### Abstract

In this paper, the results from a simulation study for the estimation of a common odds ratio in multiple 2 × 2 tables when the data are correlated within clusters are presented. The size of clusters in each stratum is modelled by the negative binomial distribution truncated below 1 with mean cluster size, μ = 4, 5, and 6, and imbalance parameter, κ = 0.6, 0.8, and 1.0. The correlation of the data is modelled by the beta-binomial distribution. A simulation study is conducted to compare the performances of the Mantel-Haenszel estimator (ψ̂_{MH}), the modified Donner-Hauck estimator (ψ̂_{MDH}) and the Rao-Scott estimator (ψ^{N}
_{RS}, ψ^{P}
_{RS}) in terms of their biases, absolute biases, mean squared errors, and 95% coverage proportions. The modified Donner-Hauck estimator ψ̂_{MDH} performs better than the other estimators in terms of the bias, absolute bias, and MSE when ψ ≥ 3 in the unbalanced design. In general, there are negligible differences in the bias, absolute bias, and MSE among the estimators when ψ = 1 or κ = 1.0. The estimator ψ̂_{MDH} has generally coverage proportions closer to the nominal level than the other estimators for ρ ≥ 0.3 in the unbalanced design. When κ = 0.8, ψ̂^{P}
_{RS} and ψ̂_{MDH} generally have coverage proportions closer to the nominal level than ψ̂_{MH} and ̂^{N}
_{RS} in the wide band. However, the differences in coverage proportions were minimal in balanced design (κ = 1.0) among the estimators. Based on the results from the simulation study, I recommend using ψ̂_{MDH} since it generally performs better than the other estimators for all factors considered (bias, absolute bias, MSE, and coverage proportions).

Original language | English (US) |
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Pages (from-to) | 47-61 |

Number of pages | 15 |

Journal | Computational Statistics and Data Analysis |

Volume | 24 |

Issue number | 1 |

Publication status | Published - Mar 6 1997 |

### Keywords

- Degree of imbalance
- Odds ratio
- Simulation

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Computational Mathematics
- Numerical Analysis
- Statistics and Probability