In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the existence and further construct such UMP unbiased tests with finite sample size. For example in the COVID-19 pandemic with limited previous assumptions on the treatment for investigation and the standard of care, adaptive clinical trials are appealing due to ethical considerations, and the ability to accommodate uncertainty while conducting the trial. Although several methods have been proposed to control type I error rates, how to find a more powerful hypothesis testing strategy is still an open question. Motivated by this problem, we propose an automatic framework of constructing test statistics and corresponding critical values via machine learning methods to enhance power in a finite sample. In this article, we particularly illustrate the performance using Deep Neural Networks (DNN) and discuss its advantages. Simulations and two case studies of adaptive designs demonstrate that our method is automatic, general and pre-specified to construct statistics with satisfactory power in finite-sample. Supplemental materials are available online including R code and an R shiny app.
翻译:在综合假设测试问题中,确定潜在的统一最强(UMP)不偏倚的测试非常有意义。除了指数式家庭典型的假设环境外,通常还很难证明存在和进一步构建这种具有有限抽样规模的不偏倚的UMP测试。例如,在CCOVID-19大流行病中,先前对调查治疗和护理标准的假设有限,适应性临床试验由于道德考虑和在进行试验时容纳不确定性的能力而具有吸引力。虽然已提出若干方法来控制I类误差率,但如何找到更强大的假设测试战略仍然是一个尚未解决的问题。受这一问题的驱使,我们提出了一个自动框架,通过机器学习方法构建测试统计数据和相应的关键值,以在有限的样本中增强权力。在本条中,我们特别介绍了使用深神经网络(DNNN)的性能,并讨论了其优点。模拟和两个适应性设计案例研究表明,我们的方法是自动的、一般的和预先指定的,以便用有限抽样来建立令人满意的统计数据。补充材料包括R码和一个闪亮的应用程序。