Various extensions of the isotonic regression problems and its applications

1.在新药与主动对照药的临床比较研究中，非劣效性假设和优效性假设的同时检验一直是一个备受关注的问题。在日本，这两个检验的显著性水平通常设置为α=0.05，但1999年引入的国际指南将非劣效性假设的α改为0.025。这自然对日本的临床试验实践产生了非常大的影响，因为根据国际指南，要证明一种测试药物的非劣效性，与日本的旧做法相比，需要大约1.3倍的样本量，才能真正等同于对照。这确实是一个需要仔细讨论的非常严肃的问题，参见Hirotsu and Hothorn（2003）。在本研究中，我们利用参数空间的划分原理，成功地将旧的日本准则与国际准则统一起来。这种方法特别有吸引力，根据临床试验的结果改变试验药物相对于对照药物的相对疗效证据的强度。它包括决策1。2.弱非劣；2、强不自卑；至少是等价的，4。优势。弱非劣性与日本实践相对应，强非劣性与国际准则相对应。然而，也有人提出了另一种方法，利用日本和国际惯例的优势。剂量-反应分析在剂量-反应分析中，提出了一种新的估计剂量-反应模式的方法来代替经典的剂量-反应函数估计。这个想法在ii期临床试验中非常有用，ii期临床试验的目的是确定临床治疗的推荐剂量。

1.A unifying approach to non-inferiority, equivalence and superiority tests via multiple decision processesIn the comparative clinical study of a new drug against an active control the simultaneous testing of the non-inferiority hypothesis and the superiority hypothesis has been of great interest. In Japan the significance level of these two tests was set commonly at α=0.05 but the α for the non-inferiority hypothesis has been altered to 0.025 by the International Guideline introduced in 1999. It naturally gives a very big impact on the Japanese practice of clinical trial since according to the International Guideline approximately 1.3 times the sample size is required as compared with the old Japanese practice for proving the non-inferiority of a test drug which is truly equivalent to the control. This is indeed a very serious problem to be discussed carefully, see also Hirotsu and Hothorn (2003). In this research we succeeded in unifying the old Japanese Guideline and the International Guideline by applying the partitioning principle of the parameter space. This method is particularly attractive changing the strength of the evidence of relative efficacy of the test drug against a control according to the achievement of the clinical trial. It includes the decisions 1. weak non-inferiority, 2. strong non-inferiority, 3. at least equivalence, and 4. superiority. The weak non-inferiority corresponds to the Japanese practice and the strong non-inferiority to the International Guideline. Yet another approach has also been proposed taking the advantages of both of the Japanese and International practices.2.Dose - response analysisIn the dose-response analysis a new approach of estimating the dose - response patterns is proposed replacing the classical estimation of dose-response function. This idea is very useful in the phase 2 clinical trial whose purpose is to decide the recommended dose for the clinical treatment.