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A machine learning-based approach for estimating and testing associations with multivariate outcomes

Author

Listed:
  • Benkeser David

    (Emory University, School of Public Health, Atlanta, 30322, USA)

  • Mertens Andrew

    (Department of Epidemiology, University of California, Berkeley, Berkeley, USA)

  • Colford John M.

    (Department of Epidemiology, University of California, Berkeley, Berkeley, USA)

  • Hubbard Alan

    (Department of Biostatistics, University of California, Berkeley, Berkeley, USA)

  • Arnold Benjamin F.

    (Francis I. Proctor Foundation, University of California, San Fransisco, USA)

  • Stein Aryeh

    (Hubert Department of Global Health, Emory University Rollins School of Public Health, Atlanta, USA)

  • van der Laan Mark J.

    (Department of Biostatistics, University of California, Berkeley, Berkeley, USA)

Abstract

We propose a method for summarizing the strength of association between a set of variables and a multivariate outcome. Classical summary measures are appropriate when linear relationships exist between covariates and outcomes, while our approach provides an alternative that is useful in situations where complex relationships may be present. We utilize machine learning to detect nonlinear relationships and covariate interactions and propose a measure of association that captures these relationships. A hypothesis test about the proposed associative measure can be used to test the strong null hypothesis of no association between a set of variables and a multivariate outcome. Simulations demonstrate that this hypothesis test has greater power than existing methods against alternatives where covariates have nonlinear relationships with outcomes. We additionally propose measures of variable importance for groups of variables, which summarize each groups’ association with the outcome. We demonstrate our methodology using data from a birth cohort study on childhood health and nutrition in the Philippines.

Suggested Citation

  • Benkeser David & Mertens Andrew & Colford John M. & Hubbard Alan & Arnold Benjamin F. & Stein Aryeh & van der Laan Mark J., 2021. "A machine learning-based approach for estimating and testing associations with multivariate outcomes," The International Journal of Biostatistics, De Gruyter, vol. 17(1), pages 7-21, May.
    • Handle: RePEc:bpj:ijbist:v:17:y:2021:i:1:p:7-21:n:7
    DOI: 10.1515/ijb-2019-0061
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    References listed on IDEAS

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    1. van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
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