<p>Detecting the absence of the mediation effect is a major focus of mediation analysis. When treatment does not influence mediators that do not affect the outcome either, testing the natural indirect effect is an interesting issue, since the asymptotic distributions of existing test statistics vary under different sub-null hypotheses. This paper introduces a novel statistical inference procedure tailored for high-dimensional mediation structures to address the issue of test conservativeness under some nontrivial sub-null hypotheses. We first suggest a procedure using a partial penalized least squares estimation and compute the inner product of the treatment-mediator and the mediator-outcome coefficients. Based on the product, we develop a Wald-type test to handle the case where the mediators affect the outcome. When the mediators do not affect the outcome, the Wald-type test statistic fails to maintain the significance level. We then construct another test for the significance level maintenance. The final test is an adaptive-to-sub-null hybrid of the two tests, which can flexibly accommodate different sub-null hypotheses and ensures that the limiting null distributions converge to a common Chi-square distribution uniformly across all sub-null hypotheses. Numerical studies are conducted to assess the finite-sample performances of the proposed test and make comparisons with existing methodologies.</p>

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An adaptive test for natural indirect effect in large-dimensional mediation analysis

  • Feng Liang,
  • Zhong Wang,
  • Lixing Zhu

摘要

Detecting the absence of the mediation effect is a major focus of mediation analysis. When treatment does not influence mediators that do not affect the outcome either, testing the natural indirect effect is an interesting issue, since the asymptotic distributions of existing test statistics vary under different sub-null hypotheses. This paper introduces a novel statistical inference procedure tailored for high-dimensional mediation structures to address the issue of test conservativeness under some nontrivial sub-null hypotheses. We first suggest a procedure using a partial penalized least squares estimation and compute the inner product of the treatment-mediator and the mediator-outcome coefficients. Based on the product, we develop a Wald-type test to handle the case where the mediators affect the outcome. When the mediators do not affect the outcome, the Wald-type test statistic fails to maintain the significance level. We then construct another test for the significance level maintenance. The final test is an adaptive-to-sub-null hybrid of the two tests, which can flexibly accommodate different sub-null hypotheses and ensures that the limiting null distributions converge to a common Chi-square distribution uniformly across all sub-null hypotheses. Numerical studies are conducted to assess the finite-sample performances of the proposed test and make comparisons with existing methodologies.