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High dimensional mediation analysis with latent variables

Author

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  • Andriy Derkach
  • Ruth M. Pfeiffer
  • Ting‐Huei Chen
  • Joshua N. Sampson

Abstract

We propose a model for high dimensional mediation analysis that includes latent variables. We describe our model in the context of an epidemiologic study for incident breast cancer with one exposure and a large number of biomarkers (i.e., potential mediators). We assume that the exposure directly influences a group of latent, or unmeasured, factors which are associated with both the outcome and a subset of the biomarkers. The biomarkers associated with the latent factors linking the exposure to the outcome are considered “mediators.” We derive the likelihood for this model and develop an expectation‐maximization algorithm to maximize an L1‐penalized version of this likelihood to limit the number of factors and associated biomarkers. We show that the resulting estimates are consistent and that the estimates of the nonzero parameters have an asymptotically normal distribution. In simulations, procedures based on this new model can have significantly higher power for detecting the mediating biomarkers compared with the simpler approaches. We apply our method to a study that evaluates the relationship between body mass index, 481 metabolic measurements, and estrogen‐receptor positive breast cancer.

Suggested Citation

  • Andriy Derkach & Ruth M. Pfeiffer & Ting‐Huei Chen & Joshua N. Sampson, 2019. "High dimensional mediation analysis with latent variables," Biometrics, The International Biometric Society, vol. 75(3), pages 745-756, September.
    • Handle: RePEc:bla:biomet:v:75:y:2019:i:3:p:745-756
    DOI: 10.1111/biom.13053
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    Cited by:

    1. Meng An & Haixiang Zhang, 2023. "High-Dimensional Mediation Analysis for Time-to-Event Outcomes with Additive Hazards Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    2. Lola Etiévant & Vivian Viallon, 2022. "On some limitations of probabilistic models for dimension‐reduction: Illustration in the case of probabilistic formulations of partial least squares," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(3), pages 331-346, August.
    3. Yanyi Song & Xiang Zhou & Min Zhang & Wei Zhao & Yongmei Liu & Sharon L. R. Kardia & Ana V. Diez Roux & Belinda L. Needham & Jennifer A. Smith & Bhramar Mukherjee, 2020. "Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies," Biometrics, The International Biometric Society, vol. 76(3), pages 700-710, September.

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