Left-censored dementia incidences in estimating cohort effects
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Left-censored dementia incidences in estimating cohort effects Rafael Weißbach1 · Yongdai Kim2 · Achim Dörre1 · Anne Fink3 · Gabriele Doblhammer3,4 Received: 26 June 2019 / Accepted: 26 August 2020 © The Author(s) 2020
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. Keywords Censoring · Conditional likelihood · Confidence interval · Dementia · Hazard rate
1 Introduction 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) (Doblhammer et al.
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Rafael Weißbach [email protected]
1
Chair in Statistics and Econometrics, Faculty for Economic and Social Sciences, University of Rostock, 18051 Rostock, Germany
2
Department of Statistics, Seoul National University, Seoul, Korea
3
German Center for Neurodegenerative Diseases, Bonn, Germany
4
Chair in Empirical Social Research/Demography, Faculty for Economic and Social Sciences, University of Rostock, Rostock, Germany
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R. Weißbach et al.
2013; Wu et al. 2016). From data of the nine-year period 2004 until 2012, we observe, for the German population born between 1900 and 1954, the ages at which dementia is diagnosed. For insurants of Germany’s largest Health insurance, we drew a simple random sample of 250,000 persons in 2004. An insurant with dementia incidence before the study period, i.e. prior to 2004, is left-censored. 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. Given that our data are a random sample, covariates are random as well, and we maximize the likelihood, conditional on the covariates (CMLE). In order to derive consistency and asymptotic normality for double censoring, as Ren and Gu (1997) and Cai and Cheng (2004) do, we apply the results about M-estimation, however for a different model or criterion funct
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