Various extensions of the isotonic regression problems and its applications

1.通过多个决策过程进行非劣势、等价性和优势性检验的统一方法在新药与积极对照的临床比较研究中，同时检验非劣势假说和优势假说一直是人们非常感兴趣的问题。在日本，这两个测试的显着性水平通常被设定为α=0.025，但非自卑假设的α已被1999年引入的国际指南改为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，与日本证明测试药物的非劣性的旧做法相比，大约需要1.3倍的样本量，这才真正等同于对照。这确实是一个需要仔细讨论的非常严重的问题，另见Hirotsu和Hothorn(2003)。在本研究中，我们应用参数空间的划分原理，成功地统一了旧的日本指南和国际指南。这种方法特别有吸引力，根据临床试验的成果改变测试药物相对于对照药物相对疗效的证据强度。它包括：1.弱非劣势；2.强非劣势；3.至少等价性；4.优越性。弱非劣性符合日本的惯例，强非劣性符合国际准则。2.剂量反应分析在剂量反应分析中，提出了一种新的剂量反应模式估计方法，取代了经典的剂量反应函数估计方法。这一想法在二期临床试验中非常有用，其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.