Abstract
We estimate the dementia incidence hazard in Germany for the birth cohorts 1900 until 1954 from a simple sample of Germany’s largest health insurance company. Followed from 2004 to 2012, 36,000 uncensored dementia incidences are observed and further 200,000 right-censored insurants included. From a multiplicative hazard model we find a positive and linear trend in the dementia hazard over the cohorts. The main focus of the study is on 11,000 left-censored persons who have already suffered from the disease in 2004. After including the left-censored observations, the slope of the trend declines markedly due to Simpson’s paradox, left-censored persons are imbalanced between the cohorts. When including left-censoring, the dementia hazard increases differently for different ages, we consider omitted covariates to be the reason. For the standard errors from large sample theory, left-censoring requires an adjustment to the conditional information matrix equality.
Highlights
When studying the incidence of dementia, it is necessary to acknowledge the age of a person, and useful to study the evolution over time
As the age at dementia incidence is strictly positive, the theoretical simplicity of an additive model is not appealing in demography, so that we model the effects multiplicative to the hazard as in Sect
A censoring indicator is 0, i.e. Y is uncensored, if the dementia incidence occurs in the study period
Summary
When studying the incidence of dementia, it is necessary to acknowledge the age of a person, and useful to study the evolution over time (cohort effect) Together with the 80% right-censored persons without dementia in 2013, double-censoring is the required missing data pattern (see e.g. Ren and Gu 1997; Cai and Cheng 2004; Kim et al 2013; Dörre and Weißbach 2017; Shen and Chen 2018). We estimate the effect of cohort, age and sex from the Health Claims Data (HCD), with the cohorts in decades as dummy variables. With left-censoring, the slope of that increase is smaller Another finding is that including left-censored persons increases the incidence of dementia at younger ages and attenuates the increase in dementia with age. That dementia is slightly more likely for males than for females becomes almost irrelevant after including leftcensoring
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