Analysis of prevalent cohort survival data

横断面抽样是一种数据收集方案，通常用于对病情持续时间的随访研究，即逻辑或其他限制因素排除了自病情发生以来对受试者进行随访的可能性。例如，感兴趣的情况可能是一种疾病，在医学应用中，或者在劳动力研究中的失业时期。通过横断面调查招募的受试者已经经历了感兴趣的状况的发作，比如一种疾病。此类病例在流行病学研究中被称为流行病例。众所周知，就流行病例收集的持续时间数据是有偏见的。事实上，持续时间较长的受试者被纳入样本的机会更大。在有后续行动的横断面调查中遇到的另一个复杂问题是信息性审查问题。横断面调查的后一个特点，使得在经典生存分析中直接应用现有方法，即基于事件案例的分析是不可能的。因为，失效与审查时间之间的独立性在经典背景下使用的鞅机器中起着至关重要的作用。除了上述特征，提交给我们进行分析的数据还有许多其他特点，这些特点似乎被许多其他流行的队列研究所共享。例如，在许多流行的队列研究中，确定疾病的发病是一个巨大的挑战。疾病的发病可能是完全未知的，或者充其量对许多受试者来说是不确定的。协变量的建模和分析是流行的队列研究中的另一个复杂问题。虽然在应用中经常使用Cox偏似然的修正，但可以证明，使用该模型得到的估计量虽然是一致的，但并不是最有效的。

Cross-sectional sampling is a data collection scheme often used in follow-up studies on duration of a condition when logistic or other constraints preclude the possibility of following-up subjects since initiation of the condition. The condition of interest may be, for instance, a disease, in medical applications, or the unemployment spell in labour force studies. Subjects recruited through a cross-sectional survey have already experienced the onset of the condition of interest, say a disease. Such subjects are known as prevalent cases in epidemiological studies. It is well-known that the duration data collected on prevalent cases are biased. In fact, subjects with longer duration have a greater chance to be included in the sample. A further complication encountered in a cross-sectional survery with follow-up is the issue of informative censoring. This latter feature of cross-sectional surverys, render any direct application of existing methodologies in the classical survival analysis, i.e. analysis based on incident cases, impossible. For, the independence between failure and censoring time plays a crucial role in the martingale machinary used in the classical setting. In addition to the aforementioned features, the data presented to us for analysis have quite a number of other peculiarities which are seemingly shared by many other prevalent cohort studies. Ascertainment of the disease onset is, for example, a great challenge in many prevalent cohort studies. The onset of disease may be completely unknown or, at best, known with uncertainty for many subjects. Modelling and analysis of covariates is another complicated issue in prevalent cohort studies. While a modification of Cox partial likelihood has been used quite often in application, it is possible to show that the estimators obtained using this model, while consistent, are not most efficient.