Lachin J M, Wei L J
Department of Statistics, Computer & Information Systems, George Washington University, Rockville, Maryland 20852.
Biometrics. 1988 Jun;44(2):513-28.
We present methods for the analysis of a K-variate binary measure for two independent groups where some observations may be incomplete, as in the case of K repeated measures in a comparative trial. For the K 2 X 2 tables, let theta = (theta 1,..., theta K) be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group (i = 1, 2; k = 1,..., K), such as the log odds ratio or log relative risk. The asymptotic distribution of the estimates theta = (theta 1,..., theta K) is derived. Under the assumption that theta k = theta for all k, we describe the maximally efficient linear estimator theta of the common parameter theta. Tests of contrasts on the theta are presented which provide a test of homogeneity Ha: theta k = theta l for all k not equal to l. We then present maximally efficient tests of aggregate association Hb: theta = theta 0, where theta 0 is a given value. It is shown that the test of aggregate association Hb is asymptotically independent of the preliminary test of homogeneity Ha. These methods generalize the efficient estimators of Gart (1962, Biometrics 18, 601-610), and the Cochran (1954, Biometrics 10, 417-451), Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748), and Radhakrishna (1965, Biometrics 21, 86-98) tests to nonindependent tables. The methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the National Cooperative Gallstone Study.
我们提出了针对两个独立组的K变量二元测量分析方法，其中一些观察结果可能不完整，就像在比较试验中的K次重复测量情况一样。对于K个2×2列联表，令θ = (θ₁,..., θₖ)为关联参数向量，其中θₖ是关联度量，它是每组中概率πᵢₖ（i = 1, 2；k = 1,..., K）的连续函数，例如对数优势比或对数相对风险。推导了估计值θ = (θ₁,..., θₖ)的渐近分布。在假设对所有k，θₖ = θ的情况下，我们描述了公共参数θ的最大有效线性估计量θ。给出了关于θ的对比检验，该检验提供了齐性检验Hₐ：对所有k ≠ l，θₖ = θₗ。然后我们给出了总体关联检验Hₐ：θ = θ₀的最大有效检验，其中θ₀是给定值。结果表明，总体关联检验Hₐ与齐性初步检验Hₐ渐近独立。这些方法将Gart（1962年，《生物统计学》18卷，601 - 610页）、Cochran（1954年，《生物统计学》10卷，417 - 451页）、Mantel - Haenszel（1959年，《国家癌症研究所杂志》22卷，719 - 748页）以及Radhakrishna（1965年，《生物统计学》21卷，86 - 98页）检验推广到了非独立列联表。通过对在国家合作胆结石研究中获得的肝脏活检重复形态学评估的分析来说明这些方法。
