Collaborative Research: Detecting false discoveries under dependence using mixtures

多个测试问题的统计分析围绕着同时测试产生的p值集合的分布。来自fMRI、蛋白质组学、微阵列和其他生物医学实验的数据显示出p值之间的依赖性。如果在估计错误发现率等错误控制措施时不考虑这种依赖性，统计推断会得出生物学上不相关的结论。该提案描绘了一个面向模型的方法，多个假设检验的灵活和准确的建模的联合分布的p值在依赖的情况下，使用混合物。另一个理论目标是研究偏态混合模型的性质。通过将依赖性纳入p值模型，拟议的研究提供了对错误发现的有效控制，特别是在复杂的生物医学应用中。多假设检验是科学家有效分析大规模复杂生物医学数据（如基因表达数据、蛋白质组数据或脑成像数据）的主要统计工具之一。在这种生物医学应用中的疾病关联研究需要同时测试数千个基因或蛋白质或大脑区域的关联的显著性。将一个基因或一种蛋白质鉴定为与给定疾病潜在相关的基因或蛋白质被称为发现。然而，在大规模的生物医学研究中，存在通过做出太多错误发现而积累错误的风险。拟议的研究通过提供大规模疾病关联研究中错误率的准确估计，极大地影响了生物医学应用中的统计实践。研究人员专门为自闭症患者的MRI研究中的脑成像应用开发了错误控制机制。 该项目以研究生教育和培训的形式影响人力资源开发。

Statistical analysis of multiple testing problems revolves around the distribution of the collection of p-values arising from simultaneous tests. Data from fMRI, Proteomics, Microarray and other biomedical experiments exhibit dependence among p-values. Statistical inference yields biologically irrelevant conclusions if such dependence is not taken into consideration while estimating error control measures such as the false discovery rate. This proposal delineates a model oriented approach to multiple hypotheses testing by flexible and accurate modeling of the joint distribution of the p-values in dependent situations using mixtures. An additional theoretical goal the investigators study properties of skew-mixture models. By incorporating dependence in the model for the p-values, the proposed research provides valid controls of false discoveries, especially in complex biomedical applications. The proposed methodologies provide a foundation for statistical analysis in large dependent multiple testing situations and will spawn new research in the area of false discovery control.Multiple hypothesis testing is one of the primary statistical tools available to the scientists for efficiently analyzing large-scale complex biomedical data such as gene-expression data, protemics data or brain imaging data. Disease association studies in such biomedical applications require testing significance of association of several thousand genes or proteins or brain regions, simultaneously. Identification of a gene or a protein as being potentially associated with a given disease is called a discovery. However, in large scale biomedical studies there is a risk of accumulating error via making too many false discoveries. The proposed research substantially influences the practice of statistics in biomedical applications by providing accurate estimates of error rates in large scale disease association studies. The investigators specifically develop error control mechanism for brain imaging applications in MRI studies of autistic patients. The project impacts human resource development in the form of graduate student education and training.