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

本研究将开发统计方法，用于分析分类 数据，特别是不同群体的比较。 实例是 一些列联表的常见比值比和 两组分层比较的标准化风险差 一个covariant。 所开发方法的最优性 将进行调查和建立。 似然方程为 推导 最新发展的最大似然和条件最大似然 将审查可能性方法。 这项研究已经扩展到 对一些列联表进行比较， 估计和假设检验。 这种方法尤其 用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 学科 例子包括测试哈代-温伯格定律， 在遗传学和比较黑人和白人的出生差异 具体的婴儿死亡率曲线 常见优势比的研究是 扩展到整群抽样下的情况，其中a 集群不一定是独立的。 理论和仿真 进行研究以验证所提出的方法。 渐近 在以下情况下，已为估计量建立了正态性： 分层数量变大，每个分层的样本量 有界 一个方差估计已开发的集群 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.