A Debiased Estimator for the Mediation Functional in Ultra-High-Dimensional Setting in the Presence of Interaction Effects
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| Format: | Preprint |
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2024
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| _version_ | 1866913979468611584 |
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| author | Bo, Shi Ghassami, AmirEmad Mukherjee, Debarghya |
| author_facet | Bo, Shi Ghassami, AmirEmad Mukherjee, Debarghya |
| contents | Mediation analysis is a crucial tool for uncovering the mechanisms through which a treatment affects the outcome, providing deeper causal insights and guiding effective interventions. Despite advances in analyzing the mediation effect with fixed/low-dimensional mediators and covariates, our understanding of estimation and inference of mediation functional in the presence of (ultra)-high-dimensional mediators and covariates is still limited. In this paper, we present an estimator for mediation functional in a high-dimensional setting that accommodates the interaction between covariates and treatment in generating mediators, as well as interactions between both covariates and treatment and mediators and treatment in generating the response. We demonstrate that our estimator is $\sqrt{n}$-consistent and asymptotically normal, thus enabling reliable inference on direct and indirect treatment effects with asymptotically valid confidence intervals. A key technical contribution of our work is to develop a multi-step debiasing technique, which may also be valuable in other statistical settings with similar structural complexities where accurate estimation depends on debiasing. We evaluate our proposed methodology through extensive simulation studies and apply it to the TCGA lung cancer dataset to estimate the effect of smoking, mediated by DNA methylation, on the survival time of lung cancer patients. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Debiased Estimator for the Mediation Functional in Ultra-High-Dimensional Setting in the Presence of Interaction Effects Bo, Shi Ghassami, AmirEmad Mukherjee, Debarghya Methodology Statistics Theory Mediation analysis is a crucial tool for uncovering the mechanisms through which a treatment affects the outcome, providing deeper causal insights and guiding effective interventions. Despite advances in analyzing the mediation effect with fixed/low-dimensional mediators and covariates, our understanding of estimation and inference of mediation functional in the presence of (ultra)-high-dimensional mediators and covariates is still limited. In this paper, we present an estimator for mediation functional in a high-dimensional setting that accommodates the interaction between covariates and treatment in generating mediators, as well as interactions between both covariates and treatment and mediators and treatment in generating the response. We demonstrate that our estimator is $\sqrt{n}$-consistent and asymptotically normal, thus enabling reliable inference on direct and indirect treatment effects with asymptotically valid confidence intervals. A key technical contribution of our work is to develop a multi-step debiasing technique, which may also be valuable in other statistical settings with similar structural complexities where accurate estimation depends on debiasing. We evaluate our proposed methodology through extensive simulation studies and apply it to the TCGA lung cancer dataset to estimate the effect of smoking, mediated by DNA methylation, on the survival time of lung cancer patients. |
| title | A Debiased Estimator for the Mediation Functional in Ultra-High-Dimensional Setting in the Presence of Interaction Effects |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2412.08827 |