Novel Statistical Methods for Data with Missing Values

描述（由申请人提供）：缺失协变量值在疾病风险因素研究和许多其他生物医学研究中很常见。常规使用的简单完整病例分析除了效率损失外，还存在偏倚。目前用于分析此类数据的先进统计方法在实践中的使用有限，这是因为稳健的关注或实施困难，或两者兼而有之。本项目旨在开发新的统计方法，用于回归模型中缺失协变量的建模，以使对缺失协变量的回归参数的推断稳健，高效，易于实现。该目标将通过四个步骤来实现：（1）针对复杂的缺失数据问题，提出了一个通用的半参数优势比模型。该模型使得实际中常用的似然法更加稳健、灵活，且易于应用。(2)缺失数据回归的似然方法在三个方面得到了进一步的鲁棒化。当缺失模式相对简单时，提出了优势比函数的光滑样条模型;当缺失模式相对复杂时，将似然估计量修改为双重稳健和局部有效的;提出了一般缺失数据机制下的灵敏度分析框架。(3)针对大量协变量存在缺失值的问题，研究了半参数协变量模型下基于插补完全数据的模型选择方法。这些程序可以非常有助于研究健康事件的风险因素，例如从一组受缺失值影响的潜在风险因素中识别骨折的风险因素。(4)对于正在审议的所有缺失数据问题，将开发和传播用于实施研究成果方法的软件。拟议的研究完成后，将使许多应用领域的研究人员更容易获得对缺失协变量值的生物医学数据的分析，从而促进有效利用有价值的数据，如艾滋病毒和癌症研究的数据。

DESCRIPTION (provided by applicant): Missing covariate values are common in studies of risk factors of diseases and in many other biomedical studies. Simple complete-case analysis which is routinely used suffers from bias in addition to efficiency loss. Current advanced statistical methods for analyzing such data have limited usage in practice because of the robust concern, or the difficulty in implementation, or both. This project aims at developing new statistical methods for modeling missing covariates in regression models to make inferences on regression parameters with missing covariates robust, efficient, and easy to implement. The objective is to be reached through four steps: (1) A general semi-parametric odds ratio model is proposed for complex missing data problems. The proposed model makes the likelihood approach commonly used in practice more robust and flexible, and easy to apply. (2) The likelihood method for regression with missing data is further robustified in three ways. When missing patterns are relatively simple, smoothing spline models for odds ratio function is proposed; When missing patterns are complex, likelihood estimator is modified to be doubly robust and locally efficient; A framework is proposed for sensitivity analysis with general missing data mechanisms. (3) For problems with a large number of covariates subject to missing values, model selection procedures are studied based on imputed complete data under the semiparametric covariate model. Such procedures can be very helpful in studying risk factors of health events, such as in identifying risk factors of bone fracture from a set of potential risk factors subject to missing values. (4) For all the missing data problems under consideration, software for implementing methods of the research outcomes will be developed and disseminated. The proposed research, when completed, will make analyses of biomedical data with missing covariate values more accessible to researchers in many applied fields and thus promote efficient use of valuable data, such as those from HIV and cancer studies.