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Journal ArticleDOI

Analysis of Type-II hybrid censored competing risks data

07 Aug 2017-Statistics (Taylor & Francis)-Vol. 51, Iss: 6, pp 1304-1325
TL;DR: Kundu and Gupta as mentioned in this paper provided the analysis of Type-I hybrid life-tests in presence of competing risks, when the lifetime distribution of the test subjects varied with the competing risks.
Abstract: Kundu and Gupta [Analysis of hybrid life-tests in presence of competing risks. Metrica. 2007;65:159–170] provided the analysis of Type-I hybrid censored competing risks data, when the lifetime dist...
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors adopted the competing risks model with partially observed causes of failure when the latent failure times follow Lomax life distribution under type-II generalized hybrid censoring scheme.
Abstract: Time-to- failure under different causes of failure is known as a competing risks model. Practice, competing risks data can be appeared in different applications such as engineering fields or biological and medical lifetime studies as well as other related areas. Also, the causes of failure, which are competing may be partially observed. In this paper, we adopted the competing risks model with partially observed causes of failure when the latent failure times follow Lomax life distribution under type-II generalized hybrid censoring scheme. The maximum likelihood estimators of the model parameters with the associated confidence intervals are discussed. Moreover, Bayes estimators under importance sampling procedure with probability credible intervals are developed. The results are discussed using both real and simulated data sets for illustration purposes. Finally, the Monte Carlo simulation experiments are performed to assess and compare the different proposed methods with some brief comments.

6 citations

Journal ArticleDOI
01 Jul 2022
TL;DR: In this article , the authors adopted the competing risks model with partially observed causes of failure when the latent failure times follow Lomax life distribution under type-II generalized hybrid censoring scheme.
Abstract: Time-to- failure under different causes of failure is known as a competing risks model. Practice, competing risks data can be appeared in different applications such as engineering fields or biological and medical lifetime studies as well as other related areas. Also, the causes of failure, which are competing may be partially observed. In this paper, we adopted the competing risks model with partially observed causes of failure when the latent failure times follow Lomax life distribution under type-II generalized hybrid censoring scheme. The maximum likelihood estimators of the model parameters with the associated confidence intervals are discussed. Moreover, Bayes estimators under importance sampling procedure with probability credible intervals are developed. The results are discussed using both real and simulated data sets for illustration purposes. Finally, the Monte Carlo simulation experiments are performed to assess and compare the different proposed methods with some brief comments.

6 citations

Journal ArticleDOI
TL;DR: Flexible generalizations of the AFT model are proposed and goodness-of-fit (GOF) tests for the given models are proposed.
Abstract: The accelerated failure time (AFT) model is most commonly used model in accelerated life testing (ALT). This model is restrictive as failure time distributions under different constant stresses differ only in terms of scale. If it is not the case, most papers on ALT use a generalization of the AFT model supposing that under different stresses not only scale but also shape parameters are different. This model has an undesirable property for accelerated experiments—the survival functions corresponding to usual and accelerated stresses intersect. In this paper, we propose flexible generalizations of the AFT model. Estimation procedures and properties of estimators are discussed. Goodness-of-fit (GOF) tests for the given models are proposed. Examples of data analysis are provided. Generalization of the results in case of step stresses is presented.

5 citations


Cites background from "Analysis of Type-II hybrid censored..."

  • ...The recent developments are given in [5]–[9], [12]– [15], [17], [25], and [26]....

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Journal ArticleDOI
31 Jan 2019
TL;DR: In this article, the authors proposed an alternative method, the so-called expected value approach, introduced in Gorny (2017), to derive the exact distribution of the MLEs.
Abstract: In simple step-stress models based on exponential distributions, the distributions of the MLEs are commonly obtained using the moment generating function. In this paper, we propose an alternative method, the so-called expected value approach, introduced in Gorny (2017) to derive the exact distribution of the MLEs. Moreover, we discuss the benefits of this technique. Further, assuming uniformly distributed lifetimes, we show that the MLEs are also explicitly available and that their distributions are discrete for both the cumulative exposure and the tampered failure rate model. Additionally, we illustrate that confidence regions as well as confidence intervals can be established utilizing a connection to the multinomial distribution. The results are illustrated by an illustrative example as well as simulation results.

