Analysis of Doubly Truncated 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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“…( 2013 ); Frank et al. ( 2019 ); Dörre and Emura ( 2019 ). Here we simulate (i) homogeneous Markov processes, i.e.…”

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confidence: 99%

Left-censored dementia incidences in estimating cohort effects

et al. 2020

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“…On the other hand, the simulations also show that some initial values tend to diverge for small sample sizes, and hence, the randomization algorithm to search initial values plays a crucial role to guarantee the eventual convergence. An alternative is to apply the moment-based method of Frank and Dörre (2017) and Chapter 5 of Dörre and Emura (2019) in an attempt to find consistent initial estimates. However, the method involves nonparametric estimation of relevant quantities, which is not always consistent unless some support conditions are satisfied.…”

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confidence: 99%

Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

et al. 2020

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Doubly-truncated data arise in many fields, including economics, engineering, medicine, and astronomy. This article develops likelihood-based inference methods for lifetime distributions under the log-location-scale model and the accelerated failure time model based on doubly-truncated data. These parametric models are practically useful, but the methodologies to fit these models to doubly-truncated data are missing. We develop algorithms for obtaining the maximum likelihood estimator under both models, and propose several types of interval estimation methods. Furthermore, we show that the confidence band for the cumulative distribution function has closedform expressions. We conduct simulations to examine the accuracy of the proposed methods. We illustrate our proposed methods by real data from a field reliability study, called the Equipment-S data.

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“…While we consider the statistical inference of the truncated normal distribution at zero in this paper, the proposed approaches can be extended to the doubly truncated normal distribution and the singly truncated normal distribution at any fixed truncation point. The statistical inference on the doubly truncated distribution with unknown truncation points in [24] provides a good starting point for discussion and further research. Extensive work needs to be carried out in this direction.…”

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confidence: 99%

Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring

Zeng

Gui

2021

Entropy

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In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches.

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Analysis of Doubly Truncated Data

Cited by 22 publications

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Left-censored dementia incidences in estimating cohort effects

Left-censored dementia incidences in estimating cohort effects

Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring

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