Adaptive linear step-up procedures that control the false discovery rate
控制错误发现率的自适应线性逐步上升程序AI 解读 ↓
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控制错误发现率的自适应线性逐步上升程序
- 研究问题
- 当部分零假设不成立时，如何估计真实零假设数量并调整多重检验水平，在提高检验能力的同时维持错误发现率控制？
- 方法与思路
- 作者提出两阶段程序：先用线性逐步上升检验估计真实零假设数量，再调整第二阶段水平，并分析及模拟不同方案。
- 材料陈述的贡献
- 摘要称证明一般形式两阶段程序的错误发现率控制，模拟显示检验能力改善，并在所研究正依赖设定中比较各方案的控制表现。
- 阅读关注点
- 应核对两阶段水平的具体规则、控制定理的独立性或依赖条件，以及正依赖部分哪些结论属于理论、哪些来自模拟。
- 阅读边界
- 所给材料为版本未注明的 OpenAlex 索引摘要；不能把原程序在正依赖下的保证直接移用于所有自适应变体，也不能外推所考察设定。
原文摘要
The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in which the linear step-up procedure is used in stage one to estimate m0, providing a new level q′ which is used in the linear step-up procedure in the second stage. We prove that a general form of the two-stage procedure controls the false discovery rate at the desired level q. This framework enables us to study analytically the properties of other procedures that exist in the literature. A simulation study is presented that shows that two-stage adaptive procedures improve in power over the original procedure, mainly because they provide tighter control of the false discovery rate. We further study the performance of the current suggestions, some variations of the procedures, and previous suggestions, in the case where the test statistics are positively dependent, a case for which the original procedure controls the false discovery rate. In the setting studied here the newly proposed two-stage procedure is the only one that controls the false discovery rate. The procedures are illustrated with two examples of biological importance.