  High-dimensional biomarkers such as genomics are increasingly being measured
in randomized clinical trials. Consequently, there is a growing interest in
developing methods that improve the power to detect biomarker-treatment
interactions. We adapt recently proposed two-stage interaction detecting
procedures in the setting of randomized clinical trials. We also propose a new
stage 1 multivariate screening strategy using ridge regression to account for
correlations among biomarkers. For this multivariate screening, we prove the
asymptotic between-stage independence, required for family-wise error rate
control, under biomarker-treatment independence. Simulation results show that
in various scenarios, the ridge regression screening procedure can provide
substantially greater power than the traditional one-biomarker-at-a-time
screening procedure in highly correlated data. We also exemplify our approach
in two real clinical trial data applications.