4 citations

Journal ArticleDOI
21 Dec 2022-Energies
TL;DR: In this article , a competing risks model with dependent causes of failure is considered under left-truncated and right-censoring scenario, and estimation of model parameters and reliability indices are proposed from classic and Bayesian approaches, respectively.
Abstract: In this paper, a competing risks model with dependent causes of failure is considered under left-truncated and right-censoring scenario. When the dependent failure causes follow a Marshall–Olkin bivariate exponential distribution, estimation of model parameters and reliability indices are proposed from classic and Bayesian approaches, respectively. Maximum likelihood estimators and approximate confidence intervals are constructed, and conventional Bayesian point and interval estimations are discussed as well. In addition, E-Bayesian estimators are proposed and their asymptotic behaviors have been investigated. Further, another objective-Bayesian analysis is also proposed when a noninformative probability matching prior is used. Finally, extensive simulation studies are carried out to investigate the performance of different methods. Two real data examples are presented to illustrate the applicability.

2 citations

References
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Journal ArticleDOI
TL;DR: This book complements the other references well, and merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any Ž eld.
Abstract: (2003). The Statistical Analysis of Failure Time Data. Technometrics: Vol. 45, No. 3, pp. 265-266.

4,600 citations


"Analysis of Type-II hybrid censored..." refers background in this paper

  • ...Moreover, it is observed by Kundu [19] that in case of exponential orWeibull lifetime distributions, both the approaches, namely the latent failure time model of Cox [1] or the cause-specific hazard functions model of Prentice et al. [2], provide the same likelihood function, although their interpretations are different....

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  • ...Among different methods, the two most popular approaches to analyse competing risks data are the following: (i) latent failure timemodel as suggested by Cox [1] or (ii) cause-specific hazard functions model as suggested by Prentice et al. [2]....

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  • ...It may be mentioned that although the assumption of independence of the two failure time distributions T1 and T2 seems to be very restrictive, it has been shown by Tsiatis [17] that without the presence of covariates the independence between T1 and T2 cannot be tested using the data only, see also Kalbfleisch and Prentice [18] in this respect....

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Journal ArticleDOI
TL;DR: It is argued that the problem of estimation of failure rates under the removal of certain causes is not well posed until a mechanism for cause removal is specified, and a method involving the estimation of parameters that relate time-dependent risk indicators for some causes to cause-specific hazard functions for other causes is proposed for the study of interrelations among failure types.
Abstract: Distinct problems in the analysis of failure times with competing causes of failure include the estimation of treatment or exposure effects on specific failure types, the study of interrelations among failure types, and the estimation of failure rates for some causes given the removal of certain other failure types. The usual formation of these problems is in terms of conceptual or latent failure times for each failure type. This approach is criticized on the basis of unwarranted assumptions, lack of physical interpretation and identifiability problems. An alternative approach utilizing cause-specific hazard functions for observable quantities, including time-dependent covariates, is proposed. Cause-specific hazard functions are shown to be the basic estimable quantities in the competing risks framework. A method, involving the estimation of parameters that relate time-dependent risk indicators for some causes to cause-specific hazard functions for other causes, is proposed for the study of interrelations among failure types. Further, it is argued that the problem of estimation of failure rates under the removal of certain causes is not well posed until a mechanism for cause removal is specified. Following such a specification, one will sometimes be in a position to make sensible extrapolations from available data to situations involving cause removal. A clinical program in bone marrow transplantation for leukemia provides a setting for discussion and illustration of each of these ideas. Failure due to censoring in a survivorship study leads to further discussion.

1,429 citations


"Analysis of Type-II hybrid censored..." refers background in this paper

  • ...[25], provide the same likelihood function, although their interpretations are different....

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Journal ArticleDOI
TL;DR: The relationship between the net and the crude probabilities of survival was established by Therorems 1 and 2 as mentioned in this paper, which showed that, without the not directly verifiable assumption that in their joint distribution the variables Y1, Y2,..., Yk are mutually independent, a given set of crude survival probabilities Qi(t) does not identify the corresponding net probabilities.
Abstract: For an experimental animal exposed to k greater than 1 possible risks of death R1, R2, ..., Rk, the term i-th potential survival time designates a random variable Yi supposed to represent the age at death of the animal in hypothetical conditions in which Ri is the only possible risk. The probability that Yi will exceed a preassigned t is called the i-th net survival probability. The results of a survival experiment are represented by k "crude" survival functions, empirical counterparts of the probabilities Qi(t) that an animal will survive at least up to the age t and eventually die from Ri. The analysis of a survival experiment aims at estimating the k net survival probabilities using the empirical data on those termed crude. Therorems 1 and 2 establish the relationship between the net and the crude probabilities of survival. In particular, Theorem 2 shows that, without the not directly verifiable assumption that in their joint distribution the variables Y1, Y2, ..., Yk are mutually independent, a given set of crude survival probabilities Qi(t) does not identify the corresponding net probabilities. An example shows that the results of a customary method of analysis, based on the assumption that Y1, Y2, ..., Yk are independent, may have no resemblance to reality.

