Nearest neighbor hazard estimation with left-truncated duration data

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.

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“…For an introduction to truncation see Weißbach et al. ( 2013 ); Frank et al. ( 2019 ); Dörre and Emura ( 2019 ).…”

Section: Discussionmentioning

confidence: 99%

Left-censored dementia incidences in estimating cohort effects

et al. 2020

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“…The size of the truncated sample was subsequently considered again as random in Woodroofe (1985), and conditioning was used to prove consistency. Neighbouring contemporaneous work on truncation in survival analysis, mostly semi-and non-parametrically are (Shen 2010;Moreira and de Uña-Álvarez 2010;Weißbach et al 2013;Emura et al 2015Emura et al , 2017Frank et al 2019;Dörre 2020).…”

Section: Introductionmentioning

confidence: 99%

Truncating the exponential with a uniform distribution

Weißbach

Wied

2021

Stat Papers

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For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution. Hence, the data is a truncated empirical process that we can approximate by a Poisson process when only a small portion of the sample is observed, as is the case for our applications. We derive the likelihood from standard arguments for point processes, acknowledging the size of the latent sample as the second parameter, and derive the maximum likelihood estimator for both. Consistency and asymptotic normality of the estimator for the Exponential parameter are derived from standard results on M-estimation. We compare the design with a simple random sample assumption for the observed durations. Theoretically, the derivative of the log-likelihood is less steep in the truncation-design for small parameter values, indicating a larger computational effort for root finding and a larger standard error. In applications from the social and economic sciences and in simulations, we indeed, find a moderately increased standard error when acknowledging truncation.

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Strong consistency of the general rank estimator

Bindele

2016

Communications in Statistics - Theory and Methods

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Nearest neighbor hazard estimation with left-truncated duration data

Cited by 4 publications

References 22 publications

Left-censored dementia incidences in estimating cohort effects

Left-censored dementia incidences in estimating cohort effects

Truncating the exponential with a uniform distribution

Strong consistency of the general rank estimator

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