June 2024 Variance as a predictor of health outcomes: Subject-level trajectories and variability of sex hormones to predict body fat changes in peri- and postmenopausal women
Irena Chen, Zhenke Wu, Siobán D. Harlow, Carrie A. Karvonen-Gutierrez, Michelle M. Hood, Michael R. Elliott
Author Affiliations +
Ann. Appl. Stat. 18(2): 1642-1667 (June 2024). DOI: 10.1214/23-AOAS1852


Longitudinal biomarker data and cross-sectional outcomes are routinely collected in modern epidemiology studies, often with the goal of informing tailored early intervention decisions. For example, hormones, such as estradiol (E2) and follicle-stimulating hormone (FSH), may predict changes in womens’ health during the midlife. Most existing methods focus on constructing predictors from mean marker trajectories. However, subject-level biomarker variability may also provide critical information about disease risks and health outcomes. Current literature does not provide statistical models to investigate such relationships with valid uncertainty quantification. In this paper we develop a fully Bayesian joint model that estimates subject-level means, variances, and covariances of multiple longitudinal biomarkers and uses these as predictors to evaluate their respective associations with a cross-sectional health outcome. Simulations demonstrate excellent recovery of true model parameters. The proposed method provides less biased and more efficient estimates, relative to alternative approaches that either ignore subject-level differences in variances or perform two-stage estimation where estimated marker variances are treated as observed. Empowered by the model, analyses of women’s health data reveal, for the first time, that larger variability of E2 was associated with slower increases in waist circumference across the menopausal transition.

Funding Statement

This work was supported by National Institute on Aging Grant 1-R56-AG066693. Zhenke Wu and Irena Chen were were also partially supported in part by seed grants from Michigan Institute of Data Science and Michigan Precision Health.


The Study of Women’s Health Across the Nation (SWAN) has grant support from the National Institutes of Health (NIH), DHHS, through the National Institute on Aging (NIA), the National Institute of Nursing Research (NINR), and the NIH Office of Research on Women’s Health (ORWH) (Grants U01NR004061; U01AG012505, U01AG012535, U01AG012531, U01AG012539, U01AG012546, U01AG012553, U01AG012554, U01AG012495, and U19AG063720). This work also was supported by National Institute on Aging Grant 1-R56-AG066693. The content of this article is solely the responsibility of the authors and does not necessarily represent the official views of the NIA, NINR, ORWH, or the NIH. This research also was supported in part through computational resources and services provided by Advanced Research Computing (ARC), a division of Information and Technology Services (ITS) at the University of Michigan, Ann Arbor.

Clinical Centers: University of Michigan, Ann Arbor—Carrie Karvonen-Gutierrez, PI 2021–present, Siobán Harlow, PI 2011–2021, MaryFran Sowers, PI 1994–2011; Massachusetts General Hospital, Boston, MA—Sherri-Ann Burnett-Bowie, PI 2020–present; Joel Finkelstein, PI 1999–2020; Robert Neer, PI 1994–1999; Rush University, Rush University Medical Center, Chicago, IL—Imke Janssen, PI 2020–Present; Howard Kravitz, PI 2009–2020; Lynda Powell, PI 1994–2009; University of California, Davis/Kaiser—Elaine Waetjen and Monique Hedderson, PIs 2020–present; Ellen Gold, PI 1994–2020; University of California, Los Angeles—Arun Karlamangla, PI 2020–present; Gail Greendale, PI 1994–2020; Albert Einstein College of Medicine, Bronx, NY—Carol Derby, PI 2011–present, Rachel Wildman, PI 2010–2011; Nanette Santoro, PI 2004–2010; University of Medicine and Dentistry–New Jersey Medical School, Newark—Gerson Weiss, PI 1994–2004, and the University of Pittsburgh, Pittsburgh, PA—Rebecca Thurston, PI 2020–present; Karen Matthews, PI 1994–2020.

NIH Program Office: National Institute on Aging, Bethesda, MD—Rosaly Correa-de-Araujo 2020–present; Chhanda Dutta 2016–present; Winifred Rossi 2012–2016; Sherry Sherman 1994–2012; Marcia Ory 1994–2001; National Institute of Nursing Research, Bethesda, MD—Program Officers.

Central Laboratory: University of Michigan, Ann Arbor—Daniel McConnell (Central Ligand Assay Satellite Services).

Coordinating Center: University of Pittsburgh, Pittsburgh, PA—Maria Mori Brooks, PI 2012–present; Kim Sutton-Tyrrell, PI 2001–2012; New England Research Institutes, Watertown, MA—Sonja McKinlay, PI 1995–2001.

Steering Committee: Susan Johnson, Current Chair, Chris Gallagher, Former Chair.

We thank the study staff at each site and all the women who participated in SWAN.

We also thank the University of Michigan SWAN team for providing the datasets used in our analysis. We also thank the kind users from the Stan Forums for providing suggestions for approaching the three-trajectory modeling setting. With regards to model implementation, we would like to thank Daniel Barker, Brock Palen, and Logan A. Walls for their assistance with writing efficient model code and programming the simulation replicates to run on the University of Michigan ARC-TS computing cluster.


Download Citation

Irena Chen. Zhenke Wu. Siobán D. Harlow. Carrie A. Karvonen-Gutierrez. Michelle M. Hood. Michael R. Elliott. "Variance as a predictor of health outcomes: Subject-level trajectories and variability of sex hormones to predict body fat changes in peri- and postmenopausal women." Ann. Appl. Stat. 18 (2) 1642 - 1667, June 2024. https://doi.org/10.1214/23-AOAS1852


Received: 1 November 2022; Revised: 1 October 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1852

Keywords: Estradiol , follicle-stimulating hormone , Hamiltonian Monte Carlo , Joint models , menopause , Study of Women’s Health Across the Nation (SWAN) , subject-level variability , variance component priors

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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