Semiparametric statistical methods for censored or missing data and their applications in survival analysis and other related areas

在医学、经济学、社会科学、工程学和其他领域，从业者经常面临探索结果变量和协变量集之间的关系以用于预测目的的问题。由于数据的删失和缺失，标准的统计方法往往不能直接用于解决问题。几乎所有的科学学科都会出现删失数据和缺失数据。例如，在临床试验中，研究人员感兴趣的是评估治疗对HIV-1血清阳性吸毒者生存率的影响，并对其他预测协变量进行调整，如BMI（体重指数）和年龄。当研究终止时，一些患者可能仍然存活，并且他们的生存时间被删失。又例如，部分病人的尸体解剖可能未能进行，而失败的原因亦不清楚。在这种情况下，删失指标的某些值缺失。在许多情况下，人们只是简单地删除任何数据被审查或丢失的记录，并进行所谓的“完整案例分析”。这样的分析可能导致严重的偏见和错误的结论。此外，可能有许多协变量，很难选择重要的协变量。例如，研究人员需要在微阵列分析中选择活性基因来预测患者的存活率。基因表达数据的高维性是一个挑战。这个建议是开发半参数模型，以解决上述真实的应用中出现的所有问题。半参数模型是同时包含参数和非参数分量的模型。这类模型允许灵活的协变量效应;它们起着降维的作用，避免了维数灾难;这类模型中的估计量比传统的参数模型和纯非参数模型更稳健和有效。因此，半参数模型的研究具有挑战性和价值。拟议研究的成果将有助于统计理论的发展，并有助于为所有加拿大人带来繁荣的好处。此外，这项研究将大大有助于高素质的加拿大年轻专业人员的培训。

In medicine, economics, social science, engineering and other fields, practitioners are often faced with problems of exploring the relationship between an outcome variable and a set of covariates for prediction purposes. The standard statistical methods are often not directly available to solve the problems due to censored and missing data. Censored and missing data arise in almost all scientific disciplines. For example, in a clinical trial, the investigators are interested in evaluating the effect of a treatment on survival in HIV-1 seropositive drug users, adjusted for other predictive covariates such as BMI (body mass index) and age. Some patients may be still alive when the study terminates and their survival times are censored. In another example, autopsy for some patients may not be carried out and the failure causes are unknown. In this situation, some values of censoring indicators are missing. In many cases, people just simply delete records for which any data are censored or missing, and conduct the so-called "complete-case analysis". Such an analysis can lead to severe biases and wrong conclusions. Moreover, there may be many covariates and it is difficult to select important ones. For instance, investigators need to select active genes to predict patients' survival in microarray analysis. There is a challenge of high dimensionality of the gene expression data. This proposal is to develop semiparametric models to address all the issues arising from the aforementioned real applications. Semiparametric models are the models that include both a parametric and nonparametric component. Such models allow flexible covariate effects; they play the role of dimension reduction and avoid the curse of dimensionality; estimators in such models are more robust and efficient than in traditional parametric models and pure nonparametric models. Therefore, it is challenging and rewarding to work on semiparametric models. The outcomes of the proposed research will make contributions to the development of statistical theory and help bring the benefits of prosperity to all Canadians. In addition, the research will contribute significantly to the training of highly qualified young Canadian professionals.