IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v79y2023i2p788-798.html
   My bibliography  Save this article

Robust approach to combining multiple markers to improve surrogacy

Author

Listed:
  • Xuan Wang
  • Layla Parast
  • Larry Han
  • Lu Tian
  • Tianxi Cai

Abstract

Identifying effective and valid surrogate markers to make inference about a treatment effect on long‐term outcomes is an important step in improving the efficiency of clinical trials. Replacing a long‐term outcome with short‐term and/or cheaper surrogate markers can potentially shorten study duration and reduce trial costs. There is sizable statistical literature on methods to quantify the effectiveness of a single surrogate marker. Both parametric and nonparametric approaches have been well developed for different outcome types. However, when there are multiple markers available, methods for combining markers to construct a composite marker with improved surrogacy remain limited. In this paper, building on top of the optimal transformation framework of Wang et al. (2020), we propose a novel calibrated model fusion approach to optimally combine multiple markers to improve surrogacy. Specifically, we obtain two initial estimates of optimal composite scores of the markers based on two sets of models with one set approximating the underlying data distribution and the other directly approximating the optimal transformation function. We then estimate an optimal calibrated combination of the two estimated scores which ensures both validity of the final combined score and optimality with respect to the proportion of treatment effect explained by the final combined score. This approach is unique in that it identifies an optimal combination of the multiple surrogates without strictly relying on parametric assumptions while borrowing modeling strategies to avoid fully nonparametric estimation which is subject to the curse of dimensionality. Our identified optimal transformation can also be used to directly quantify the surrogacy of this identified combined score. Theoretical properties of the proposed estimators are derived, and the finite sample performance of the proposed method is evaluated through simulation studies. We further illustrate the proposed method using data from the Diabetes Prevention Program study.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:788-798
    DOI: 10.1111/biom.13677
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13677
    Download Restriction: no

    File URL: https://libkey.io/10.1111/biom.13677?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ying Huang & Peter B. Gilbert, 2011. "Comparing Biomarkers as Principal Surrogate Endpoints," Biometrics, The International Biometric Society, vol. 67(4), pages 1442-1451, December.
    2. 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.
    3. 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.
    4. Susan Athey & Raj Chetty & Guido W. Imbens & Hyunseung Kang, 2019. "The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely," NBER Working Papers 26463, National Bureau of Economic Research, Inc.
    5. Min Zhang & Anastasios A. Tsiatis & Marie Davidian, 2008. "Improving Efficiency of Inferences in Randomized Clinical Trials Using Auxiliary Covariates," Biometrics, The International Biometric Society, vol. 64(3), pages 707-715, September.
    6. Marshall M. Joffe & Tom Greene, 2009. "Related Causal Frameworks for Surrogate Outcomes," Biometrics, The International Biometric Society, vol. 65(2), pages 530-538, June.
    7. John P. Klein & Per Kragh Andersen, 2005. "Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function," Biometrics, The International Biometric Society, vol. 61(1), pages 223-229, March.
    8. Tyler J. VanderWeele, 2013. "Surrogate Measures and Consistent Surrogates," Biometrics, The International Biometric Society, vol. 69(3), pages 561-565, September.
    9. Jane Xu & Scott L. Zeger, 2001. "The Evaluation of Multiple Surrogate Endpoints," Biometrics, The International Biometric Society, vol. 57(1), pages 81-87, March.
    10. Yue Wang & Jeremy M. G. Taylor, 2002. "A Measure of the Proportion of Treatment Effect Explained by a Surrogate Marker," Biometrics, The International Biometric Society, vol. 58(4), pages 803-812, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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 2024.
    4. Denis Agniel & Layla Parast, 2021. "Evaluation of longitudinal surrogate markers," Biometrics, The International Biometric Society, vol. 77(2), pages 477-489, June.
    5. Zhichao Jiang & Peng Ding & Zhi Geng, 2016. "Principal causal effect identification and surrogate end point evaluation by multiple trials," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 829-848, September.
    6. Ying Huang & Shibasish Dasgupta, 2019. "Likelihood-Based Methods for Assessing Principal Surrogate Endpoints in Vaccine Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 504-523, December.
    7. Gilbert Peter B. & Blette Bryan S. & Hudgens Michael G. & Shepherd Bryan E., 2020. "Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 54-69, January.
    8. Michael J. Martens & Brent R. Logan, 2020. "Group sequential tests for treatment effect on survival and cumulative incidence at a fixed time point," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 603-623, July.
    9. Gilbert Peter B. & Gabriel Erin E. & Huang Ying & Chan Ivan S.F., 2015. "Surrogate Endpoint Evaluation: Principal Stratification Criteria and the Prentice Definition," Journal of Causal Inference, De Gruyter, vol. 3(2), pages 157-175, September.
    10. Fatema Shafie Khorassani & Jeremy M. G. Taylor & Niko Kaciroti & Michael R. Elliott, 2023. "Incorporating Covariates into Measures of Surrogate Paradox Risk," Stats, MDPI, vol. 6(1), pages 1-23, February.
    11. Manabu Kuroki, 2016. "The Identification of Direct and Indirect Effects in Studies with an Unmeasured Intermediate Variable," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 228-245, March.
    12. 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.
    13. Shan Huang & Chen Wang & Yuan Yuan & Jinglong Zhao & Jingjing Zhang, 2023. "Estimating Effects of Long-Term Treatments," Papers 2308.08152, arXiv.org.
    14. Tyler J. VanderWeele, 2013. "Surrogate Measures and Consistent Surrogates," Biometrics, The International Biometric Society, vol. 69(3), pages 561-565, September.
    15. Ying Huang & Peter B. Gilbert & Julian Wolfson, 2013. "Design and Estimation for Evaluating Principal Surrogate Markers in Vaccine Trials," Biometrics, The International Biometric Society, vol. 69(2), pages 301-309, June.
    16. Gilbert Peter B. & Blette Bryan S. & Shepherd Bryan E. & Hudgens Michael G., 2020. "Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 54-69, January.
    17. Ying Huang, 2018. "Evaluating principal surrogate markers in vaccine trials in the presence of multiphase sampling," Biometrics, The International Biometric Society, vol. 74(1), pages 27-39, March.
    18. Layla Parast & Tanya P. Garcia & Ross L. Prentice & Raymond J. Carroll, 2022. "Robust methods to correct for measurement error when evaluating a surrogate marker," Biometrics, The International Biometric Society, vol. 78(1), pages 9-23, March.
    19. Yechan Park & Yuya Sasaki, 2024. "A Bracketing Relationship for Long-Term Policy Evaluation with Combined Experimental and Observational Data," Papers 2401.12050, arXiv.org.
    20. Rui Zhuang & Ying Qing Chen, 2020. "Measuring Surrogacy in Clinical Research," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 295-323, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:788-798. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.