Testing high-dimensional mediation effect with arbitrary exposure–mediator coefficients

Yinan Lin (), Zijian Guo (), Baoluo Sun () and Zhenhua Lin ()
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Yinan Lin: Chongqing Normal University
Zijian Guo: Rutgers University
Baoluo Sun: National University of Singapore
Zhenhua Lin: National University of Singapore

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 34, issue 3, No 2, 530-579

Abstract: Abstract In response to the unique challenge created by high-dimensional mediators in mediation analysis, this paper presents a novel procedure for testing the nullity of the mediation effect in the presence of high-dimensional mediators. The procedure incorporates two distinct features. Firstly, the test remains valid under all cases of the composite null hypothesis, including the challenging scenario where both exposure–mediator and mediator–outcome coefficients are zero. Secondly, it does not impose structural assumptions on the exposure–mediator coefficients, thereby allowing for an arbitrarily strong exposure–mediator relationship. To the best of our knowledge, the proposed test is the first of its kind to provably possess these two features in high-dimensional mediation analysis. The validity and consistency of the proposed test are established, and its numerical performance is showcased through simulation studies. The application of the proposed test is demonstrated by examining the mediation effect of DNA methylation between smoking status and lung cancer development.

Keywords: High-dimensional inference; Bias correction; Mediation analysis; Composite hypothesis; Super-efficiency; 62F03 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11749-025-00971-z

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