Left-Truncated Health Insurance Claims Data: Theoretical Review and Empirical Application

At the beginning of 2004, we draw a sample of size 0.25 million people from the inventory of the health insurer AOK. We followed their health claims until 2013. Our aim is the effect a stroke on the dementia onset probability, for Germans born in the first half of the 20$^{th}$ century. People deceased before 2004 are randomly left-truncated. Filtrations, modelling the missing data, enable to circumvent the unknown number of truncated persons by using a conditional instead of the full likelihood. Dementia onset after 2013 is a conditionally fixed right-censoring event. For each observed health history, Jacod's formula yields the conditional likelihood contribution. Asymptotic normality of the estimated intensities is derived, relative to a sample size definition that includes the truncated people. Yet, the standard error is observable. 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 [0.050,0.056]. 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.