Mathematical Methods for Small--Sample Biostatistical Inference

小样本生物统计推断的数学方法

• 批准号: 0505499
• 负责人: John Kolassa
• 金额: --
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505499&HistoricalAwards=false
• 关键词: Mathematical; Methods; Small; Sample; Biostatistical

The investigator applies various mathematical methodsto extend the range of application of saddlepointapproximation techniques and exact enumeration techniquesin statistical inference. These techniques are applied tomulti-dimensional conditional inference, achieved primarilyby developing new approximations to multivariate tailprobabilities for some component of a vector of sufficientstatistics conditional on the remaining components, andmethods for calculating these tail probabilities exactly.Particular attention is paid to probability modelswhose sufficient statistics have lattice distributions,since standard asymptotic techniques frequently failin this context. These models, including logistic andPoisson regression and contingency table models, arevery frequently used in applied biostatistical work.Specifically, this research includes the applicationof multidimensional saddlepoint approximations toorder--restricted hypotheses. It extends existingApproximations applicable to continuous distributions togeneral non-lattice distributions. It develops guidelinesfor tuning approximate conditional inferential methods toobtain higher power. Computational algorithms developedas part of this work are publicly available.Many current statistical techniques rely on mathematical approximations;the accuracy of these approximations ranges from very good to inadequate.This research involves approximations known to be almost always of highaccuracy, and applies them in some statistical contexts that are widelyused by scientists in a variety of disciplines. This research allowsinvestigators to draw valid conclusions from smaller data sets,particularly in cases when important research questions are phrased in termsof a number of quantities that must be accounted for. This situation occurs in a wide range of areas, from finance to political science to medicine.For example, a new medical therapy might be expected to lead to improvements,potentially measured in a number of ways. The investigator wishes todemonstrate that individuals receiving the new therapy at least as well according to all of the potential measures, and better on at least onemeasure, than do patients on the original therapy. Standard statisticalmethods do not handle such situations in an efficient way; the currentresearch represents a significant improvement.

研究者应用各种数学方法来扩展鞍点近似技术和精确枚举技术在统计推断中的应用范围。 这些技术应用于多维条件推理，主要是通过开发新的多元尾部概率近似值来实现，该近似值对于足够统计量向量的某些分量以剩余分量为条件，以及精确计算这些尾部概率的方法。特别关注其足够统计量具有格子分布的概率模型，因为标准渐近技术经常在这方面失败。 语境。 这些模型，包括逻辑回归和泊松回归以及列联表模型，在应用生物统计工作中非常频繁地使用。具体来说，本研究包括多维鞍点近似在有序限制假设中的应用。 它将适用于连续分布的现有近似扩展到一般非格分布。 它制定了调整近似条件推理方法以获得更高功效的指南。 作为这项工作的一部分开发的计算算法是公开可用的。许多当前的统计技术依赖于数学近似；这些近似的准确性从非常好到不足不等。这项研究涉及已知几乎总是高精度的近似，并将它们应用于一些被各个学科的科学家广泛使用的统计环境中。 这项研究使研究人员能够从较小的数据集中得出有效的结论，特别是在重要的研究问题以必须考虑的许多数量来表达的情况下。 这种情况发生在从金融到政治学再到医学的广泛领域。例如，一种新的医学疗法可能有望带来改善，这可以通过多种方式来衡量。 研究者希望证明接受新疗法的个体在所有可能的衡量标准上至少与接受原始疗法的患者一样好，并且至少在一项衡量标准上更好。 标准统计方法无法有效处理此类情况；目前的研究取得了显着的进步。