Inference and variable selection in semiparametric survival models with censored or missing data

每年有数百万人死于癌症。有证据表明，癌症患者的生存时间取决于许多危险因素。有些危险因素是显而易见的，而且研究得很充分，例如吸烟习惯和酗酒，而其他许多危险因素隐藏在人类的基因和dna中，不容易观察和处理。近年来，生物医学技术的突破使人们能够获得成千上万的基因表达测量，以及有关患者生存结果的临床信息。在这种情况下，研究人员和从业人员感兴趣的是(1)识别与生存相关的特征（或基因，协变量），以便他们可以检查它们的精确作用，以及(2)开发特征与生存时间之间关系的多变量模型，该模型可用于预测新的观察中的生存，并确定更好的癌症治疗策略。由于数据的高维性，从数十万个预测因子中找到数十个重要变量是一项前所未有的挑战，患者或观察的数量通常在数十或数百个。这就像在一个巨大的干草堆里找几根针一样困难。提出的新统计方法解决了变量选择中的难题。提出的方案包括方法论研究和高素质人才培训（HQP）的大量新问题。该计划所涉及的理论发展将扩展当前关于高维生存数据统计理论的知识范围。所提出的统计方法在癌症和艾滋病等人类疾病的流行病学研究中有相当大的实际应用。预期的结果将发表在被评审的科学期刊上，并将被从业者用于识别与疾病相关的重要基因，准确预测生存，然后为患者提供更好的医疗保健和各种疾病的新治疗方案。

Millions of people are killed by cancer each year. There are evidences that the survival time of cancer patients depends on many risk factors. Some of the risk factors are obvious and well studied, e.g. smoke habits and alcohol abuse, while many others are hidden in the human's genes and DNAs, which are not easy to observe and handle. In recent years, breakthroughs in biomedical technology have made it possible to obtain hundreds of thousands of gene expression measurements, along with the clinical information about the survival outcomes of patients. In this case, researchers and practitioners are interested in (1) identifying features (or genes, covariates) that are associated with survival, so that they can examine their precise roles, and (2) developing a multivariate model for the relationship between the features and the survival time that can be used to predict survival in a new observation and to identify better treatment strategies for cancers. Due to the high dimensionality of the data, it is an unprecedented challenge to find tens of important variables out of hundreds of thousands of predictors, with number of patients or observations usually in tens or hundreds. This is as hard as finding a couple of needles in a huge haystack. The proposed new statistical methods meet the challenges and shed light on the difficult problems in variable selection. The proposed program includes a wealth of new problems for methodological research and training of highly qualified personnel (HQP). The theoretical developments involved in this program will extend the scope of current knowledge about statistical theory for high-dimensional survival data. The proposed statistical methods have considerable practical applications in prevalence studies of human diseases such as cancer and AIDS. The anticipated results will be published in refereed scientific journals, and will be used by practitioners to identify important genes related to diseases, predict survival accurately, and then provide better health care for patients and new treatment solutions for various diseases.