An evaluation of simple methods for the estimation of a common odds ratio in clusters with variable size

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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 (ψ̂MH), the modified Donner-Hauck estimator (ψ̂MDH) and the Rao-Scott estimator (ψN RS, ψP RS) in terms of their biases, absolute biases, mean squared errors, and 95% coverage proportions. The modified Donner-Hauck estimator ψ̂MDH 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 ψ̂MDH 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, ψ̂P RS and ψ̂MDH generally have coverage proportions closer to the nominal level than ψ̂MH 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 ψ̂MDH since it generally performs better than the other estimators for all factors considered (bias, absolute bias, MSE, and coverage proportions).

Original languageEnglish (US)
Pages (from-to)47-61
Number of pages15
JournalComputational Statistics and Data Analysis
Volume24
Issue number1
StatePublished - Mar 6 1997

Fingerprint

Common ratio
Odds Ratio
Estimator
Evaluation
Coverage
Proportion
Unbalanced Designs
Odds ratio
Simulation Study
Categorical or nominal
Beta-binomial Distribution
2 × 2 Table
Balanced Design
Negative binomial distribution

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

Cite this

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title = "An evaluation of simple methods for the estimation of a common odds ratio in clusters with variable size",
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 (ψ̂MH), the modified Donner-Hauck estimator (ψ̂MDH) and the Rao-Scott estimator (ψN RS, ψP RS) in terms of their biases, absolute biases, mean squared errors, and 95{\%} coverage proportions. The modified Donner-Hauck estimator ψ̂MDH 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 ψ̂MDH 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, ψ̂P RS and ψ̂MDH generally have coverage proportions closer to the nominal level than ψ̂MH 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 ψ̂MDH since it generally performs better than the other estimators for all factors considered (bias, absolute bias, MSE, and coverage proportions).",
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N2 - 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 (ψ̂MH), the modified Donner-Hauck estimator (ψ̂MDH) and the Rao-Scott estimator (ψN RS, ψP RS) in terms of their biases, absolute biases, mean squared errors, and 95% coverage proportions. The modified Donner-Hauck estimator ψ̂MDH 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 ψ̂MDH 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, ψ̂P RS and ψ̂MDH generally have coverage proportions closer to the nominal level than ψ̂MH 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 ψ̂MDH since it generally performs better than the other estimators for all factors considered (bias, absolute bias, MSE, and coverage proportions).

AB - 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 (ψ̂MH), the modified Donner-Hauck estimator (ψ̂MDH) and the Rao-Scott estimator (ψN RS, ψP RS) in terms of their biases, absolute biases, mean squared errors, and 95% coverage proportions. The modified Donner-Hauck estimator ψ̂MDH 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 ψ̂MDH 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, ψ̂P RS and ψ̂MDH generally have coverage proportions closer to the nominal level than ψ̂MH 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 ψ̂MDH since it generally performs better than the other estimators for all factors considered (bias, absolute bias, MSE, and coverage proportions).

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