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并量化发病年龄对痴呆症患者存活率的影响是痴呆症研究人员最感兴趣的问题之一。事件队列研究被认为是解决此类问题的黄金标准，在该研究中，招募了无疾病的人，并对其进行跟踪，直到死亡、失去随访或研究终止。然而，后勤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，数据通常从更可行的流行队列研究中收集，通过横断面调查招募患病个体，追溯确定他们的发病时间，并对他们进行跟踪，直到死亡或失去随访。这种设计通常更容易进行，也更具成本效益，但它产生的数据包含了系统性偏差，如果忽略这些偏差，可能会导致错误的结论。特别是，疾病持续时间较长的个体被抽样方案高估了。当这样的持续时间受到正确的审查时，审查是信息丰富的。为了利用流行病例跟踪研究的数据来衡量不同协变量对发病率的影响，应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，人们需要使用发病率和流行率之间的联系，同时考虑到信息性审查和协变量偏差。在对持续时间的分布建模时，在估计某些协变量的影响时有一个复杂的因素。例如，总体而言，发病年龄越大，痴呆症患者的生存时间就越短。这些信息根据发病年龄对患者的生存进行随机排序，进而在衡量不同协变量对发病率的影响时施加限制。虽然我研究的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结构相似的流行队列研究。在随机排序下，从流行的队列生存数据中进行条件密度的非参数和半参数估计本身就具有独立的意义。首先，我计划扩展Park等人的工作。当数据形成来自目标人群的有偏样本时，将工作扩展到处理第二步中的连续协变量，然后攻击关联回归。解决变量选择、拟合度检验和有影响力的诊断学等问题，同时考虑信息性审查、协变量偏差和随机排序等问题，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.