Consider lifetimes originating at a series of calendar times \( t_{1} ,t_{2} , \ldots \). At a certain time \( t_{0} \) a cross-sectional sample is taken, generating a sample of current durations (backward recurrence times) of survivors until \( t_{0} \) and a prevalent cohort study consisting of survival times left-truncated at the current durations. A Lexis diagram is helpful in visualizing this situation. Survival analysis based on current durations and prevalent cohort studies is now well-established as long as all covariates are observed. The general problems with unobserved covariates have been well understood for ordinary prospective follow-up studies, with the good help of hazard rate models incorporating frailties: as for ordinary regression models, the added noise generates attenuation in the regression parameter estimates. For prevalent cohort studies this attenuation remains, but in addition one needs to take account of the differential selection of the survivors from initiation \( t_{i} \) to cross-sectional sampling at \( t_{0} \). This paper intends to survey the recent development of these matters and the consequences for routine use of hazard rate models or accelerated failure time models in the many cases where unobserved heterogeneity may be an issue. The study was inspired by concrete problems in the study of time-to-pregnancy, and we present various simulation results inspired by this particular application.

中文翻译：

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流行的队列研究和未观察到的异质性。

请考虑源自一系列日历时间\（t_ {1}，t_ {2}，\ ldots \）的生命周期。在某个时间\（t_ {0} \）上获取横截面样本，生成直到\（t_ {0} \）之前幸存者当前持续时间（向后复发时间）的样本，并进行包括生存期在内的广泛队列研究在当前持续时间被左截断的时间。Lexis图有助于可视化这种情况。只要观察到所有协变量，就可以很好地建立基于当前持续时间和流行队列研究的生存分析。未观察到的协变量的一般问题在结合了脆弱性的危险率模型的良好帮助下，对于普通的前瞻性随访研究已经广为人知：对于普通的回归模型，增加的噪声会在回归参数估计中产生衰减。对于流行的队列研究，这种衰减仍然存在，但除此之外，还需要考虑幸存者从起始\（t_ {i} \）到\（t_ {0} \）处的横截面采样的差异选择。。本文旨在调查这些问题的最新发展，以及在许多情况下可能会出现未观察到的异质性的情况下，使用风险率模型或加速故障时间模型的常规后果。这项研究是受怀孕时间研究中的具体问题启发的，我们提供了受此特定应用启发的各种模拟结果。