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Multiple Testing in a Two-Stage Adaptive Design With Combination Tests Controlling FDR

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  • Sanat K. Sarkar
  • Jingjing Chen
  • Wenge Guo

Abstract

Testing multiple null hypotheses in two stages to decide which of these can be rejected or accepted at the first stage and which should be followed up for further testing having had additional observations is of importance in many scientific studies. We develop two procedures, each with two different combination functions, Fisher's and Simes', to combine p -values from two stages, given prespecified boundaries on the first-stage p -values in terms of the false discovery rate (FDR) and controlling the overall FDR at a desired level. The FDR control is proved when the pairs of first- and second-stage p -values are independent and those corresponding to the null hypotheses are identically distributed as a pair ( p 1 , p 2 ) satisfying the p -clud property. We did simulations to show that (1) our two-stage procedures can have significant power improvements over the first-stage Benjamini--Hochberg (BH) procedure compared to the improvement offered by the ideal BH procedure that one would have used had the second stage data been available for all the hypotheses, and can continue to control the FDR under some dependence situations, and (2) can offer considerable cost savings compared to the ideal BH procedure. The procedures are illustrated through a real gene expression data. Supplementary materials for this article are available online.

Suggested Citation

  • Sanat K. Sarkar & Jingjing Chen & Wenge Guo, 2013. "Multiple Testing in a Two-Stage Adaptive Design With Combination Tests Controlling FDR," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1385-1401, December.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1385-1401
    DOI: 10.1080/01621459.2013.835662
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    References listed on IDEAS

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    1. Posch, Martin & Zehetmayer, Sonja & Bauer, Peter, 2009. "Hunting for Significance With the False Discovery Rate," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 832-840.
    2. Brannath W. & Posch M. & Bauer P., 2002. "Recursive Combination Tests," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 236-244, March.
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    Cited by:

    1. Ron Berman & Christophe Van den Bulte, 2022. "False Discovery in A/B Testing," Management Science, INFORMS, vol. 68(9), pages 6762-6782, September.
    2. Yi-Hui Zhou & Paul Brooks & Xiaoshan Wang, 2018. "A Two-Stage Hidden Markov Model Design for Biomarker Detection, with Application to Microbiome Research," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 41-58, April.

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