In prevalent cohort studies with follow-up, if disease duration is the focus, the date of onset must be obtained retrospectively. For some diseases, such as Alzheimer’s disease, the very notion of a date of onset is unclear, and it can be assumed that the reported date of onset acts only as a proxy for the unknown true date of onset. When adjusting for onset dates reported with error, the features of left-truncation and potential right-censoring of the failure times must be modeled appropriately. Under the assumptions of a classical measurement error model for the onset times and an underlying parametric failure time model, we propose a maximum likelihood estimator for the failure time distribution parameters which requires only the observed backward recurrence times. Costly and time-consuming follow-up may therefore be avoided. We validate the maximum likelihood estimator on simulated datasets under varying parameter combinations and apply the proposed method to the Canadian Study of Health and Aging dataset.

中文翻译：

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在初始发病日期的测量中具有不确定性的流行队列数据的参数化建模。

在广泛的队列研究中，如果以疾病持续时间为重点，则必须回顾性地确定发病日期。对于某些疾病，例如阿尔茨海默氏病，起病日期的概念尚不清楚，可以假设报告的起病日期仅代表未知的真实起病日期。在调整报告有错误的开始日期时，必须对失败时间的左截断和可能的右删失进行适当建模。在针对开始时间的经典测量误差模型和潜在的参数故障时间模型的假设下，我们为故障时间分布参数提出了一个最大似然估计器，该估计器仅需要观察到的向后递归时间。因此可以避免昂贵且费时的随访。