STATISTICAL INFERENCE FOR SPARSE CATEGORICAL DATA

与健康有关的科学数据往往是按分类尺度衡量的。 显示这些数据的表通常是稀疏的，只有很少的观测值 在许多类别中。 两个常见的原因是（1）研究可能有一个小 受试者数量，由于成本、伦理或患者可用性，或 (2)对响应的重复测量可能会产生较大的 多维表 研究重点是开发 这种稀疏数据的统计方法。 小样本分析：将开发精确和接近精确的方法 来推断分类反应之间的关联。 新的方法包括修改后的条件独立性测试， 比通常的保守性小;相应的置信区间 对于分层2X2情况下的比值比效应， 普通的一 精确的统计推断将进一步发展， 涉及有序分类反应的关联和相互作用。 重复分类测量数据：将进一步开发方法 描述分类反应如何在不同场合和根据 协变量的值，特别强调顺序响应 案子 拟开发的模型包括参数模型和非参数模型 针对特定受试者效应、潜在类别和混合的模型版本 模型和边际分布模型。 新开发的最大 似然算法将被用来拟合一些模型，是笨拙的 用标准的方法来处理。 模型将应用于相关的生物医学问题。 比如说， 精确的方法是有用的，使治疗的比较， 小样本和大样本时的分类响应 近似值是不可信的。 主题特定的模型是有用的 用于交叉研究和 描述随机临床试验中的场合效应， 在治疗期开始和结束时进行观察。 潜在类别模型是评估评分者间信度的有用工具。

Data in health-related sciences are often measured on categorical scales. Tables that display such data are often sparse, having few observations in many categories. Two common reason are (1) the study may have a small number of subjects, because of cost, ethics, or patient availability, or (2) repeated measurement of responses may produce a large multidimensional table. The proposed research focuses on developing statistical methodology for such sparse data. Small-sample analyses: Exact and nearly exact methods will be developed for making inferences about associations between categorical responses. New methods include a modified test of conditional independence that is less conservative than the usual one; a corresponding confidence interval for an odds ratio effect in the stratified 2X2 case in narrower than the usual one. Exact statistical inference will be further developed for associations and interactions involving ordered categorical responses. Repeated categorical measurement data: Methods will be further developed to describe how categorical response vary across occasions and according to values of covariates, with special emphasis on the ordinal-response case. Models to be developed include parametric and non-parametric versions of models for subject-specific effects, latent class and mixture models, and models for marginal distributions. A newly developed maximum likelihood algorithm will be utilized to fit some models that are awkward to handle with standard methods. Models will be applied to relevant biomedical problems. For instance, exact methods are useful for making comparison of treatment on a categorical response when the sample size is small and large-sample approximations are untrustworthy. The subject-specific models are useful for subjects-wise comparisons of treatments in cross-over studies and in describing occasion effects in randomized clinical trials that involve making observations at the beginning and end of a treatment period. Latent class models are useful assessing inter-rater reliability.