Open Access
2023 Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with varying-coefficient models
Congmin Liu, Zhuowei Sun, Hongyuan Cao
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Electron. J. Statist. 17(2): 3103-3142 (2023). DOI: 10.1214/23-EJS2175


We consider varying-coefficient models for mixed synchronous and asynchronous longitudinal covariates, where asynchronicity refers to the misalignment of longitudinal measurement times within an individual. We propose three different methods of parameter estimation and inference. The first method is a one-step approach that estimates non-parametric regression functions for synchronous and asynchronous longitudinal covariates simultaneously. The second method is a two-step approach in which synchronous longitudinal covariates are regressed with the longitudinal response by centering the synchronous longitudinal covariates first and, in the second step, the residuals from the first step are regressed with asynchronous longitudinal covariates. The third method is the same as the second method except that in the first step, we omit the asynchronous longitudinal covariate and include a non-parametric intercept in the regression analysis of synchronous longitudinal covariates and the longitudinal response. We further construct simultaneous confidence bands for the non-parametric regression functions to quantify the overall magnitude of variation. Extensive simulation studies provide numerical support for the theoretical findings. The practical utility of the methods is illustrated on a dataset from the ADNI study.


We thank Ting Li for help with data acquisition. Data used in preparation of this article were obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) database ( As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at:

We thank the editor and anonymous reviewers’ comments that streamline this paper. Most of this work was conducted when Congmin Liu was a visiting student at Florida State University. She is grateful for the support and hospitality of the statistics department at Florida State University.


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Congmin Liu. Zhuowei Sun. Hongyuan Cao. "Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with varying-coefficient models." Electron. J. Statist. 17 (2) 3103 - 3142, 2023.


Received: 1 May 2022; Published: 2023
First available in Project Euclid: 14 November 2023

arXiv: 2305.17662
Digital Object Identifier: 10.1214/23-EJS2175

Primary: 62G05 , 62G20
Secondary: 62G15

Keywords: Asynchronous longitudinal data , convergence rate , kernel-weighting , simultaneous confidence band , varying-coefficient

Vol.17 • No. 2 • 2023
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