Asymptotic properties of likelihood ratio statistics on non-inferiority hypothesis testing

非劣性假设检验似然比统计的渐近性质

• 批准号: 16500178
• 负责人: TAKAGI Yoshiji
• 金额: $ 1.86万
• 依托单位: Osaka Prefecture University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16500178/
• 关键词: non-inferiority hypothesis; exponential distribution; type I censored data; likelihood ratio statistic; k-sample problem; normal distribution; non-differentiable point; ワイブル分布; パラメータ直交化変換; non-inferiority; 条件付尤度

We have the following two research results.1.The non-inferiority testing problem between some treatments is discussed in survival model where the underlying distribution is exponential and data are subject to type I censoring. The asymptotic distribution of the likelihood ratio statistic is derived in two-sample and k-sample cases. One testing procedure for the non-inferiority testing hypotheses is proposed based on the likelihood ratio statistic.2.The non-inferiority testing problem between two treatments is discussed based on the likelihood ratio statistic. Let the underlying distribution for the two treatments be normally distributed with mean θ and μ, respectively, and common unknown variance. We consider the following general hypotheses including the non-inferiority hypotheses : H_0:θ≧h(μ) v.s. H_1:θ<h(μ), where h(μ)is any continuous and strictly increasing function. In this situation, the asymptotic distribution of the log-likelihood ratio statistic is obtained under the true value on the boundary of the hypotheses. When the true value is any differentiable point, the asymptotic distribution becomes 1/2+(1/2)x^2_1 irrespective to the function h(μ), where x^2_1 is the chi-squared random variable with one degree of freedom. On the other hand, if the true point is any non-differentiable point for the function h(,μ), the asymptotic distribution is expressed in the form depending on right and left differential coefficients of the function h(μ).

主要研究结果如下：1.在指数分布和I型截尾的生存模型中，讨论了治疗方案间的非劣效性检验问题。在两样本和k样本情形下，得到了似然比统计量的渐近分布。提出了一种基于似然比统计量的非劣效性检验假设的检验方法。2.讨论了基于似然比统计量的两种治疗方案之间的非劣效性检验问题。假设两种处理的基础分布均为正态分布，分别具有均值θ和μ，以及共同的未知方差。我们考虑以下一般假设，包括非劣效性假设：H_0：θ h（μ）v.s. H_1：θ<h（μ），其中h（μ）是任意连续的严格增函数。在这种情况下，对数似然比统计量的渐近分布是在假设边界上的真值下得到的。当真值是任意可微点时，渐近分布变为1/2+（1/2）x^2_1，与函数h（μ）无关，其中x^2_1是具有一个自由度的卡方随机变量。另一方面，如果真点是函数h（，μ）的任何不可微点，则渐近分布表示为依赖于函数h（μ）的左右微分系数的形式。