### Abstract

A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel-Haenszel chi-square statistic (χ_{MH}
^{2}), the adjusted Mantel-Haenszel chi-square statistics of Rao and Scott using both an unpooled design effect (χ_{RSN}
^{2}) and a pooled design effect (χ_{RSP}
^{2}), the adjusted Mantel-Haenszel chi-square statistic of Donald and Donner (χ_{DD}
^{2}), the chi-square statistic using the GEE approach (χ_{GEE}
^{2}), the adjusted Mantel-Haenszel chi-square statistic of Begg (χ_{B}
^{2}), the Wald (χ_{W}
^{2}), the robust Wald (χ_{RW}
^{2}), the score (χ_{S}
^{2}), the robust score (χ_{RS}
^{2}), and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χ_{ZBP}
^{2} and χ_{ZBN}
^{2}). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χ_{RS}
^{2} and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χ_{ZBP}
^{2} and χ_{ZBN}
^{2}) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intrachister correlation is zero or the cluster sizes are balanced. χ_{RS}
^{2} performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.

Original language | English (US) |
---|---|

Pages (from-to) | 375-390 |

Number of pages | 16 |

Journal | Biometrical Journal |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - 2002 |

### Fingerprint

### Keywords

- Correlated binary data
- Mantel-Haenszel
- Randomization trial

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Biometrical Journal*,

*44*(3), 375-390. https://doi.org/10.1002/1521-4036(200204)44:3<375::AID-BIMJ375>3.0.CO;2-S

**Cluster randomization trials : A simulation study.** / Song, James X.; Ahn, Chul.

Research output: Contribution to journal › Article

*Biometrical Journal*, vol. 44, no. 3, pp. 375-390. https://doi.org/10.1002/1521-4036(200204)44:3<375::AID-BIMJ375>3.0.CO;2-S

}

TY - JOUR

T1 - Cluster randomization trials

T2 - A simulation study

AU - Song, James X.

AU - Ahn, Chul

PY - 2002

Y1 - 2002

N2 - A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel-Haenszel chi-square statistic (χMH 2), the adjusted Mantel-Haenszel chi-square statistics of Rao and Scott using both an unpooled design effect (χRSN 2) and a pooled design effect (χRSP 2), the adjusted Mantel-Haenszel chi-square statistic of Donald and Donner (χDD 2), the chi-square statistic using the GEE approach (χGEE 2), the adjusted Mantel-Haenszel chi-square statistic of Begg (χB 2), the Wald (χW 2), the robust Wald (χRW 2), the score (χS 2), the robust score (χRS 2), and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χZBP 2 and χZBN 2). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χRS 2 and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χZBP 2 and χZBN 2) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intrachister correlation is zero or the cluster sizes are balanced. χRS 2 performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.

AB - A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel-Haenszel chi-square statistic (χMH 2), the adjusted Mantel-Haenszel chi-square statistics of Rao and Scott using both an unpooled design effect (χRSN 2) and a pooled design effect (χRSP 2), the adjusted Mantel-Haenszel chi-square statistic of Donald and Donner (χDD 2), the chi-square statistic using the GEE approach (χGEE 2), the adjusted Mantel-Haenszel chi-square statistic of Begg (χB 2), the Wald (χW 2), the robust Wald (χRW 2), the score (χS 2), the robust score (χRS 2), and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χZBP 2 and χZBN 2). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χRS 2 and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χZBP 2 and χZBN 2) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intrachister correlation is zero or the cluster sizes are balanced. χRS 2 performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.

KW - Correlated binary data

KW - Mantel-Haenszel

KW - Randomization trial

UR - http://www.scopus.com/inward/record.url?scp=0036013103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036013103&partnerID=8YFLogxK

U2 - 10.1002/1521-4036(200204)44:3<375::AID-BIMJ375>3.0.CO;2-S

DO - 10.1002/1521-4036(200204)44:3<375::AID-BIMJ375>3.0.CO;2-S

M3 - Article

AN - SCOPUS:0036013103

VL - 44

SP - 375

EP - 390

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 3

ER -