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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675752
• 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.************

当响应是事件发生时间结局（如患者寿命、失败时间）时，数据通常被删失，并涉及时间依赖性协变量。例如，在一项临床试验中，研究人员感兴趣的是评估治疗对HIV-1血清阳性吸毒者生存率的影响，这些吸毒者调整了其他预测协变量，如BMI（身体质量指数）和年龄。一些患者在研究终止时可能仍然存活。因此，对这些患者的生存时间进行删失。另一方面，当患者来自不同的健康中心时，同一中心的患者之间可能存在依赖性。本研究提案的部分目标是开发改进的非/半参数回归模型，用于删失和聚类样本的固定和混合协变量效应，并研究估计量的大样本性能及其效率和最佳收敛速度。 在许多领域，如医学、农业、工业、工程学、生物科学、社会学，经常出现涉及类似但独立的调查序列的情况。在这种情况下，感兴趣的参数往往会随着序列以未知的概率分布前进而不可预测地变化，因此不能做出通常称为贝叶斯决策的最小风险决策。然而，从之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。本研究的部分目的是提出改进的/单调EB估计/测试程序时，响应由一些参数分布建模，并调查的速度和最佳可能的速度，这些程序的风险接近最小贝叶斯风险。 几乎在每一个学科中，响应都取决于几个因果协变量（例如，胰岛素依赖性糖尿病男性中的碳水化合物取决于他的年龄、体重、蛋白质等）。并且人们经常面临为了预测和预报目的而对协变量的响应数据建模的问题。本研究提案的部分目标是将预测/预测问题的研究扩展到同时处理两个或多个模型系统的情况，其中响应取决于两组或多组协变量。我们利用协变量的所有信息来拟合模型，以提供最佳的预测/预报程序。这种技术最初在经济学中被称为看似不相关的回归系统，在其他学科中越来越受欢迎，如社会和生物科学，流行病学，地理学，工程学和可靠性。在这种系统独立发生的情况下，我们计划应用经验贝叶斯方法来获得更好的程序。*