Statistical Methodologies for Competing Risks

在生物医学研究的生存数据分析中经常出现竞争风险。本研究计划的主要目标是为存在竞争风险的多事件聚类数据开发适当的统计方法。我建议开发一个渐进的竞争风险模型作为一个经典的竞争风险模型，在每个阶段的个人可以经历不同的事件的扩展。该模型将进一步发展，以适当考虑复杂的相关结构。具体来说，我有四个目标，这项研究：（1）开发一个通用的方法来模拟连续事件的竞争风险的存在;（2）处理复杂的依赖结构;（3）纳入时间依赖或区间删失协变量;（4）评估模型的预测性能。目的（一）：在存在竞争风险的情况下，为相关生存数据建立多阶段疾病过程中发生的连续事件的渐进模型。我们将开发一个渐进的竞争风险模型，使用两种常用的方法的基础上的原因特定的风险和子分布风险回归。然后，我们将评估竞争事件对每个事件阶段发展感兴趣事件的绝对风险的影响。目标（二）：开发统计方法来处理由于个人内部多个事件之间的相关性和家庭成员之间的相关性而发生的复杂依赖结构。基于个体特异性和家族特异性的随机变量，可以采用嵌套脆弱性模型来适应分层依赖。此外，Copula模型将用于连接多个结果的边缘分布，而嵌套脆弱模型将考虑复杂的家庭相关性。目的（3）：为所提出的模型建立时间依赖或区间删失协变量的统计方法。区间删失数据出现在纵向研究中，其中事件的时间没有直接观察到，但只知道发生在一个时间间隔内。我们将开发估计程序来处理区间删失数据，特别是将时间依赖或区间删失协变量纳入所提出的模型，以检查它们在多个疾病过程的不同阶段的影响。目的（4）：在疾病过程中存在沿着竞争性风险的情况下，制定未来事件发生风险的预测措施。我们将根据目标1中提出的模型推导出几种预测措施，如累积发生率函数和转移概率。此外，我们将导出一个动态累积函数，该函数估计在固定时间窗口内发生感兴趣事件的条件概率（例如，5-年预测）。对于统计推断，我们将进一步开发稳健的方差估计和置信区间，用于比较不同协变量集的累积发生率曲线或动态预测曲线。基于提出的预测措施，我们将评估和比较模型的预测性能。我们认为，拟议的发展和评估的统计方法，从相关的生存数据中存在的竞争风险的多事件过程将有重要的应用遗传和生物医学研究问题，特别是阐明许多复杂疾病的遗传基础。

Competing risks often arise in the analysis of survival data in biomedical research. The primary objective of this research program is to develop appropriate statistical methodology for clustered data with multiple events in the presence of competing risks. I propose to develop a progressive competing risks model as an extension of a classical competing risks model where at each stage individuals can experience different events. This model will be further developed to appropriately take into account the complex correlation structures. Specifically, I have four aims for this research: (1) to develop a general methodology for modeling successive events in the presence of competing risks; (2) to handle complex dependence structures; (3) to incorporate time-dependent or interval-censored covariates; (4) to evaluate the predictive performance of the model. Aim (1): Establish a progressive model for successive events occurring in multiple-stage disease processes for correlated survival data in the presence of competing risks. We will develop a progressive competing risk model using two commonly used approaches based on the cause-specific hazard and subdistribution hazard regressions. We will then evaluate the impact of competing events on the absolute risks of developing the event of interest at each event stage. Aim (2): Develop statistical approaches for handling complex dependence structures occurring due to the correlation among multiple events within individuals and the correlation among family members. Nested frailty models can be adopted to accommodate the hierarchical dependencies based on individual-specific and family-specific random variables. In addition, Copula models will be adopted for joining marginal distributions of multiple outcomes while nested frailty models will take into account complex familial correlations. Aim (3): Develop statistical methods for time-dependent or interval-censored covariates for the proposed models. Interval-censored data arise in longitudinal studies where the time to an event is not directly observed but is known only to have occurred within an interval of time. We will develop estimation procedures to handle interval-censored data, especially to incorporate time-dependent or interval-censored covariates into the proposed model to examine their effects at different stages of multiple disease processes. Aim (4): Develop predictive measures for the risk of developing a future event in the presence of competing risks along the disease process. We will derive several predictive measures such as cumulative incidence functions and transition probabilities based on the model proposed in Aim 1. In addition, we will derive a dynamic cumulative function that estimates the conditional probability of developing an event of interest within a fixed window of time (e.g., 5-year prediction). For statistical inference, we will further develop the robust variance estimates and confidence intervals for comparing cumulative incidence curves or dynamic prediction curves at different covariate sets. Based on the proposed predictive measures, we will evaluate and compare the predictive performance of the model. We believe that the proposed development and evaluation of statistical methodologies for multiple event processes obtained from correlated survival data in the presence of competing risks will have important applications to genetic and biomedical research problems, in particular, to elucidate the genetic basis of many complex diseases.