Statistical methodologies for survival data with possible correlated survival times or a possible surviving fraction

这项研究的目标是调查与生存数据相关的一些重要的统计问题，并提出创新的统计模型和方法来分析数据。其中一些问题与适当处理生存数据有关，可能存在存活或治愈的部分。我们将提出新的检验方法来检测存活分数的存在，新的模型来处理聚集数据中生存时间之间可能的相关性，以及新的模型和方法来处理可能丢失的协变量。我们将研究最近提出的一些半参数曲线模型的模型可辨识性和渐近性质。我们还将研究新的统计方法，以提高现有模型和方法的稳健性或效率。我们将考虑基于零膨胀泊松模型的离散数据的类似问题。其他问题与衡量生存数据的时间相关协变量/标记物的诊断和预测能力有关。我们将提出新的方法来评估生存数据的时间相关协变量/标记物的诊断和预测准确性。我们将考虑具有生存分数的生存数据的新评估方法。我们还将研究新的方法来定位标记物/协变量，以便在具有多种治疗方法的临床试验中为治疗选择提供更好的指导。完成后，该程序将通过提供新的统计模型和方法来分析具有可能相关的生存时间或可能的生存分数的生存数据，从而为生存分析做出贡献。这将极大地扩大生存模型在健康相关研究、工程学、计量经济学和生物学中的适用性，这些领域中研究的数据类型在本项目中是常见的。它还将通过提供适合于培训的各种级别的研究项目，为硕士和博士水平的研究生培训和研究员做出贡献。这项研究计划有望在一流的生物统计期刊上发表高质量的文章。

The objective of this research program is to investigate some important statistical issues related to survival data and to propose innovative statistical models and methods to analyze the data. Some of the issues relate to properly handling survival data with a possible surviving or cure fraction. We will propose new test procedures to detect the presence of the surviving fraction, new models to deal with possible correlation among survival times in clustered data, and new models and methods to deal with possible missing covariates. We will investigate the model identifiability and asymptotic properties of some recently proposed semiparametric cure models. We will also investigate new statistical approaches that improve the robustness or the efficiency of existing models and methods. We will consider similar issues for discrete data based on zero-inflated Poisson model. Other issues relate to measuring diagnostic and predictive power of time-dependent covariates/markers for survival data. We will propose new methods to evaluate diagnostic and predictive accuracy of time-dependent covariates/markers for survival data. We will consider new evaluation methods for survival data with a surviving fraction. We will also investigate new methods to locate markers/covariates that provide better guidelines in treatment selection in clinical trails with multiple treatments available. When finished, this program will contribute to survival analysis by providing novel statistical models and methods for analyzing survival data with possible correlated survival times or a possible surviving fraction. It will greatly expand the applicability of the survival models in health related studies, engineering, econometrics, and biology, where the types of the data investigated in this program are commonly found. It will also contribute to graduate students training, both Master's level and PhD level, and research fellows by providing various levels of research projects suitable for the training. High quality publications in the first rate biostatistical journals can be expected from this research program.