Group sequential BH and its adaptive versions controlling the FDR

• Published in: Journal of statistical planning and inference Vol. 199; pp. 219 - 235
• Main Authors: Sarkar, Sanat K., Chen, Aiying, He, Li, Guo, Wenge
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2019
• Subjects: Adaptive procedure; BH procedure; False discovery rate; Group sequential design; Multiple testing; Positive dependence; Adaptive procedure; False discovery rate; Group sequential design; Positive dependence; Multiple testing; BH procedure
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2018.07.001

This paper considers the problem of simultaneous testing of multiple hypotheses in a multi-stage group sequential setting subject to control over the false discovery rate (FDR). A multi-stage group sequential form of the BH procedure is developed, and a proof of its FDR control for p-values satisfying a positive dependence condition both between and within stages is given. This group sequential BH is adapted to the proportion of true nulls in two different ways, resulting in the proposal of two adaptive group sequential BH. While one of these adaptive procedures is theoretically shown to control its FDR when the p-values are positively dependent between but independent within stages, the other one’s FDR control is assessed through simulations. Comparative performance studies of the proposed procedures in terms of FDR control, power, and proportion of sample saved carried out through extensive simulations provide evidence of superior performance of the proposed adaptive procedures. •BH method is extended from single to multiple stages in a group sequential setting.•Error spending function is used to allocate a nominal level for the FDR control at each stage.•The group sequential BH controls FDR under positive dependence both within and between stages.•Two different adaptive versions of group sequential BH are given.