Negative control is a common technique in scientific investigations and broadly refers to the situation where a null effect (''negative result'') is expected. Motivated by a real proteomic dataset, we will present three promising and closely connected methods of using negative controls to assist simultaneous hypothesis testing. The first method uses negative controls to construct a permutation p-value for every hypothesis under investigation, and we give several sufficient conditions for such p-values to be valid and positive regression dependent on the set (PRDS) of true nulls. The second method uses negative controls to construct an estimate of the false discovery rate (FDR), and we give a sufficient condition under which the step-up procedure based on this estimate controls the FDR. The third method, derived from an existing ad hoc algorithm for proteomic analysis, uses negative controls to construct a nonparametric estimator of the local false discovery rate. We conclude with some practical suggestions and connections to some closely related methods that are propsed recently.
翻译:负对照是科学研究中常用的技术,广泛地指期望出现零效应(“负面结果”)的情况。本文以一个真实的蛋白质组学数据集为背景,提出了三种利用负对照协助同时进行假设检验的方法。第一种方法使用负对照构建每个正在研究的假设的置换p值,并给出了几个足够条件,使得这些p值在真实的零假设的集合上为有效的且是PRDS(正的回归依赖于集合)的。第二种方法使用负对照构建错误发现率(FDR)的估计,并给出了一个足够条件,使基于这个估计的逐步过程控制FDR。第三种方法是从一个用于蛋白质组学分析的现有的专利算法中得出的,利用负对照构建局部错误发现率的非参数估计。文章最后提出了一些实用建议,并与最近提出的一些相关方法进行了联系。