From the inventory of the health insurer AOK in 2004, we draw a sample of a quarter million people and follow each person’s health claims continuously until 2013. Our aim is to estimate the effect of a stroke on the dementia onset probability for Germans born in the first half of the 20th century. People deceased before 2004 are randomly left-truncated, and especially their number is unknown. Filtrations, modelling the missing data, enable circumventing the unknown number of truncated persons by using a conditional likelihood. Dementia onset after 2013 is a fixed right-censoring event. For each observed health history, Jacod’s formula yields its conditional likelihood contribution. Asymptotic normality of the estimated intensities is derived, related to a sample size definition including the number of truncated people. The standard error results from the asymptotic normality and is easily computable, despite the unknown sample size. The claims data reveal that after a stroke, with time measured in years, the intensity of dementia onset increases from 0.02 to 0.07. Using the independence of the two estimated intensities, a 95% confidence interval for their difference is [0.053, 0.057]. The effect halves when we extend the analysis to an age-inhomogeneous model, but does not change further when we additionally adjust for multi-morbidity.

根据 2004 年健康保险公司 AOK 的清单，我们抽取了 25 万人的样本，并持续跟踪每个人的健康声明，直到 2013 年。我们的目标是估计中风对出生在德国的德国人痴呆症发作概率的影响20 世纪上半叶。2004 年之前死亡的人被随机左截断，尤其是他们的人数未知。过滤，对缺失数据进行建模，可以通过使用条件似然来规避未知数量的截断人员。2013年后痴呆发作是固定的右删失事件。对于每个观察到的健康史，Jacod 的公式产生其条件似然贡献。推导出估计强度的渐近正态性，与样本量定义相关，包括被截断的人数。标准误差由渐近正态性产生，并且很容易计算，尽管样本量未知。索赔数据显示，中风后，随着时间的推移，痴呆症发作的强度从 0.02 增加到 0.07。使用两个估计强度的独立性，它们差异的 95% 置信区间为 [0.053，0.057]。当我们将分析扩展到年龄不均匀模型时，效果减半，但当我们额外调整多种发病率时，效果不会进一步改变。053, 0.057]。当我们将分析扩展到年龄不均匀模型时，效果减半，但当我们额外调整多种发病率时，效果不会进一步改变。053, 0.057]。当我们将分析扩展到年龄不均匀模型时，效果减半，但当我们额外调整多种发病率时，效果不会进一步改变。