STATISTICAL METHODS FOR THE COMMON ODDS RATIO OF A NUMBER OF CONTINGENCY TABLES

这项研究将发展统计方法来分析范畴 数据，特别是在不同群体的比较中。以下是例子 几个列联表的常见赔率比和 两组分层后标准化风险差异的比较 通过一个协变量。所开发方法的最优性 将被调查并确定。似然方程式将是 派生的。新发展的极大似然和条件极大值 将对似然方法进行检查。这项研究已经延长了 以下列形式对若干列联表进行比较 估计和假设检验。这种方法论特别是 有助于检测病例对照中匹配的充分性 流行病学研究、生物医学研究、遗传学和其他 纪律。例如，测试哈代-温伯格定律 遗传学中的阶层和比较出生时的黑人和白人的差异 特定的婴儿死亡率曲线。常见赔率比的研究是 推广到整群抽样的情况，其中 集群不一定是独立的。理论和仿真 为了验证所提出的方法，进行了研究。渐近的 在以下情况下，已为估计量建立正态分布 地层数量变大，每一层的样本量为 有界的。已经为集群开发了一个方差估计器 取样。

This study will develop statistical methods for analyzing categorical data, particularly in the comparison of different groups. Examples are the common odds ratios for a number of contingency tables and the standardized risk difference in the comparison of two groups stratified by a covariate. The optimality properties of the developed methodology will be investigated and established. The likelihood equations are to be derived. The newly developed, maximum likelihood and conditional maximum likelihood methodologies are to be examined. The study has been extended to do a comparison of a number of contingency tables in the form of estimation and hypothesis testing. This methodology is particularly useful in detecting the adequacy of matching in the case-control epidemiological studies, biomedical studies, genetics and other disciplines. Examples include testing the Hardy-Weinberg Law across strata in genetics and comparing the black-white differences in birth specific infant mortality curves. The study of the common odds ratio is extended to the case under cluster sampling, where the units within a cluster are not necessarily independent. Theoretical and simulation studies are conducted to validate the proposed methodology. Asymptotic normality has been established for the estimator in the case when the number of strata becomes large and the sample sizes for each stratum are bounded. A variance estimator has been developed for the cluster sampling.