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Methods of estimation in log odds ratio regression models.

N E Breslow, J Cologne

    Biometrics
    |December 1, 1986
    PubMed
    Summary

    McCullagh's approximation for log odds ratio regression shows minimal bias in most scenarios. This statistical method closely matches conditional analysis results for case-control data, unlike Davis's generalization.

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    Area of Science:

    • Statistics
    • Biostatistics
    • Epidemiology

    Background:

    • Conditional maximum likelihood estimation is a standard in log odds ratio regression.
    • Approximation methods are used to simplify complex statistical calculations.
    • Evaluating the accuracy of these approximations is crucial for reliable data analysis.

    Purpose of the Study:

    • To assess the asymptotic bias of McCullagh's approximation for conditional maximum likelihood estimators in log odds ratio regression.
    • To compare the performance of McCullagh's approximation with a generalization of the Mantel-Haenszel estimator using real case-control data.

    Main Methods:

    • The study analyzes McCullagh's approximation for bias in log odds ratio regression models.
    • It applies the approximation to two case-control datasets.
    • Performance is evaluated against conditional maximum likelihood analysis and Davis's generalized Mantel-Haenszel estimator.

    Main Results:

    • McCullagh's approximation demonstrates negligible asymptotic bias, except with large odds ratios and small sample sizes in 2x2 tables.
    • Results from McCullagh's approximation were nearly identical to the conditional analysis on the tested datasets.
    • Davis's generalized Mantel-Haenszel estimator did not approximate conditional results as effectively.

    Conclusions:

    • McCullagh's approximation is a reliable method for log odds ratio regression, offering results comparable to conditional analysis in most practical situations.
    • The approximation's validity is robust, with limitations only under extreme conditions of large odds ratios and very small cell counts.
    • Davis's estimator is less suitable for approximating conditional maximum likelihood estimates in these models.

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