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Reduced bias estimation of the log odds ratio

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  • Asma Saleh

    (University College London)

Abstract

Analysis of binary matched pairs data is problematic due to infinite maximum likelihood estimates of the log odds ratio and potentially biased estimates, especially for small samples. We propose a penalised version of the log-likelihood function based on adjusted responses which always results in a finite estimator of the log odds ratio. The probability limit of the adjusted log-likelihood estimator is derived and it is shown that in certain settings the maximum likelihood, conditional and modified profile log-likelihood estimators drop out as special cases of the former estimator. We implement indirect inference to the adjusted log-likelihood estimator. It is shown, through a complete enumeration study, that the indirect inference estimator is competitive in terms of bias and variance in comparison to the maximum likelihood, conditional, modified profile log-likelihood and Firth’s penalised log-likelihood estimators.

Suggested Citation

  • Asma Saleh, 2024. "Reduced bias estimation of the log odds ratio," Statistical Papers, Springer, vol. 65(8), pages 5293-5331, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01593-7
    DOI: 10.1007/s00362-024-01593-7
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    References listed on IDEAS

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    1. N Lunardon, 2018. "On bias reduction and incidental parameters," Biometrika, Biometrika Trust, vol. 105(1), pages 233-238.
    2. N. Sartori, 2003. "Modified profile likelihoods in models with stratum nuisance parameters," Biometrika, Biometrika Trust, vol. 90(3), pages 533-549, September.
    3. Ken Butler & Michael A. Stephens, 2017. "The Distribution of a Sum of Independent Binomial Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 557-571, June.
    4. Ioannis Kosmidis & David Firth, 2021. "Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models," Biometrika, Biometrika Trust, vol. 108(1), pages 71-82.
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