712 citations

Book
01 Jan 2003
TL;DR: The Basis for, and Advantages of, Bayesian Model Estimation via Repeated Sampling via Repeations Sampling are explained and models for Spatial Outcomes and Geographical Association are described.
Abstract: Preface. The Basis for, and Advantages of, Bayesian Model Estimation via Repeated Sampling. Hierarchical Mixture Models. Regression Models. Analysis of Multi-Level Data. Models for Time Series. Analysis of Panel Data. Models for Spatial Outcomes and Geographical Association. Structural Equation and Latent Variable Models. Survival and Event History Models. Modelling and Establishing Causal Relations: Epidemiological Methods and Models. Index.

596 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider life tests which are truncated, where the underlying life distribution is specified by a p.d. of the exponential form, and give exact formulae for a decision procedure given in [2].
Abstract: It is frequently desirable on practical grounds to terminate a life test by a preassigned time $T_0$. In this paper we consider life tests which are truncated as follows. With $n$ items placed on test, it is decided in advance that the experiment will be terminated at $\min (X_{r0,n}, T_0)$, where $X_{r0,n}$ is a random variable equal to the time at which the $r_0$th failure occurs and $T_0$ is a truncation time, beyond which the experiment will not be run. Both $r_0$ and $T_0$ are assigned before experimentation starts. If the experiment is terminated at $X_{r0,n}$ (that is, if $r_0$ failures occur before time $T_0$), then the action in terms of hypothesis testing is the rejection of some specified null-hypothesis. If the experiment is terminated at time $T_0$ (that is, if the $r_0$th failure does not occur before time $T_0$), then the action in terms of hypothesis testing is the acceptance of some specified null-hypothesis. While truncated procedures can be considered for any life distribution, we limit ourselves here to the case where the underlying life distribution is specified by a p.d.f. of the exponential form, $f(x; \theta) = \theta^{-1}e^{-x/\theta}, x > 0, \theta > 0$. The practical justification for using this kind of distribution as a first approximation to a number of test situations is discussed in a recent paper by Davis [1]. It is a common assumption for electron tube life. Two situations are considered. The first is the nonreplacement case in which a failure occurring during the test is not replaced by a new item. The second is the replacement case where failed items are replaced at once by new items drawn at random from the same p.d.f. as the original $n$ items. Formulae are given for $E_\theta(r)$, the expected number of observations to reach a decision; for $E_\theta(T)$, the expected waiting time to reach a decision; and for $L(\theta)$, the probability of accepting the hypothesis that $\theta = \theta_0$, the value associated with the null-hypothesis, when $\theta$ is the true value. Some procedures are worked out for finding truncated tests meeting specified conditions, and practical illustrations are given. It is an intrinsic feature of all life test decision procedures that they are in some sense truncated, although not necessarily by a fixed time $T_0$. In Section 3 we give exact formulae for $E_\theta(r)$ and $E_\theta(T)$ for a decision procedure given in [2]. There is a close relation between these results and those in Section 2.

545 citations


"Analysis of Type-II hybrid censored..." refers background or methods in this paper

  • ...Since the introduction of the Type-I HCS of Epstein [4], extensive work has been done on Type-I hybrid censoring schemes, see, for example, Fairbanks et al....

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  • ...Since the introduction of the Type-I HCS of Epstein [4], extensive work has been done on Type-I hybrid censoring schemes, see, for example, Fairbanks et al. [5], Chen and Bhattacharyya [6], Gupta and Kundu [7], Dube et al. [8], Kundu [9], Chandrasekhar et al. [10], and the references cited therein....

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  • ...Epstein [4] first introduced this HCS, and it is also known as Type-I HCS....

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