Inferring reproducible relationships between biological variables remains a challenge in the statistical analysis of omics data. For example, methods that identify statistical associations may lack interpretability or reproducibility. The situation can be greatly improved, however, by introducing the measure of stability into the association, where small perturbations in the data do not affect the association. We developed this concept into a new statistical framework called StableMate. Given data observed in different environments or conditions, such as experimental batches or disease states, StableMate identifies predictors which are environment-agnostic or specific in predicting the response using stabilised regression.StableMate is a flexible framework that can be applied to a wide range of biological data types and questions. We applied StableMate to 1) RNA-seq data of breast cancer to discover genes and gene modules that consistently predict estrogen receptor expression across disease conditions, 2) metagenomics data to identify fecal microbial species that show persistent association with colon cancer across studies from different countries and 3) single cell RNA-seq data of glioblastoma to discern signature genes associated with development of microglia to a pro-tumour phenotype regardless of cell location in the core.StableMate is an innovative, adaptable and efficient variable selection framework that achieves a comprehensive characterisation of a biological system for a wide range of biological data types for regression and classification analyses.