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的结果（例如患者的寿命，失败时间）时，数据通常会受到审查并涉及依赖时间的协变量。例如，在一项临床试验中，研究人员有兴趣评估治疗对HIV-1血清阳性药物使用者对其他预测性协变量（例如BMI（身体混乱指数）和年龄）的影响。研究终止时，一些患者可能仍然活着。因此，这些患者的生存时间进行了审查。另一方面，当患者从不同的健康中心带走时，同一中心的患者之间可能存在依赖性。这项研究建议的一部分是为了开发改进的非/半参数回归模型，用于固定和混合的协方差效应与经过审查和集群样本，并研究估计量的较大样本性能及其效率及其最佳收敛速度和最佳收敛速度。在这种情况下，感兴趣的参数通常会随着序列的进展而随着未知概率分布的进展而变得不可预测，因此无法做出最小的风险决策，通常所谓的贝西决策。但是，有时可以利用从先前调查中收集的信息来制定决定，即普遍称为经验贝叶斯的决定，风险接近最低贝叶斯风险。这项研究的一部分目的是提出改进/单调EB估计/测试程序，当响应以某些参数分布建模并调查这些程序的风险与最小贝叶斯的风险相处的速度和最佳速度时。蛋白质等）通常面临着建模协变量的响应数据的问题，以预测和预测目的。该研究建议的一部分目标是将有关预测/预测问题的研究扩展到我们同时处理两个或多个模型系统的情况，在这种情况下，响应取决于两套或多套协变量。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/预测程序。这项技术是经济学最初是看似无关的回归体系，在其他学科中越来越流行，例如社会和生物科学，流行病学，地理，工程和可靠性。在某些这种系统独立发生的情况下，我们计划采用经验贝叶斯方法来获得更好的程序。************