Two-stage penalized regression screening to detect biomarker-treatment interactions in randomized clinical trials

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 familywise 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.