Novel Statistical Methods for Data with Missing Values

描述(由申请人提供)：在疾病风险因素研究和许多其他生物医学研究中，缺少协变量值是很常见的。常规使用的简单完整案例分析除了效率损失外，还存在偏差。目前用于分析这类数据的先进统计方法在实践中的使用有限，原因是存在强烈的关切，或实施困难，或两者兼而有之。这个项目的目的是开发新的统计方法来建模回归模型中的缺失协变量，以对具有缺失协变量的回归参数进行稳健、高效和易于实现的推断。研究目标通过四个步骤来实现：(1)针对复杂缺失数据问题，提出了一种通用的半参数优势比模型。该模型使实际中常用的似然方法具有更强的稳健性和灵活性，更易于应用。(2)对缺失数据回归的似然方法从三个方面作了进一步的改进。当缺失模式相对简单时，提出了概率比函数的光滑样条模型；当缺失模式较复杂时，改进了似然估计，使其具有双重稳健性和局部有效性；提出了一般缺失数据机制下的敏感度分析框架。(3)对于协变量数量较多且存在缺失值的问题，研究了半参数协变量模型下基于输入完全数据的模型选择方法。这类程序可以非常有助于研究健康事件的风险因素，例如从一组可能存在缺失值的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。这项拟议的研究完成后，将使许多应用领域的研究人员更容易对缺少协变量值的生物医学数据进行分析，从而促进有效利用有价值的数据，例如来自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.