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- W4294175144 abstract "We discuss several approaches to defining power in studies designed around the Benjamini-Hochberg (BH) false discovery rate (FDR) procedure. We focus primarily on the textit{average power} and the $lambda$-textit{power}, which are the expected true positive fraction and the probability that the true positive fraction exceeds $lambda$, respectively. We prove results concerning strong consistency and asymptotic normality for the positive call fraction (PCF), the true positive fraction (TPF) and false discovery fraction (FDF). Convergence of their corresponding expected values, including a convergence result for the average power, follow as a corollaries. After reviewing what is known about convergence in distribution of the errors of the plugin procedure, (Genovese, 2004), we prove central limit theorems for fully empirical versions of the PCF, TPF, and FDF, using a result for stopped stochastic processes. The central limit theorem (CLT) for the TPF is used to obtain an approximate expression for the $lambda$-power, while the CLT for the FDF is used to introduce an approximate procedure for determining a suitably small nominal FDR that results in a speicified bound on the FDF with stipulated high probability. The paper also contains the results of a large simulation study covering a fairly substantial portion of the space of possible inputs encountered in application of the results in the design of a biomarker study, a micro-array experiment and a GWAS study." @default.
- W4294175144 created "2022-09-02" @default.
- W4294175144 creator A5003906407 @default.
- W4294175144 date "2018-01-11" @default.
- W4294175144 modified "2023-10-14" @default.
- W4294175144 title "Average Power and $lambda$-power in Multiple Testing Scenarios when the Benjamini-Hochberg False Discovery Rate Procedure is Used" @default.
- W4294175144 doi "https://doi.org/10.48550/arxiv.1801.03989" @default.
- W4294175144 hasPublicationYear "2018" @default.
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