Greenland S, Robins J M
Biometrics. 1985 Mar;41(1):55-68.
Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.
布雷斯洛（1981年，《生物统计学》68卷，73 - 84页）表明，在稀疏分层中，曼特尔 - 亨泽尔优势比是共同优势比的一致估计量。然而，对于队列研究而言，估计共同风险比或风险差异可能更有意义。在二项式稀疏数据模型下，曼特尔 - 亨泽尔风险比和风险差异估计量在稀疏分层中是一致的，而最大似然估计量和加权最小二乘估计量存在偏差。在泊松稀疏数据模型下，在原假设下，曼特尔 - 亨泽尔和最大似然率比估计量具有相等的渐近方差且是一致的，而加权最小二乘估计量再次存在偏差；类似地，在共同率差异估计量中，加权最小二乘估计量存在偏差，而采用“曼特尔 - 亨泽尔”权重的估计量在稀疏数据中是一致的。对于所有曼特尔 - 亨泽尔估计量，都可以推导出在稀疏数据和大分层中都一致的方差估计量。
