JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1207 10.6339/25-JDS1207 Computing in Data Science The R Package geeVerse for Ultra-High-Dimensional Heterogeneous Data Analysis with Generalized Estimating Equations ZuTianhaitianhai.zu@utsa.edu1∗ GreenBrittany2 https://orcid.org/0000-0002-2859-3093 YuYan3 Department of Operations and Analytics, University of Texas at San Antonio, United States of America Department of Information Systems, Analytics, and Operations, University of Louisville, United States of America Department of Operations, Business Analytics and Information Systems, University of Cincinnati, United States of America Corresponding author Email: tianhai.zu@utsa.edu. 20251811202500120 Supplementary Material

We provide supplementary material with a detailed model and an explanation of the computational algorithms used in geeVerse. We also provide the replication script for this paper at a public repository: Github.

11920252112025 2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2025 Open access article under the CC BY license.

High or ultra-high-dimensional data are becoming increasingly common in various fields. They often display diverse characteristics, including heterogeneity, longitudinal responses, and imbalanced measurements. These complexities make it challenging to integrate different modeling options and their combinations in order to fully leverage this rich data source. This paper provides an easy-to-use, and stand-alone, R package, geeVerse, that can implement any combination of 1) simultaneous variable selection and estimation, 2) quantile regression or mean regression for heterogeneous data, 3) longitudinal or cross-sectional data analysis, 4) balanced or imbalanced data, and 5) moderate, high, or even ultra-high-dimensional data. To accomplish this, we propose computationally efficient implementations of penalized generalized estimating equations (GEE) for quantile and mean regression. We present multiple applications with ultra-high-dimensional data including analysis of a resampled genetic dataset, quantile and mean regressions, analysis of cross-sectional and longitudinal data, differing correlation structures, and differing number of repeated measurements per subject. We also demonstrate our approach on two real data applications.

 GEE longitudinal data quantile variable selection References 1000 Genomes Project Consortium (2015). A global reference for human genetic variation. Nature, 526(7571): 68–74. https://doi.org/10.1038/nature15393 Bates DM, Watts DG (1988). Nonlinear Regression Analysis and Its Applications. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York. Carey VJ, Lumley TS, Moler C, Ripley B (2023). gee: Generalized estimation equation solver. R Package version 4.13–26. Deshpande V, Deshpande MV (2023). pgee.mixed: Penalized generalized estimating equations for bivariate mixed outcomes. R Package version 0.1.0. Eddelbuettel D, François R (2011). Rcpp: Seamless R and C++ integration. Journal of Statistical Software, 40: 1–18. https://doi.org/10.18637/jss.v040.i08 Efron B, Tibshirani RJ (1994). An Introduction to the Bootstrap. Chapman and Hall/CRC, Boca Raton. Evangelou E, Warren HR, Mosen-Ansorena D, Mifsud B, Pazoki R, Gao H, et al. (2018). Genetic analysis of over 1 million people identifies 535 new loci associated with blood pressure traits. Nature Genetics, 50(10): 1412–1425. https://doi.org/10.1038/s41588-018-0205-x Fan J, Li R (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456): 1348–1360. https://doi.org/10.1198/016214501753382273 Fan J, Lv J (2008). Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(5): 849–911. https://doi.org/10.1111/j.1467-9868.2008.00674.x Højsgaard S, Halekoh U, Yan J (2006). The R package geepack for generalized estimating equations. Journal of Statistical Software, 15: 1–11. Inan G, Wang L (2017). PGEE: An R package for analysis of longitudinal data with high-dimensional covariates. R Journal, 9(1): 393–402. Javanmard A, Montanari A (2014). Confidence intervals and hypothesis testing for high-dimensional statistical models. Journal of Machine Learning Research, 15: 2869–2909. Koenker R (2025). quantreg: Quantile Regression. R package version 6.1. Koenker R, Bassett Jr G (1978). Regression quantiles. Econometrica: Journal of the Econometric Society, 46: 33–50. https://doi.org/10.2307/1913643 Li Y, Gao X, Xu W (2023). LassoGEE: High-dimensional lasso generalized estimating equations. R Package version 1.0. Liang KY, Zeger SL (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1): 13–22. https://doi.org/10.1093/biomet/73.1.13 McDaniel LS, Henderson NC, Rathouz PJ (2013). Fast pure R implementation of GEE: Application of the matrix package. The R journal, 5(1): 181–187. https://doi.org/10.32614/RJ-2013-017 National Center for Biotechnology Information (2025). Framingham Heart Study. https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000007.v35.p16. DbGaP Study Accession: phs000007.v35.p16. [Accessed: 2025-08-18]. Nocedal J, Wright SJ (2006). Numerical Optimization. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2nd edition. Rizopoulos D (2010). JM: An R package for the joint modelling of longitudinal and time-to-event data. Journal of Statistical Software, 35(9): 1–33. https://doi.org/10.18637/jss.v035.i09 Saldana DF, Feng Y (2018). SIS: An R package for sure independence screening in ultrahigh-dimensional statistical models. Journal of Statistical Software, 83(2): 1–25. https://doi.org/10.18637/jss.v083.i02 Sherwood B, Maidman A, Li S (2023). rqPen: Penalized quantile regression. Version 4.1. Spellman PT, Sherlock G, Zhang MQ, Iyer VR, Anders K, Eisen MB, et al. (1998). Comprehensive identification of cell cycle–regulated genes of the yeast saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell, 9(12): 3273–3297. https://doi.org/10.1091/mbc.9.12.3273 Su Z, Marchini J, Donnelly P (2011). HAPGEN2: Simulation of multiple disease SNPs. Bioinformatics (Oxford, England), 27(16): 2304–2305. Tibshirani R (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society Series B-Methodological, 58(1): 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x Tibshirani RJ, Taylor J, Lockhart R, Tibshirani RJ (2016). Exact post-selection inference for sequential regression procedures. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(1): 127–158. https://doi.org/10.1111/rssb.12107 van de Geer S, Bühlmann P, Ritov Y, Dezeure R (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. Annals of Statistics, 42(3): 1166–1202. Wang L, Chen G, Li H (2007). Group SCAD regression analysis for microarray time course gene expression data. Bioinformatics, 23(12): 1486–1494. https://doi.org/10.1093/bioinformatics/btm125 Wang L, Zhou J, Qu A (2012). Penalized generalized estimating equations for high-dimensional longitudinal data analysis. Biometrics, 68(2): 353–360. https://doi.org/10.1111/j.1541-0420.2011.01678.x Zu T, Lian H, Green B, Yu Y (2023). Ultra-high dimensional quantile regression for longitudinal data: An application to blood pressure analysis. Journal of the American Statistical Association, 118(541): 97–108. https://doi.org/10.1080/01621459.2022.2128806