Two-sample Parametric Hypothesis Testing

In hypothesis testing, it is usually of great interest to find a test with satisfactory power and a controlled type I error rate. Some optimal tests, such as the uniformly most powerful (UMP) test and the uniformly most powerful (UMP) unbiased test, can be derived analytically under some standard settings, for instance, exponential distribution families. However, in the adaptive clinical trial as a real-world problem, it is challenging to prove the existence of such an optimal test and to further obtain the test analytically. In this chapter, we introduce a two-stage framework to have the first DNN constructing testing statistics and the second DNN approximating critical values in two-group composite hypothesis testing. An application to the sample size reassessment adaptive clinical trial is conducted to show that the DNN -assisted hypothesis testing has a controlled type I error rate and a better power performance than some existing methods. Additional sensitivity analyses are performed to demonstrate the robustness of the proposed method.