HAZARD REGRESSION AND OTHER POLYNOMIAL SPLINE METHODS

风险回归和其他多项式样条方法

• 批准号: 6172985
• 负责人: Charles L Kooperberg
• 金额: $ 11.26万
• 依托单位: FRED HUTCHINSON CANCER RESEARCH CENTER
• 依托单位国家: 美国
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-04-01 至 2003-03-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/6172985
• 关键词: computer program /software; data collection methodology /evaluation; human data; mathematical model; method development; model design /development; statistics /biometry

DESCRIPTION: There are numerous situations in which observed data is generated by some unknown mechanism, where interest lies in estimating a function that is related to a model for the data. It is proposed to model the corresponding unknown functions in a linear space of smooth piecewise polynomials. An algorithm employing stepwise addition and deletion of basis functions is used to determine this space adaptively. In the proportional hazards model, the dependence of the survival times on the covariates is modeled fully parametrically. Hazard regression (HARE) employs an adaptive algorithm based on piecewise polynomials to model the conditional log-hazard function. It does not assume a proportional hazard model. It is proposed to develop and investigate a number of extensions to HARE involving missing data, time dependent covariates, categorical predictors with many levels, dependent data and family studies. For problems of moderate size the POLYCLASS method of the proposer and collaborators for polychotomous regression and classification is claimed to be competitive with other classification methods while providing reliable estimates of conditional class probabilities. An algorithm based on the stochastic gradient method makes the POLYCLASS method applicable to large data sets. It is proposed to develop a corresponding model selection algorithm. Triogram is the name given by the proposer for a function estimation method which using piecewise linear, bivariate splines based on an adaptively constructed triangulation. It is proposed to develop methods based on the triogram that yield smoother estimates than do the current methods and that select the basis functions more effectively. It is proposed to investigate statistical modeling with free knot splines, where knot locations are treated as parameters. It is claimed that this makes it possible to obtain standard errors that take into account the uncertainty in the knot positions and should provide new insight about inference for adaptive polynomial spline methodologies. Publicly available software for the proposed methodologies will be developed.

描述：在许多情况下，观测数据被 由某种未知机制生成，其中感兴趣的是估计 与数据模型相关的函数。建议将其建模为 分段光滑线性空间中相应的未知函数 多项式。一种分步增删基的算法 函数用于自适应地确定该空间。 在比例风险模型中，生存时间依赖于 协变量完全以参数形式建模。危险回归(HARE) 采用一种基于分段多项式的自适应算法来建模 条件对数风险函数。它不假定存在成比例的风险。 模特。建议开发和研究一些扩展到 涉及缺失数据的共享、时间相关协变量、分类 有多个层次的预测者，依赖的数据和家庭研究。 对于中等大小的问题，提出的多类方法和 多分类回归和分类的合作者声称 与其他分类方法竞争，同时提供可靠的 条件类概率的估计。一种基于 随机梯度法使多类方法适用于大型 数据集。建议制定相应的模型选择 算法。三叉图是提出者为函数指定的名称 基于分段线性、二元样条法的估计方法 一种自适应构建的三角剖分。有人建议开发一些方法 基于产生比当前更平滑的估计的三叉图 方法，并且更有效地选择基函数。 建议使用自由结样条来研究统计建模， 其中节点位置被视为参数。据称，这是 使得有可能获得考虑到 结点位置的不确定性，并应提供有关 自适应多项式样条方法的推理。 建议的方法的公开软件将是 发展起来的。