, pp. 1971-1982. https://doi.org/10.1002/sim.846

**Sample size calculations for clustered binary data.** / Jung, Sin Ho; Kang, Seung Ho; Ahn, Chul.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sample size calculations for clustered binary data

AU - Jung, Sin Ho

AU - Kang, Seung Ho

AU - Ahn, Chul

PY - 2001/7/15

Y1 - 2001/7/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035879532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035879532&partnerID=8YFLogxK

U2 - 10.1002/sim.846

DO - 10.1002/sim.846

M3 - Article

C2 - 11427953

AN - SCOPUS:0035879532

VL - 20

SP - 1971

EP - 1982

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 13

ER -