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Mantel–Haenszel estimators of odds ratios for stratified dependent binomial data

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  • Suesse, Thomas
  • Liu, Ivy

Abstract

A standard approach to analyzing n binary matched pairs usually represented in n 2×2 tables is to apply a subject-specific model; for the simplest situation it is the so-called Rasch model. An alternative population-averaged approach is to apply a marginal model to the single 2×2 table formed by n subjects. For the situation of having an additional stratification variable with K levels forming K 2×2 tables, standard fitting approaches, such as generalized estimating equations and maximum likelihood, or, alternatively, the standard Mantel–Haenszel (MH) estimator, can be applied. However, while all these standard approaches are consistent under a large-stratum limiting model, they are not consistent under a sparse-data limiting model. In this paper, we propose a new MH estimator and a variance estimator that are both dually consistent: consistent under both large-stratum and sparse-data limiting situations. In a simulation study, the properties of the proposed estimators are confirmed, and the estimator is compared with standard marginal methods. The simulation study also considers the case when the homogeneity assumption of the odds ratios does not hold, and the asymptotic limit of the proposed MH estimator under this situation is derived. The results show that the proposed MH estimator is generally better than the standard estimator, and the same can be said about the associated Wald-type confidence intervals.

Suggested Citation

  • Suesse, Thomas & Liu, Ivy, 2012. "Mantel–Haenszel estimators of odds ratios for stratified dependent binomial data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2705-2717.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2705-2717
    DOI: 10.1016/j.csda.2012.02.015
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    References listed on IDEAS

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    1. Haber, Michael, 1985. "Maximum likelihood methods for linear and log-linear models in categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 3(1), pages 1-10, May.
    2. Alan Agresti & I-Ming Liu, 1999. "Modeling a Categorical Variable Allowing Arbitrarily Many Category Choices," Biometrics, The International Biometric Society, vol. 55(3), pages 936-943, September.
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    Cited by:

    1. Thomas Suesse & Ivy Liu, 2013. "Modelling Strategies for Repeated Multiple Response Data," International Statistical Review, International Statistical Institute, vol. 81(2), pages 230-248, August.
    2. Thomas Suesse & Ivy Liu, 2019. "Mantel–Haenszel estimators of a common odds ratio for multiple response data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 57-76, March.

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