Bayesian estimation of a lifetime distribution under double truncation caused by time-restricted data collection

Dörre, Achim

doi:10.1007/s00362-017-0968-7

Cited by 23 publications

(12 citation statements)

References 14 publications

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“…See Mandel, de Uña‐Álvarez, Simon, and Betensky () for further discussion and access to the recent literature. Applications with doubly truncated data include, among others, astronomy (Efron & Petrosian, ), epidemiology (Mandel et al., ; Zhu & Wang, ), reliability engineering (Ye & Tang, ), and finance (Dörre, ).…”

Section: Discussionmentioning

confidence: 99%

Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Uña‐Álvarez

2020

Biometrical J

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Registry data typically report incident cases within a certain calendar time interval. Such interval sampling induces double truncation on the incidence times, which may result in an observational bias. In this paper, we introduce nonparametric estimation for the cumulative incidences of competing risks when the incidence time is doubly truncated. Two different estimators are proposed depending on whether the truncation limits are independent of the competing events or not. The asymptotic properties of the estimators are established, and their finite sample performance is investigated through simulations. For illustration purposes, the estimators are applied to childhood cancer registry data, where the target population is peculiarly defined conditional on future cancer development. Then, in our application, the cumulative incidences inform on the distribution by age of the different types of cancer. K E Y W O R D Sinterval sampling, multi-state data, survival analysis 852

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Section: Discussionmentioning

confidence: 99%

Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Uña‐Álvarez

2020

Biometrical J

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“…By conditioning on the random sample size n, however, we construct a likelihood function with proper iid terms. For more technical details in a similar model, see Dörre (2020).…”

Section: Likelihood Functionmentioning

confidence: 99%

“…Parametric models have been developed partly to address the drawbacks of the nonparametric approach (see Emura et al 2017;Dörre and Emura 2019). In Dörre (2020), fully parametric models have been studied in a setting similar to the one studied here. Finally, semi-parametric models (see Wang 1989;Shen 2010b) have been proposed in the context of double truncation.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric likelihood inference for heterogeneous survival data under double truncation based on a Poisson birth process

Dörre

2021

Jpn J Stat Data Sci

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We study a selective sampling scheme in which survival data are observed during a data collection period if and only if a specific failure event is experienced. Individual units belong to one of a finite number of subpopulations, which may exhibit different survival behaviour, and thus cause heterogeneity. Based on a Poisson process model for individual emergence of population units, we derive a semiparametric likelihood model, in which the birth distribution is modeled nonparametrically and the lifetime distributions parametrically, and define maximum likelihood estimators. We propose a Newton–Raphson-type optimization method to address numerical challenges caused by the high-dimensional parameter space. The finite-sample properties and computational performance of the proposed algorithms are assessed in a simulation study. Personal insolvencies are studied as a special case of double truncation and we fit the semiparametric model to a medium-sized dataset to estimate the mean age at insolvency and the birth distribution of the underlying population.

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“…He et al [30] presented an optimization design method for implementing reliability analysis with truncated normal random variables. Dörre [31] proposed a Bayesian estimation method for lifetime inference based on doubly truncated time-restricted samples. New Bayesian estimation methods about lifetime inferences can be found in the literature.…”

Section: Historical Review and Literature Reviewmentioning

confidence: 99%

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

et al. 2020

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The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.

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Bayesian estimation of a lifetime distribution under double truncation caused by time-restricted data collection

Cited by 23 publications

References 14 publications

Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Semiparametric likelihood inference for heterogeneous survival data under double truncation based on a Poisson birth process

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

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