bi-level variable selection, gene–environment interaction, repeated measurements, generalized estimating equation, quadratic inference function, Genetics, QH426-470

In high-dimensional data analysis, the bi-level (or the sparse group) variable selection can simultaneously conduct penalization on the group level and within groups, which has been developed for continuous, binary, and survival responses in the literature. Zhou et al. (2022) (PMID: 35766061) has further extended it under the longitudinal response by proposing a quadratic inference function-based penalization method in gene–environment interaction studies. This study introduces “springer,” an R package implementing the bi-level variable selection within the QIF framework developed in Zhou et al. (2022). In addition, R package “springer” has also implemented the generalized estimating equation-based sparse group penalization method. Alternative methods focusing only on the group level or individual level have also been provided by the package. In this study, we have systematically introduced the longitudinal penalization methods implemented in the “springer” package. We demonstrate the usage of the core and supporting functions, which is followed by the numerical examples and discussions. R package “springer” is available at Visa.