Tests and Classifications in Adaptive Designs with Applications

Statistical tests for biomarker identification and classification methods for patient grouping are two important topics in adaptive designs of clinical trials. In this article, we evaluate four test methods for biomarker identification: a model-based identification method, the popular t-test, the nonparametric Wilcoxon Rank Sum test, and the Least Absolute Shrinkage and Selection Operator (Lasso) method. For selecting the best classification methods in Stage 2 of an adaptive design, we examine classification methods including the recently developed machine learning approaches such as Random Forest, Lasso and Elastic-Net Regularized Generalized Linear Models (Glmnet), Support Vector Machine (SVM), Gradient Boosting Machine (GBM), and Extreme Gradient Boost- ing (XGBoost). Statistical simulations are carried out in our study to assess the performance of biomarker identification methods and the classification methods. The best identification method and the classification technique will be selected based on the True Positive Rate (TPR,also called Sensitivity) and the True Negative Rate (TNR,also called Specificity). The optimal test method for gene identification and classification method for patient grouping will be applied to the Adap- tive Signature Design (ASD) for the purpose of evaluating the performance of ASD in different situations, including simulated data and a real data set for breast cancer patients.