Incidence regression, variable selection and conditional density estimation from prevalent cohort survival data under stochastic constraints

确定痴呆症的重要危险因素和量化发病年龄对痴呆症生存率的影响是痴呆症研究人员最感兴趣的问题之一。事件队列研究招募了无病个体并对其进行随访，直至死亡、失访或研究终止，被认为是解决此类问题的金标准。然而，逻辑或其他限制因素可能会排除进行事件队列研究的可能性。因此，数据通常是从更可行的流行队列研究中收集的，通过横断面调查招募患病个体，回顾性地确定其发病时间，并对其进行随访，直至死亡或失访。这种设计通常更容易进行，成本效益高，但它产生的数据包含系统性偏差，如果忽视可能导致错误的结论。特别是，疾病持续时间较长的个体在抽样方案中的代表性过高。当这样的持续时间受到右删失时，删失是信息性的。也知道这样的抽样方案会导致协变量偏倚。 为了使用流行病例的随访研究数据来衡量不同协变量对发病率的影响，应该通过将发病率和持续时间的分布建模为协变量的函数来建立发病率模型。然后需要使用发病率和患病率之间的联系，同时考虑信息删失和协变量偏倚。在对持续时间的分布进行建模时，在估计某些协变量的影响时存在一个复杂的因素。例如，总体而言，发病年龄越大，痴呆症的生存期越短。这些信息根据发病年龄对疾病的生存率进行了随机排序，这反过来又在测量不同协变量对发病率的影响时施加了限制。 虽然我的研究动机来自加拿大健康与老龄化研究（CSHA），但我想开发的方法同样适用于任何其他具有类似结构的流行队列研究。随机排序下流行队列生存数据的条件密度的非参数和半参数估计本身具有独立的意义。首先，我计划扩展Park等人的工作。（2012，Biometrika）当数据形成目标人群的有偏样本时，扩展工作以在第二步中处理连续协变量，然后攻击发生率回归。解决诸如变量选择、拟合优度检验和有影响力的诊断等问题，同时考虑到信息审查、协变量偏差和随机排序，需要开发新的模型和方法。

Identifying important risk factors of dementia and quantifying the effect of age-at-onset on survival with dementia are among the questions of prime interest to researchers in dementia. The incident cohort study, in which disease-free individuals are recruited and followed until death, loss to follow-up or study termination, is considered to be the gold standard for addressing such questions. Logistic or other constraints may however preclude the possibility of conducting an incident cohort study. Thus data are often collected from the more feasible prevalent cohort study, whereby diseased individuals are recruited through a cross-sectional survey, determining their onset time retrospectively and following them until death or loss to follow-up. This design is often easier to conduct and cost effective, but the data it generates incorporate systematic bias that if ignored can lead to incorrect conclusions. In particular, individuals with longer disease duration times are overrepresented by the sampling scheme. When such duration times are subject to right censoring, the censoring is informative. It is also known that such sampling scheme induces covariate bias. To measure the effect of different covariates on the incidence rates using data from follow-up studies on prevalent cases, one should develop a model for incidence rate through modelling the prevalence rate and the distribution of the duration times as functions of covariates. One needs then use the connection between incidence and prevalence rates while accounting for informative censoring and covariate bias. There is a complicating factor in estimation of the effect of some covariates when modelling distribution of the duration times. For instance, overall, the greater the age-at-onset, the shorter the survival with dementia. This information imposes a stochastic ordering on survival with the disease according to the age-at-onset which, in turn, imposes a constraint when measuring the effect of different covariates on the incidence rate. Although the motivation for my study comes from the Canadian Study of Health and Aging (CSHA), but the methodology that I want to develop applies equally to any other prevalent cohort study with similar structure. Non- and semi-parametric estimation of conditional densities from prevalent cohort survival data under stochastic ordering is of independent interest on its own. First, I plan to extend the work of Park et al. (2012, Biometrika) when the data form a biased sample from the target population, extending the work to handle continuous covariates in the second step and then attack the incidence regression. Addressing issues like variable selection, goodness--of--fit tests and influential diagnostics, among others, while accounting for informative censoring, covariate bias and stochastic ordering require development of new models and methodologies.