STATISTICAL INFERENCE FOR SPARSE CATEGORICAL DATA

与健康相关的科学中的数据通常是以绝对的尺度来衡量的。 显示此类数据的表通常很稀疏，观测值很少 在许多类别中。两个常见的原因是(1)研究可能有很小的 受试者的数量，由于成本、伦理或患者的可用性，或者 (2)对反应的重复测量可能会产生大量的 多维表格。建议的研究重点是开发 对于如此稀疏的数据的统计方法。 小样本分析：将开发精确和接近精确的方法 用于对绝对回答之间的关联做出推断。 新方法包括修改后的条件独立性测试，即 不像通常的那样保守；相应的可信区间 对于分层的2X2情况下的比数比效应 和往常一样。将进一步发展精确的统计推断，以 涉及有序的分类反应的关联和互动。 重复分类测量数据：方法将进一步发展 描述断然回答如何在不同场合和不同情况下发生变化 对协变量的取值，特别强调顺序响应 凯斯。待开发的模型包括参数模型和非参数模型 针对特定主题效果、潜伏类和混合体的模型版本 模型和边际分布模型。一个新开发的最大值 利用似然算法对一些难于处理的模型进行拟合 用标准方法处理。 模型将被应用于相关的生物医学问题。例如, 精确的方法对于比较治疗方法是有用的。 样本量小和大时的分类反应--样本 近似值是不可信的。特定于主题的模型非常有用 对于交叉研究中和在 描述随机临床试验中的时机效应，包括 在治疗周期开始和结束时进行观察。 潜在类别模型是评估评分者间可靠性的有用工具。

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.