Statistical Methods for the Design and Analysis of Studies with Incomplete Data

缺失数据是一个常见的问题，可以在任何研究设置中遇到的，由于在研究的实施中意想不到的问题。从这样的研究中得出的结论只有在统计分析中适当处理缺失的数据时才有效。然而，在有多种机制导致失踪的情况下，统计方法不发达。如果兴趣在于由几个可能缺失的变量构造的复合分数，那么缺失的数据机制将是复杂的，模型错误规范将成为一个真正的问题。我将开发统计方法，并为这些环境中的有效分析策略提供实用建议。******此外，数据缺失可能是由于设计造成的。当评估一个变量的成本特别高时，只针对预先指定的验证子集对其进行度量变得越来越普遍。验证子集的最优选择可以带来极大的效率提升。然而，在纵向研究中，确定这种最优子样本的统计方法尚不发达。我将开发有效的多相响应相关设计，以指导在纵向队列研究中每一波数据收集中测量昂贵暴露变量的个体选择。这些程序将是自适应的，并将利用在以前的时间点收集的信息。将推导出最优设计，结果是信息量最大的完全观察子样本，以最大限度地提高参数估计的精度，并大大提高显著性检验的能力。******这个创新的研究项目将利用我的专业知识开发新颖的统计方法，有效地设计和分析不完整数据的研究，并为8名统计和生物统计研究生提供先进的统计研究培训。该程序将为研究人员提供强大的设计工具，以进行具有昂贵协变量的纵向队列研究，并在单个研究中可能存在不同的缺失来源时，为适当的分析策略提供重要见解。这一理论统计研究的动机是与加拿大各地的应用研究人员合作；该项目的结果将为研究人员设计诸如加拿大老龄化纵向研究等研究提供新的工具，并将为从事研究人员分析涉及感染性疾病（如艾滋病毒）和非传染性疾病（如心脏病）的复杂风险因素的研究提供更高的有效性。简而言之，这项研究计划将使许多研究领域受益，这些领域正在努力应对数据丢失和数据收集预算限制所带来的挑战

Missing data is a common problem that can be encountered in any research setting due to unanticipated problems in the implementation of a study. Conclusions drawn from such a study are only valid if the missing data are appropriately handled in the statistical analyses. However, statistical methodology is underdeveloped in settings where there are multiple mechanisms contributing to missingness. If interest lies in a composite score that is constructed from several potentially missing variables, then the missing data mechanism will be complex and model misspecification becomes a real concern. I will develop statistical methodologies and provide practical recommendations for effective analysis strategies in these settings.******Additionally, missing data can arise by design. When a variable is particularly expensive to assess, it is increasingly common to measure it only for a prespecified validation subset. Optimal selection of the validation subset can lead to great efficiency gains. However, statistical methods for determining such optimal subsamples are underdeveloped in longitudinal studies. I will develop efficient multiphase response-dependent designs to guide selection of individuals for measurement of expensive exposure variables at each wave of data collection in longitudinal cohort studies. These procedures will be adaptive and will exploit information gathered at previous time points. Optimal designs will be derived that result in the most informative completely-observed subsample to maximize the precision of parameter estimates and greatly increase the power of significance tests.******This innovative research program will capitalize on my expertise to develop novel statistical methodology for efficient design and analysis of studies with incomplete data and to provide advanced statistical research training for 8 statistics and biostatistics graduate students. This program will provide powerful design tools for researchers conducting longitudinal cohort studies with expensive covariates and provide important insight into appropriate analysis strategies when there may be distinct sources of missingness within a single study. This theoretical statistics research has been motivated by collaborations with applied researchers throughout Canada; the results from this program will provide novel tools to researchers designing studies such as the Canadian Longitudinal Study on Aging, and will offer increased validity to engaged researchers performing analyses of studies involving complex risk factors for both infectious disease (eg, HIV) and non-infectious diseases (eg, heart disease). In short, this research program will benefit many fields of research which struggle with challenges arising from missing data and budgetary constraints in data collection.**