A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence
In forestry, many processes of interest are binary and they can be modeled using lifetime analysis. However, available data are often incomplete, being interval- and right-censored as well as lefttruncated, which may lead to biased parameter estimates. While censoring can be easily considered in lifetime analysis, left truncation is more complicated when individual age at selection is unknown. In this study, we designed and tested a maximum likelihood estimator that deals with left truncation by taking advantage of prior knowledge about the time when the individuals enter the experiment. Whenever a model is available for predicting the time of selection, the distribution of the delayed entries can be obtained using Bayes’ theorem. It is then possible to marginalize the likelihood function over the distribution of the delayed entries in the experiment to assess the joint distribution of time of selection and time to event. This estimator was tested with continuous and discrete Gompertz-distributed lifetimes. It was then compared with two other estimators: a standard one in which left truncation was not considered and a second estimator that implemented an analytical correction. Our new estimator yielded unbiased parameter estimates with empirical coverage of confidence intervals close to their nominal value. The standard estimator leaded to an overestimation of the long-term probability of survival
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Format: | artículo biblioteca |
Language: | English |
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Routledge
2018
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Subjects: | Lifetime analysis, Left truncation, Likelihood estimation, Marginal likelihood, Bayes’ theorem, Gompertz hazard, |
Online Access: | http://hdl.handle.net/20.500.12792/626 http://hdl.handle.net/10261/289293 |
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dig-inia-es-10261-2892932023-02-15T09:44:18Z A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence Manso, R. Calama Sainz, Rafael Argimiro Pardos Mínguez, Marta Fortin, M. Lifetime analysis Left truncation Likelihood estimation Marginal likelihood Bayes’ theorem Gompertz hazard In forestry, many processes of interest are binary and they can be modeled using lifetime analysis. However, available data are often incomplete, being interval- and right-censored as well as lefttruncated, which may lead to biased parameter estimates. While censoring can be easily considered in lifetime analysis, left truncation is more complicated when individual age at selection is unknown. In this study, we designed and tested a maximum likelihood estimator that deals with left truncation by taking advantage of prior knowledge about the time when the individuals enter the experiment. Whenever a model is available for predicting the time of selection, the distribution of the delayed entries can be obtained using Bayes’ theorem. It is then possible to marginalize the likelihood function over the distribution of the delayed entries in the experiment to assess the joint distribution of time of selection and time to event. This estimator was tested with continuous and discrete Gompertz-distributed lifetimes. It was then compared with two other estimators: a standard one in which left truncation was not considered and a second estimator that implemented an analytical correction. Our new estimator yielded unbiased parameter estimates with empirical coverage of confidence intervals close to their nominal value. The standard estimator leaded to an overestimation of the long-term probability of survival 2023-02-15T09:44:18Z 2023-02-15T09:44:18Z 2018 artículo Journal of Applied Statistics 45 (12): 2107-2127 (2018) 0266-4763 http://hdl.handle.net/20.500.12792/626 http://hdl.handle.net/10261/289293 10.1080/02664763.2017.1410527 1360-0532 en none Routledge |
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Lifetime analysis Left truncation Likelihood estimation Marginal likelihood Bayes’ theorem Gompertz hazard Lifetime analysis Left truncation Likelihood estimation Marginal likelihood Bayes’ theorem Gompertz hazard |
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Lifetime analysis Left truncation Likelihood estimation Marginal likelihood Bayes’ theorem Gompertz hazard Lifetime analysis Left truncation Likelihood estimation Marginal likelihood Bayes’ theorem Gompertz hazard Manso, R. Calama Sainz, Rafael Argimiro Pardos Mínguez, Marta Fortin, M. A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
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In forestry, many processes of interest are binary and they can be modeled using lifetime analysis. However, available data are often incomplete, being interval- and right-censored as well as lefttruncated, which may lead to biased parameter estimates. While censoring can be easily considered in lifetime analysis, left truncation is more complicated when individual age at selection is unknown. In this study, we designed and tested a maximum likelihood estimator that deals with left truncation by taking advantage of prior knowledge about the time when the individuals enter the experiment. Whenever a model is available for predicting the time of selection, the distribution of the delayed entries can be obtained using Bayes’ theorem. It is then possible to marginalize the likelihood function over the distribution of the delayed entries in the experiment to assess the joint distribution of time of selection and time to event. This estimator was tested with continuous and discrete Gompertz-distributed lifetimes. It was then compared with two other estimators: a standard one in which left truncation was not considered and a second estimator that implemented an analytical correction. Our new estimator yielded unbiased parameter estimates with empirical coverage of confidence intervals close to their nominal value. The standard estimator leaded to an overestimation of the long-term probability of survival |
format |
artículo |
topic_facet |
Lifetime analysis Left truncation Likelihood estimation Marginal likelihood Bayes’ theorem Gompertz hazard |
author |
Manso, R. Calama Sainz, Rafael Argimiro Pardos Mínguez, Marta Fortin, M. |
author_facet |
Manso, R. Calama Sainz, Rafael Argimiro Pardos Mínguez, Marta Fortin, M. |
author_sort |
Manso, R. |
title |
A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
title_short |
A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
title_full |
A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
title_fullStr |
A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
title_full_unstemmed |
A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
title_sort |
maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence |
publisher |
Routledge |
publishDate |
2018 |
url |
http://hdl.handle.net/20.500.12792/626 http://hdl.handle.net/10261/289293 |
work_keys_str_mv |
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