Statistical quantification of confounding bias in machine learning models.

BACKGROUND: The lack of nonparametric statistical tests for confounding bias significantly hampers the development of robust, valid, and generalizable predictive models in many fields of research. Here I propose the partial confounder test, which, for a given confounder variable, probes the null hypotheses of the model being unconfounded. RESULTS: The test provides a strict control for type I errors and high statistical power, even for nonnormally and nonlinearly dependent predictions, often seen in machine learning. Applying the proposed test on models trained on large-scale functional brain connectivity data (N= 1,865) (i) reveals previously unreported confounders and (ii) shows that state-of-the-art confound mitigation approaches may fail preventing confounder bias in several cases. CONCLUSIONS: The proposed test (implemented in the package mlconfound; https://mlconfound.readthedocs.io) can aid the assessment and improvement of the generalizability and validity of predictive models and, thereby, fosters the development of clinically useful machine learning biomarkers.