Efficient Analysis of Competing Risks Models with Missing Data

在艾滋病毒疫苗效力研究中，可能缺失了非常高比例的相关标记，这一问题归因于艾滋病毒不断演变的性质。本文提出了几种有效的统计方法来处理竞争风险模型下的缺失点。研究者将研究具有时变效应的标记特异性比例风险模型和标记特异性Cox模型。在所提出的模型下，标记特异性疫苗的效力可以用其中一个回归函数来表示。为了评估标记特异性疫苗的效果及其对标记的依赖性，研究者研究了具有时变效应的标记特异性比例风险模型和标记特异性Cox模型，这些模型在标记变量的每个水平上都保持不变。在标记、故障时间和协变量之间有一个内在的结构。对给定辅助变量的标记变量的条件分布的任意建模，如现有文献中所做的那样，可能会与基础模型发生冲突并导致不一致。研究者提出了一个两阶段的方法来实现更有效的估计程序。第一阶段导出了逆概率加权完全情况估计量。在第一阶段估计量的基础上，利用增广逆概率加权完全情况法的思想，得到了两阶段有效估计过程。将制定统计程序，以便更有效地评价艾滋病毒疫苗的效力。竞争风险模型中缺失标记的问题并不是艾滋病毒疫苗功效试验所独有的。其他统计模型的分析使用竞争风险数据与缺失标记也将进行研究。提出的方法将在理论上得到证明，在模拟中进行评估，并应用于分析艾滋病毒疫苗功效试验。随机安慰剂对照的预防性HIV疫苗疗效试验的目的是评估疫苗预防感染的效果与暴露于疫苗结构中所代表的HIV毒株的遗传距离之间的关系。研究者提出了一些有效的统计方法来评估艾滋病毒疫苗的有效性，当遗传距离（或标记）的高百分比可能由于艾滋病毒的进化性质而丢失。缺失的标记也可能出现在其他医学研究的竞争性风险数据中。研究者建议在具有时变效应的标记特异性比例风险模型和标记特异性Cox模型下研究疫苗的效力。这些模型对研究HIV疫苗的有效性有明确的生物学解释。其他使用竞争风险数据和缺失标记的统计模型也将被研究。拟议的研究将提供开发更有效疫苗所需的关键统计工具，并丰富对相互竞争的风险数据的风险分析具有重要影响的统计工具集合。

In the HIV vaccine efficacy study, a very high percentage of marks of interest may be missing and the problem is attributed to the evolving nature of the HIV viruses. This proposal proposes some efficient statistical methods for dealing with missing marks under competing risks models. The investigator will investigate the mark-specific proportional hazards model and the mark-specific Cox model with time-varying effects. The mark-specific vaccine efficacies can be expressed in terms of one of the regression functions under the proposed models. To evaluate mark-specific vaccine effects and its dependence on the mark, the investigator studies the mark-specific proportional hazards model and the mark-specific Cox model with time-varying effects that hold at each level of the mark variable. There is a built-in structure between the mark, failure times and covariates. Arbitrary modeling of the conditional distributions of the mark variable given theauxiliary variables, as did in the existing literature, may run into conflicts with the underlying models and result in inconsistency. The investigator proposes a two-stage approach to achieve more efficient estimation procedures. The inverse probability weighted complete-case estimators are derived in the first stage. The two-stage efficient estimation procedure is obtained using the idea of the augmented inverse probability weighted complete-case method and based on the first stage estimators. The statistical procedures will be developed to more effectively evaluate HIV vaccine efficacies. The problems of missing marks in competing risks models are not unique to the HIV vaccine efficacy trials. The analysis of other statistical models using competing risks data with missing marks will also be studied. The proposed methods will be justified theoretically, evaluated in simulations and applied to analyze the HIV vaccine efficacy trials.An objective of randomized placebo-controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain(s) represented in the vaccine construct. The investigator proposes some efficient statistical methods to evaluate the HIV vaccine efficacies when a high percentage of the genetic distances (or marks) may be missing due to the evolving nature of the HIV viruses. The missing marks can also occur in competing risks data from other medical studies. The investigator proposes to study the vaccine efficacies under the mark-specific proportional hazards model and the mark-specific Cox model with time-varying effects. These models have clear biological interpretations for studying HIV vaccine efficacies. Other statistical models using competing risks data with missing marks will also be studied. The proposed research would provide critical statistical tools needed for developing more effective vaccines and enrich a collection of statistical tools which have important impact on the risk analysis of competing risks data.