Non/semiparametric methods for nonlinear/hazards/cencored regression; Nonparametric monotone empirical Bayes; Non/semiparametric seemingly unrelated regression

用于非线性/风险/中心回归的非/半参数方法；

• 批准号: RGPIN-2017-05047
• 负责人: Singh, Radhey
• 金额: $ 1.17万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=665295
• 关键词: Non; semiparametric; methods; nonlinear; hazards

When the response is the time-to-event outcome such as lifetimes of patients, failure times, the data are often censored and involve time dependent covariates. For example, in a clinical trial, the researchers are interested in evaluating the effect of a treatment on survival in the HIV-1 seropositive drug users adjusted for other predictive covariates such as BMI (body mess index) and age. Some patients may still be alive when the study terminates. Hence, the survival time of these patients are censored. On the other hand, when patients are taken from different health centers, there might be a dependence between patients in the same centers. Part of the objective of this research proposal is to develop improved non/semi-parametric regression models for fixed and mixed covariate effects with censored and clustered samples and to investigate the large sample performance of the estimators as well as their efficiency and the optimal convergence rates.**** In many fields, like medicine, agriculture, industry, engineering, biological sciences, sociology, often situations involving sequences of similar but independent investigations arise. In such situations the parameter of interest often varies unpredictably as the sequence progresses with unknown probability distribution, and hence a minimum risk decision, what is usually called Baysian decision, can not be made. However, the information collected from the previous investigations can sometimes be utilized to formulate a decision, what is popularly known as empirical Bayes decision, with risk close to the minimum Bayes risk. Part of the objective of this research is to propose improved/monotone EB estimation/test procedures when the responses are modeled by some parametric distribution and to investigate the speed and the best possible speed with which the risk of these procedures approach to the minimum Bayes risk.**** In almost every discipline a response depends on several causal covariates, (e.g., carbohydrate in an insulin dependent diabetic male depends on his age, weight, protein etc.) and one is often faced with the problem of modeling the response data on the covariates for forecasting and prediction purpose. Part of the objectives of this research proposal is to extend the research on forecasting/prediction problem to the situations where we deal simultaneously with two or more systems of models where responses depend on two or more sets of covariates. We utilize all the information on covariates to fit models to provide the best prediction/forecasting procedures. This technique, what is originally known in economics, as the system of seemingly unrelated regressions, is becoming more and more popular in other disciplines such as social and biological sciences, epidemiology, geography, engineering and reliability. In some situations where such system occurs independently, we plan to apply empirical Bayes method to obtain better procedures.************

当反应是事件发生的时间结果时，如患者的寿命、失败次数，数据通常是被审查的，并且涉及时间依赖协变量。例如，在一项临床试验中，研究人员感兴趣的是，根据BMI(身体混乱指数)和年龄等其他预测协变量进行调整后，评估治疗对HIV-1血清阳性吸毒者生存的影响。当研究结束时，一些患者可能还活着。因此，这些患者的生存时间是经过审查的。另一方面，当患者从不同的健康中心被带走时，同一中心的患者之间可能存在依赖关系。这项研究的部分目的是为删失和聚集样本下的固定和混合协变量效应建立改进的非参数/半参数回归模型，并调查估计量的大样本性能以及它们的效率和最优收敛速度。*在许多领域，如医学、农业、工业、工程、生物科学、社会学，经常出现类似但独立调查序列的情况。在这种情况下，当序列以未知的概率分布进行时，感兴趣的参数经常不可预测地变化，因此不能做出通常所称的贝叶斯决策的最小风险决策。然而，从以前的调查中收集的信息有时可以用来制定决策，即通常所说的经验贝叶斯决策，其风险接近最小贝叶斯风险。这项研究的部分目的是提出改进的/单调EB估计/测试程序，当响应由某些参数分布建模时，并调查这些程序的风险接近最小贝叶斯风险的速度和最佳可能速度。*在几乎每个学科中，响应依赖于几个因果协变量(例如，胰岛素依赖型糖尿病男性的碳水化合物取决于他的年龄、体重、蛋白质等)。为了预测和预测的目的，人们经常面临对协变量上的响应数据进行建模的问题。本研究方案的部分目的是将预测/预测问题的研究扩展到同时处理两个或更多个模型系统的情况，其中响应依赖于两个或更多组协变量。我们利用所有关于协变量的信息来拟合模型，以提供最佳的预测/预测程序。这种技术最初在经济学中被称为看似无关的回归系统，在社会科学和生物科学、流行病学、地理学、工程学和可靠性等其他学科中越来越受欢迎。在这种系统独立出现的情况下，我们计划应用经验贝叶斯方法来获得更好的程序。*