March 2024 Using simultaneous regression calibration to study the effect of multiple error-prone exposures on disease risk utilizing biomarkers developed from a controlled feeding study
Yiwen Zhang, Ran Dai, Ying Huang, Ross Prentice, Cheng Zheng
Author Affiliations +
Ann. Appl. Stat. 18(1): 125-143 (March 2024). DOI: 10.1214/23-AOAS1782


Systematic measurement error in self-reported data creates important challenges in association studies between dietary intakes and chronic disease risks, especially when multiple dietary components are studied jointly. The joint regression calibration method has been developed for measurement error correction when objectively measured biomarkers are available for all dietary components of interest. Unfortunately, objectively measured biomarkers are only available for very few dietary components, which limits the application of the joint regression calibration method. Recently, for single dietary components, controlled feeding studies have been performed to develop new biomarkers for many more dietary components. However, it is unclear whether the biomarkers separately developed for single dietary components are valid for joint calibration. In this paper we show that biomarkers developed for single dietary components cannot be used for joint regression calibration. We propose new methods to utilize controlled feeding studies to develop valid biomarkers for joint regression calibration to estimate the association between multiple dietary components simultaneously with the disease of interest. Asymptotic distribution theory for the proposed estimators is derived. Extensive simulations are performed to study the finite sample performance of the proposed estimators. We apply our methods to examine the joint effects of sodium and potassium intakes on cardiovascular disease incidence using the Women’s Health Initiative cohort data. We identify positive associations between sodium intake and cardiovascular diseases as well as negative associations between potassium intake and cardiovascular disease.

Funding Statement

This work was supported in part by grant R01 CA119171 from the U.S. National Cancer Institute and R01 GM106177 and U54 GM115458 from the National Institute of General Medical Sciences.
The WHI programs are funded by the National Heart, Lung, and Blood Institute, National Institutes of Health, U.S. Department of Health and Human Services through contracts, HHSN268201600018C, HHSN268201600001C, HHSN268201600002C, HHSN268201600003C, and HHSN268201600004C.


The authors acknowledge the following investigators in the Women’s Health Initiative (WHI) Program: Program Office: Jacques E. Rossouw, Shari Ludlam, Dale Burwen, Joan McGowan, Leslie Ford, and Nancy Geller, National Heart, Lung, and Blood Institute, Bethesda, Maryland; Clinical Coordinating Center, Women’s Health Initiative Clinical Coordinating Center: Garnet L. Anderson, Ross L. Prentice, Andrea Z. LaCroix, and Charles L. Kooperberg, Public Health Sciences, Fred Hutchinson Cancer Research Center, Seattle, Washington; Investigators and Academic Centers: JoAnn E. Manson, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts; Barbara V. Howard, MedStar Health Research Institute/Howard University, Washington, DC; Marcia L. Stefanick, Stanford Prevention Research Center, Stanford, California; Rebecca Jackson, The Ohio State University, Columbus, Ohio; Cynthia A. Thomson, University of Arizona, Tucson/Phoenix, Arizona; Jean Wactawski-Wende, University at Buffalo, Buffalo, New York; Marian C. Limacher, University of Florida, Gainesville/Jacksonville, Florida; Robert M. Wallace, University of Iowa, Iowa City/ Davenport, Iowa; Lewis H. Kuller, University of Pittsburgh, Pittsburgh, Pennsylvania; and Sally A. Shumaker, Wake Forest University School of Medicine, Winston-Salem, North Carolina; Women’s Health Initiative Memory Study: Sally A. Shumaker, Wake Forest University School of Medicine, Winston-Salem, North Carolina. For a list of all the investigators who have contributed to WHI science, please visit:

Decisions concerning study design, data collection and analysis, interpretation of the results, the preparation of the manuscript, and the decision to submit the manuscript for publication resided with committees that comprised WHI investigators and included National Heart, Lung, and Blood Institute representatives. The contents of the paper are solely the responsibility of the authors.


Download Citation

Yiwen Zhang. Ran Dai. Ying Huang. Ross Prentice. Cheng Zheng. "Using simultaneous regression calibration to study the effect of multiple error-prone exposures on disease risk utilizing biomarkers developed from a controlled feeding study." Ann. Appl. Stat. 18 (1) 125 - 143, March 2024.


Received: 1 January 2022; Revised: 1 May 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1782

Keywords: biomarker , cardiovascular disease , feeding study , measurement error , regression calibration

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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