Open Access
March 2024 Retrospective varying coefficient association analysis of longitudinal binary traits: Application to the identification of genetic loci associated with hypertension
Gang Xu, Amei Amei, Weimiao Wu, Yunqing Liu, Linchuan Shen, Edwin C. Oh, Zuoheng Wang
Author Affiliations +
Ann. Appl. Stat. 18(1): 487-505 (March 2024). DOI: 10.1214/23-AOAS1798


Many genetic studies contain rich information on longitudinal phenotypes that require powerful analytical tools for optimal analysis. Genetic analysis of longitudinal data that incorporates temporal variation is important for understanding the genetic architecture and biological variation of complex diseases. Most of the existing methods assume that the contribution of genetic variants is constant over time and fail to capture the dynamic pattern of disease progression. However, the relative influence of genetic variants on complex traits fluctuates over time. In this study, we propose a retrospective varying coefficient mixed model association test, RVMMAT, to detect time-varying genetic effect on longitudinal binary traits. We model dynamic genetic effect using smoothing splines, estimate model parameters by maximizing a double penalized quasi-likelihood function, design a joint test using a Cauchy combination method, and evaluate statistical significance via a retrospective approach to achieve robustness to model misspecification. Through simulations we illustrated that the retrospective varying-coefficient test was robust to model misspecification under different ascertainment schemes and gained power over the association methods assuming constant genetic effect. We applied RVMMAT to a genome-wide association analysis of longitudinal measure of hypertension in the Multi-Ethnic Study of Atherosclerosis. Pathway analysis identified two important pathways related to G-protein signaling and DNA damage. Our results demonstrated that RVMMAT could detect biologically relevant loci and pathways in a genome scan and provided insight into the genetic architecture of hypertension.

Funding Statement

This study was supported by National Science Foundation grant DMS1916246 and National Institutes of Health grants K01AA023321 and R01LM014087, and COBRE pilot grant GR13574.


The authors would like to thank the reviewers, Associate Editor, and Editor for their feedback that substantially improved the quality of this paper. Gang Xu’s current affiliation is Department of Biostatistics, Yale School of Public Health. Weimiao Wu’s current affiliation is Meta Platforms, Inc. Edwin C. Oh’s second affiliation is Nevada Institute of Personalized Medicine, University of Nevada.

The Multi-Ethnic Study of Atherosclerosis is supported by contracts 75N92020D00001, HHSN268201500003I, N01-HC-95159, 75N92020D00005, N01-HC-95160, 75N92020D00002, N01-HC-95161, 75N92020D00003, N01-HC-95162, 75N92020D00006, N01-HC-95163, 75N92020D00004, N01-HC-95164, 75N92020D00007, N01-HC-95165, N01-HC-95166, N01-HC-95167, N01-HC-95168 and N01-HC-95169 from the National Heart, Lung, and Blood Institute, and by grants UL1-TR-000040, UL1-TR-001079, and UL1-TR-001420 from the National Center for Advancing Translational Sciences (NCATS). The authors thank the other investigators, the staff, and the participants of the MESA study for their valuable contributions. A full list of participating MESA investigators and institutions can be found at This manuscript was not prepared in collaboration with investigators of the MESA and does not necessarily reflect the opinions or conclusions of the MESA or the NHLBI.


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Gang Xu. Amei Amei. Weimiao Wu. Yunqing Liu. Linchuan Shen. Edwin C. Oh. Zuoheng Wang. "Retrospective varying coefficient association analysis of longitudinal binary traits: Application to the identification of genetic loci associated with hypertension." Ann. Appl. Stat. 18 (1) 487 - 505, March 2024.


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

Digital Object Identifier: 10.1214/23-AOAS1798

Keywords: Generalized linear mixed model , genome-wide association study , model misspecification , time-varying genetic effect , varying coefficient model

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.18 • No. 1 • March 2024
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