STATISTICAL INFERENCE SPARSE ORDERED CATEGORICAL DATA

健康相关科学中的许多变量都是在有序的基础上进行测量的 绝对的天平。显示此类数据的联想表通常是 稀疏，在表格的许多单元格中几乎没有观测。两个常见的 原因是(1)一项研究的局限性需要小样本 大小，或(2)重复测量受试者在几个 意外事件会导致具有大量单元格的多维表。 拟议的研究重点是发展统计方法，以 这两种情况。将开发出精确的方法来制作 关于治疗和反应之间的关联的推断，调整 寻找相关的协变量。 小样本分析：有序分类的精确统计检验 对于有条件独立的假设，我们将做出回应 没有三个因素的相互作用。非空推论，如Exact 还将制定序数奇数比率的可信区间。这个 方法将连接到最近开发的对数线性模型和对数模型 对于序号数据。 重复分类测量分析：将进行两种类型的分析 考虑过了。一种类型的模型是响应的边际分布 根据协变量的值在不同的场合有所不同。另一个 类型对重复响应之间的依赖关系进行建模。特别关注 将致力于建模评分者之间的协议，这是一个重要的问题时 几位医生在分类的尺度上进行主观评估， 使用相同的样本。对于这两种分析类型，半参数方法 将被开发来处理传统的最大似然法 方法是笨拙的或不可行的。

Many variables in health-related sciences are measured on ordered categorical scales. Contingency tables that display such data are often sparse, having few observations in many cells of the table. Two common reasons for this are (1) constraints of a study necessitate a small sample size, or (2) repeated measurement of responses for subjects at several occasions results in a multidimensional table with a large number of cells. The proposed research focuses on developing statistical methodology for these two situations. Exact methods will be developed for making inferences about the association between treatment and response, adjusting for relevant covariates. Small-sample analyses: Exact statistical tests for an ordered categorical response will be developed for the hypotheses of conditional independence and no three-factor interaction. Non-null inferences, such as exact confidence intervals for ordinal odd ratios, will also be developed. The methods will be connected to recently developed loglinear and logit models for ordinal data. Repeated categorical measurement analyses: Two types of analyses will be considered. One type models how marginal distributions of the response vary across occasions and according to values of covariates. The other type models the dependence among repeated responses. Special attention will be given to modeling inter-rater agreement, an important problem when several physicians make subjective evaluations on a categorical scale, using the same sample. For both types of analyses, semi-parametric methods will be developed to handle cases in which traditional maximum likelihood approaches are awkward or infeasible.