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。一些危险因素是显而易见的，也得到了充分的研究，例如吸烟习惯和酗酒，而其他许多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获得数十万个基因表达测量以及有关患者生存结果的临床信息成为可能。在这种情况下，研究人员和从业者感兴趣的是(1)识别与生存相关的特征(或基因、协变量)，以便他们能够检查它们的确切作用，以及(2)开发特征与生存时间之间的关系的多变量模型，该模型可用于在新的观察中预测生存并确定更好的癌症治疗策略。

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.