  Detection of interactions between treatment effects and patient descriptors
in clinical trials is critical for optimizing the drug development process. The
increasing volume of data accumulated in clinical trials provides a unique
opportunity to discover new biomarkers and further the goal of personalized
medicine, but it also requires innovative robust biomarker detection methods
capable of detecting non-linear, and sometimes weak, signals. We propose a set
of novel univariate statistical tests, based on the theory of random walks,
which are able to capture non-linear and non-monotonic covariate-treatment
interactions. We also propose a novel combined test, which leverages the power
of all of our proposed univariate tests into a single general-case tool. We
present results for both synthetic trials as well as real-world clinical
trials, where we compare our method with state-of-the-art techniques and
demonstrate the utility and robustness of our approach.
