Bias-Corrected Maximum Likelihood Estimator of a Log Common Odds Ratio
针对稀疏数据，推导了对数公共优势比最大似然估计的偏差校正因子，使校正后的估计量几乎无偏且均方误差更小，适用于平衡设计或大层数情形。
A bias-correction factor for the maximum likelihood estimator of the log common odds ratio for sparse data is derived, which is applicable when the design is balanced and/or when the number of strata is large. The corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximum likelihood estimator. The correction factor for the maximum likelihood estimator approaches one as strata sizes increase. Examples demonstrate that the corrected maximum likelihood estimator and the exact conditional maximum likelihood estimator are essentially identical although the standard error of the former tends to be slightly smaller than that of the latter. It is also demonstrated that a simple version of the correction factor is a satisfactory approximation. The bias-corrected maximum likelihood estimator proposed in this paper is the extension of Breslow's (1981) and it can be useful particularly when the computational burden of the exact conditional method is excessive.