What question did this study set out to answer?

To evaluate the asymptotic consistency, bias, and efficiency of four common odds ratio estimators when data are distributed across many sparse 2 × 2 tables.

January 1, 1981Biometrika

Odds ratio estimators when the data are sparse

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Authors

NBNorman E. BreslowUniversity of Washington

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Implication

Theoretical analysis evaluates odds ratio estimators in sparse tables, demonstrating that the Mantel-Haenszel estimator maintains consistency and high efficiency.

Key Points

To evaluate the asymptotic consistency, bias, and efficiency of four common odds ratio estimators when data are distributed across many sparse 2 × 2 tables.
Evaluated four odds ratio estimators: unconditional maximum likelihood, empirical logit, conditional maximum likelihood, and the Mantel-Haenszel estimator.
Modeled large-sample asymptotic behavior under an asymptotic scheme where the number of 2 × 2 tables increases while the possible marginal configurations remain fixed.
Neither the unconditional maximum likelihood nor the empirical logit estimators converged to the true odds ratio, exhibiting persistent asymptotic bias.
Conditional maximum likelihood and Mantel-Haenszel estimators demonstrated consistency, with their asymptotic variance ratio approaching 1 under the null hypothesis.
The Mantel-Haenszel estimator maintained high relative efficiency even in the presence of moderately large odds ratios.

Cite This Study

Norman E. Breslow (1981) studied this question.

synapsesocial.com/papers/6a125e9fc031bb6829a66f93 https://doi.org/10.1093/biomet/68.1.73

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January 1, 1981Biometrika

Odds ratio estimators when the data are sparse

View Full Paper

Ask AI

Bookmark

Authors

NBNorman E. BreslowUniversity of Washington

Discussion

Member takes

Implication

Theoretical analysis evaluates odds ratio estimators in sparse tables, demonstrating that the Mantel-Haenszel estimator maintains consistency and high efficiency.

Key Points

To evaluate the asymptotic consistency, bias, and efficiency of four common odds ratio estimators when data are distributed across many sparse 2 × 2 tables.
Evaluated four odds ratio estimators: unconditional maximum likelihood, empirical logit, conditional maximum likelihood, and the Mantel-Haenszel estimator.
Modeled large-sample asymptotic behavior under an asymptotic scheme where the number of 2 × 2 tables increases while the possible marginal configurations remain fixed.
Neither the unconditional maximum likelihood nor the empirical logit estimators converged to the true odds ratio, exhibiting persistent asymptotic bias.
Conditional maximum likelihood and Mantel-Haenszel estimators demonstrated consistency, with their asymptotic variance ratio approaching 1 under the null hypothesis.
The Mantel-Haenszel estimator maintained high relative efficiency even in the presence of moderately large odds ratios.

Cite This Study

Norman E. Breslow (1981) studied this question.

synapsesocial.com/papers/6a125e9fc031bb6829a66f93 https://doi.org/10.1093/biomet/68.1.73

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