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

TL;DR

This paper develops a theoretical framework and applies it empirically to analyze how stroke influences dementia onset probability using left-truncated health insurance claims data, addressing missing data and censoring issues.

Contribution

It introduces a novel approach for handling left-truncated claims data and derives asymptotic properties of estimated intensities in this context.

Findings

Dementia onset intensity increases significantly after stroke

Estimated effect size of stroke on dementia onset is approximately 0.05

Adjusting for age and multi-morbidity reduces the effect size by half

Abstract

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.