Mathematical Sciences: Smoothed Nonparametric Hazard Regression

数学科学：平滑非参数风险回归

• 批准号: 9501893
• 负责人: Birgit Grund
• 金额: $ 7.2万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501893&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Smoothed; Nonparametric; Hazard

9501893 Grund Abstract The main objective of the project is to develop smoothing methods for nonparametric hazard regression with time-dependent regression coefficients, in the framework of an additive hazard regression model (Aalen model). The Aalen model incorporates the possibility that both value and contribution of covariates may change over time. Most important, no particular parametric shape of this time-dependence is assumed. In the current project, kernel smoothing will be used to estimate the regression coefficient curves. A major objective is to develop data-driven bandwidth selectors, and to investigate their properties. It is expected that the resulting methods will improve upon currently used empirical estimates. Moreover, kernel methods allow one to estimate the regression coefficient curves themselves, as opposed to cumulative coefficients. This is particularly important for graphical data analysis. The new smoothing methods will be implemented in XLISP-STAT, an object- oriented programming language; a user-friendly interface will be provided. Dynamic graphics will be used to support visual data exploration. As part of the project, the developed smoothing procedures will be used to analyze epidemiological data. On the side of education, the development of a new lecture course on ``Smoothing Methods in Curve Estimation'' for statistics majors at the M.S. or Ph.D. level is proposed. Research results of the current proposal will be included. Dynamic graphics software will be used to demonstrate smoothing techniques in class, thus giving students access to cutting edge technology An important problem in medicine is to predict the survival of patients, given their current condition and treatment. The condition of a patient is described by "covariate values", such as blood cholesterol, blood pressure, number of antibodies, etc. A central problem in analyzing survival data is to assess the influence of covariates; for example, to quantify by how much an elevated level of blood cholesterol increases the risk of stroke. Often the influence of covariates is known to change with time. In this case standard methods tend to fail. The proposed project develops risk estimates based on the Aalen model. This model is extremely flexible. The influence of covariates is allowed to change over time, without assuming any particular shape of this time-dependence beforehand. In this project, modern smoothing techniques will be adapted to estimate the influence of covariates. Smoothing methods are extremely useful for descriptive data analysis, and widely used in statistics. In the context of survival data, however, the use of corresponding methods is a very recent development, with many open problems. Part of the project is the user-friendly computational implementation of the newly developed estimation procedures. Interactive graphics will be used extensively to support visual data exploration. With the provided software, smoothing methods in Aalen hazard regression will be available for practitioners for the first time. The new smoothing procedures will be used to analyze epidemiological data. On the side of education, the development of a new lecture course on ``Smoothing Methods in Curve Estimation'' for statistics majors at the M.S. or Ph.D. level is proposed. Research results of the current proposal will be included. Dynamic graphics software will be used to demonstrate smoothing techniques in class, thus giving students access to cutting edge technology.

9501893 Grund摘要该项目的主要目标是在加性风险回归模型（Aalen模型）的框架内，开发具有时间依赖回归系数的非参数风险回归的平滑方法。 Aalen模型考虑了协变量的值和贡献都可能随着时间的推移而变化的可能性。 最重要的是，没有特定的参数形状的时间依赖性被假定。 在本项目中，核平滑将被用来估计回归系数曲线。 一个主要的目标是开发数据驱动的带宽选择器，并调查他们的属性。 预计由此产生的方法将改善目前使用的经验估计。 此外，核方法允许人们估计回归系数曲线本身，而不是累积系数。 这对于图形数据分析尤其重要。新的平滑方法将在XLISP-STAT中实现，这是一种面向对象的编程语言;将提供一个用户友好的界面。 动态图形将用于支持可视化数据探索。 作为该项目的一部分，开发的平滑程序将用于分析流行病学数据。在教育方面，为统计学专业开设了一门新的讲座课程“曲线估计中的平滑方法”。或博士水平提出。 本提案的研究成果将包括在内。 动态图形软件将用于演示平滑技术在课堂上，从而让学生接触到最先进的技术 医学中的一个重要问题是根据患者的当前状况和治疗来预测患者的生存。 患者的状况由“协变量值”描述，如血胆固醇、血压、抗体数量等。分析生存数据的中心问题是评估协变量的影响;例如，量化血胆固醇水平升高会增加中风风险的程度。通常，已知协变量的影响随时间变化。 在这种情况下，标准方法往往会失败。拟议项目根据Aalen模型进行风险估计。 这种模式非常灵活。 允许协变量的影响随时间变化，而不预先假设这种时间依赖性的任何特定形状。 在本项目中，将采用现代平滑技术来估计协变量的影响。 平滑方法对于描述性数据分析非常有用，在统计学中应用广泛。 然而，在生存数据的背景下，使用相应的方法是一个非常新的发展，有许多开放的问题。该项目的一部分是新开发的估算程序的用户友好的计算执行。 交互式图形将广泛用于支持可视化数据探索。 通过提供的软件，Aalen风险回归中的平滑方法将首次为从业者提供。新的平滑程序将用于分析流行病学数据。在教育方面，为统计学专业开设了一门新的讲座课程“曲线估计中的平滑方法”。或博士水平提出。 本提案的研究成果将包括在内。 动态图形软件将被用来演示平滑技术在课堂上，从而让学生获得尖端技术。