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Estimation of the optimal surrogate based on a randomized trial

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  • Brenda L. Price
  • Peter B. Gilbert
  • Mark J. van der Laan

Abstract

A common scientific problem is to determine a surrogate outcome for a long‐term outcome so that future randomized studies can restrict themselves to only collecting the surrogate outcome. We consider the setting that we observe n independent and identically distributed observations of a random variable consisting of baseline covariates, a treatment, a vector of candidate surrogate outcomes at an intermediate time point, and the final outcome of interest at a final time point. We assume the treatment is randomized, conditional on the baseline covariates. The goal is to use these data to learn a most‐promising surrogate for use in future trials for inference about a mean contrast treatment effect on the final outcome. We define an optimal surrogate for the current study as the function of the data generating distribution collected by the intermediate time point that satisfies the Prentice definition of a valid surrogate endpoint and that optimally predicts the final outcome: this optimal surrogate is an unknown parameter. We show that this optimal surrogate is a conditional mean and present super‐learner and targeted super‐learner based estimators, whose predicted outcomes are used as the surrogate in applications. We demonstrate a number of desirable properties of this optimal surrogate and its estimators, and study the methodology in simulations and an application to dengue vaccine efficacy trials.

Suggested Citation

  • Brenda L. Price & Peter B. Gilbert & Mark J. van der Laan, 2018. "Estimation of the optimal surrogate based on a randomized trial," Biometrics, The International Biometric Society, vol. 74(4), pages 1271-1281, December.
  • Handle: RePEc:bla:biomet:v:74:y:2018:i:4:p:1271-1281
    DOI: 10.1111/biom.12879
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    References listed on IDEAS

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    1. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    2. Marshall M. Joffe, 2013. "Discussion on “Surrogate Measures and Consistent Surrogates”," Biometrics, The International Biometric Society, vol. 69(3), pages 569-573, September.
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    Cited by:

    1. Guido Imbens & Nathan Kallus & Xiaojie Mao & Yuhao Wang, 2022. "Long-term Causal Inference Under Persistent Confounding via Data Combination," Papers 2202.07234, arXiv.org, revised Aug 2023.
    2. Layla Parast & Tianxi Cai & Lu Tian, 2023. "Testing for heterogeneity in the utility of a surrogate marker," Biometrics, The International Biometric Society, vol. 79(2), pages 799-810, June.
    3. Xuan Wang & Layla Parast & Larry Han & Lu Tian & Tianxi Cai, 2023. "Robust approach to combining multiple markers to improve surrogacy," Biometrics, The International Biometric Society, vol. 79(2), pages 788-798, June.
    4. Emily K. Roberts & Michael R. Elliott & Jeremy M. G. Taylor, 2023. "Solutions for surrogacy validation with longitudinal outcomes for a gene therapy," Biometrics, The International Biometric Society, vol. 79(3), pages 1840-1852, September.
    5. Layla Parast & Tianxi Cai & Lu Tian, 2021. "Evaluating multiple surrogate markers with censored data," Biometrics, The International Biometric Society, vol. 77(4), pages 1315-1327, December.

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