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Unconditional efficient one-sided confidence limits for the odds ratio based on conditional likelihood.

Chris J Lloyd1, Max V Moldovan

  • 1Melbourne Business School, Carlton 3053, Australia. c.lloyd@mbs.edu

Statistics in Medicine
|April 18, 2007
PubMed
Summary
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Researchers compared one-sided confidence limits for the odds ratio in 2x2 tables. Buehler limits derived from conditional likelihood, particularly the mid-P version, demonstrated superior performance and are recommended for general use.

Area of Science:

  • Biostatistics
  • Statistical Inference
  • Epidemiological Methods

Background:

  • Accurate confidence limits for the odds ratio in 2x2 tables are crucial for statistical inference in various scientific fields.
  • Existing methods based on asymptotic approximations or conditional distributions often exhibit poor unconditional coverage properties.

Purpose of the Study:

  • To evaluate and compare various one-sided confidence limits for the odds ratio in 2x2 contingency tables.
  • To identify confidence limits with superior unconditional coverage properties and practical performance.

Main Methods:

  • Comparison of limits based on asymptotic approximations (likelihood ratio, score, Wald statistics).
  • Evaluation of limits derived from the conditional tilted hypergeometric distribution (with and without mid-P correction).

Related Experiment Videos

  • Application of Buehler's general transformation to achieve unconditionally exact confidence limits.

    • Main Results:

    • All tested limits based on asymptotic approximations and the conditional tilted hypergeometric distribution showed inadequate unconditional coverage.
    • Buehler limits, particularly those derived from the conditional likelihood (mid-P version), exhibited the best performance in terms of mean size.
    • The proposed conditional Buehler limits offer accurate and reliable estimation for odds ratios.

    Conclusions:

    • The conditional Buehler confidence limits, especially the mid-P version, are recommended for general use in analyzing 2x2 tables.
    • These limits provide superior unconditional coverage and performance compared to previously proposed methods.
    • Recommended for use when underlying probabilities are not extreme, offering a robust statistical tool.