Nonparametric predictive inference for competing risks

Coolen‐Maturi, Tahani; Coolen‐Schrijner, Pauline; Coolen, Frank P. A.

doi:10.1243/1748006xjrr263

Cited by 15 publications

(46 citation statements)

References 21 publications

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“…Sarhan et al (2010) discussed and illustrated likelihood and classical statistical approaches to competing risks data, Coolen et al (1992) presented a Bayesian competing risk approach to reliability for heat exchangers based on expert judgements. Maturi et al (2010) presented NPI for competing risks data, in particular addressing the question due to which of the competing risks the next unit will fail. Related to this approach, Coolen-Maturi and Coolen (2011) considered the effects of unobserved, re-defined, unknown or removed competing risks.…”

Section: Introductionmentioning

confidence: 99%

“…In NPI for competing risks (Maturi et al, 2010), it is assumed that there are K failure modes and a unit fails due to the first occurrence of a failure mode, which is identified with certainty. We should point out that, in this paper, we will use the terms 'failure mode' and 'competing risk' interchangeably with the same meaning.…”

Section: Introductionmentioning

confidence: 99%

“…The NPI lower and upper survival functions for the failure time of the next unit due to failure mode k, so if the unit were only at risk from this failure mode, are denoted by S X k,n+1 (t) and S X k,n+1 (t), respectively, and are as follows (Maturi et al, 2010;Coolen et al, 2002)…”

Section: Introductionmentioning

confidence: 99%

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Nonparametric predictive inference for combined competing risks data

Coolen‐Maturi

Coolen

2014

Reliability Engineering & System Safety

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. (2014) 'Nonparametric predictive inference for combined competing risks data.', Reliability engineering system safety., 126 . pp. 87-97. Further information on publisher's website:http://dx.doi.org/10.1016/j.ress. 2014.01.007 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Reliability Engineering System Safety. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Reliability Engineering System Safety, 126, 2014, 10.1016/j.ress.2014.01.007. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe nonparametric predictive inference (NPI) approach for competing risks data has recently been presented, in particular addressing the question due to which of the competing risks the next unit will fail, and also considering the effects of unobserved, re-defined, unknown or removed competing risks. In this paper, we introduce how the NPI approach can be used to deal with situations where units are not all at risk from all competing risks. This may typically occur if one combines information from multiple samples, which can e.g. be related to further aspects of units that define the samples or groups to which the units belong or to different applications where the circumstances under which the units operate can vary. We study the effect of combining the additional information from these multiple samples, so effectively borrowing information on specific competing risks from other units, on the inferences. Such combination of information can be relevant to competing risks scenarios in a variety of application areas, including engineering and medical studies.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonparametric predictive inference for combined competing risks data

Coolen‐Maturi

Coolen

2014

Reliability Engineering & System Safety

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“…They illustrated the lower and upper marginal survival functions, so each restricted to a single failure mode. While predictive inference, as considered in this approach, is different to estimation, as it explicitly considers a single future unit instead of estimating characteristics of a population distribution, it is interesting to mention that these NPI lower and upper survival functions (Coolen et al, 2002;Maturi et al, 2010b) bound the well-known Kaplan-Meier estimator (Kaplan and Meier, 1958), which is the nonparametric maximum likelihood estimator for the population survival function in case of lifetime data with right-censored observations (Coolen and Yan, 2004;Coolen-Maturi et al, 2012c).…”

Section: Introductionmentioning

confidence: 99%

“…For comparison of more than two groups under progressive censoring schemes the expressions become quite cum-bersome, but such methods can be applied using the R commands provided by Maturi (2010). This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Predictive Inference With Combined Data Under Different Right-Censoring Schemes

Coolen‐Maturi

Coolen

2014

Journal of Statistical Theory and Practice

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. (2015) 'Nonparametric predictive inference with combined data under di erent right-censoring schemes.', Journal of statistical theory and practice., 9 (2). pp. 288-304. Further information on publisher's website: Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract This paper presents nonparametric predictive inference (NPI) for meta-analysis in which multiple independent samples of lifetime data are combined, where different censoring schemes may apply to the different samples. NPI is a frequentist statistical approach based on few assumptions and with uncertainty quantified via lower and upper probabilities. NPI has the flexibility to deal with a mixture of different types of censoring, mainly because the inferences do not depend on counterfactuals, which affect several inferences for more established frequentist approaches. We show that the combined sample, consisting of differently censored independent samples, can be represented as one sample of progressively censored data. This allows explicit formulae for the NPI lower and upper survival functions to be presented which are generally applicable. The approach is illustrated through an example using a small data set from the literature, for which several scenarios are presented.

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2014

Introduction to Imprecise Probabilities

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Nonparametric predictive inference for competing risks

Cited by 15 publications

References 21 publications

Nonparametric predictive inference for combined competing risks data

Nonparametric predictive inference for combined competing risks data

Nonparametric Predictive Inference With Combined Data Under Different Right-Censoring Schemes

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