Analysis of left truncated and right censored competing risks data

Abstract

In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing causes of failures are assumed to follow Weibull distributions with the same shape parameter but different scale parameters. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the bootstrap approach. When the common shape parameter is known, the maximum likelihood estimators of the scale parameters can be obtained in explicit forms, and when it is unknown we provide a simple iterative procedure to compute the maximum likelihood estimator of the shape parameter. The Bayes estimates and the associated credible intervals of unknown parameters are also addressed under a very flexible set of priors on the shape and scale parameters. Extensive Monte Carlo simulations are performed to compare the performances of the different methods. A numerical example is provided for illustrative purposes. Finally the results have been extended when the two competing causes of failures are assumed to be independent Weibull distributions with different shape parameters.

Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution

“…The prediction results for them are shown in Table 10. Dataset 2: The dataset used from from Kundu et al [19] is about the LTRC competing risks lifetimes of high-voltage power transformers, where there are just two failure causes.…”

“…In order to obtain the dependent LTRC competing risks data, we randomly select 10% data from Kundu et al [19] example, and treated these data as failure times due to causes one and two simultaneous. In addition, for the purpose of computational convenience, we divide all data by 100 for sake of simplicity.…”

“…Jiang et al [18] developed a nonparametric likelihood-based estimation procedure by using B-splines. Kundu et al [19] provided the Bayesian inference for the unknown parameters of MOBW distribution when LTRC competing risk model is available with independent causes. Motivated by the reasons mentioned above and due to the simplicity and practicability of the Marshall-Olkin type bivariate distribution, this paper aims to discuss the statistical inference for LTRC data with dependent competing risks.…”

Failure Analysis for Truncated and Fully Censored Lifetime Data With a Hierarchical Grid Algorithm

“…In their study, the collected power transformers lifetime data were lefttruncated at the starting date of record keeping and rightcensored at the ending date of the study. Following studies by these researchers, Balakrishnan and Mitra [4]- [6], Emura and Shiu [7], and Kundu and Mitra [8], [9] worked on likelihoodbased inference for left-truncated and right-censored data. Zhao et al [10] and Bai [11] also studied left-truncated and right-censored data in other areas, such as clinical trials.…”

Preventive Maintenance Strategy for Train Doors Based on the Competitive Weibull Theory

“…A competitive failure model is used to evaluate the reliability of a product in literatures [6] [7]. The competitive failure model for specific failure modes or processes has been established in literatures [8][9] [10]. Fault data of metro vehicles are used in this paper, and the reliability of rail transit vehicles is solved based on the competitive Weibull model, which compensates for the disadvantage of single fault mechanism processing.…”