Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Michimae, Hirofumi; Emura, Takeshi

doi:10.3390/math10132163

Cited by 13 publications

(11 citation statements)

References 55 publications

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“…As opposed to the Bayesian approach, where the dependency parameter 𝛼 is estimated, in the Maximum likelihood inference, this parameter needs to be previously defined, like, for example, as was done by Michimae and Emura. 67 In this simulation study we specify four scenarios for the dependency: 𝛼 = 0.001, assuming independence between survival and dependent censoring times; 𝛼 = 1, low correlation; 𝛼 = 3, value used in datasets generation; 𝛼 = 5, high correlation between failure and dependent censoring times. To choose the value of the dependency parameter and other specifications (distributions and number of intervals) that produce the best fit, we evaluated the maximum likelihood selection criteria: Akaike's information criteria (AIC); Schwartz's information criteria (SIC); Hannan Quinn's information criteria (HQ).…”

Section: Simulation Resultsmentioning

confidence: 99%

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Schneider,

dos Reis,

Gottselig

et al. 2023

Statistics in Medicine

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Ignoring the presence of dependent censoring in data analysis can lead to biased estimates, for example, not considering the effect of abandonment of the tuberculosis treatment may influence inferences about the cure probability. In order to assess the relationship between cure and abandonment outcomes, we propose a copula Bayesian approach. Therefore, the main objective of this work is to introduce a Bayesian survival regression model, capable of taking into account the dependent censoring in the adjustment. So, this proposed approach is based on Clayton's copula, to provide the relation between survival and dependent censoring times. In addition, the Weibull and the piecewise exponential marginal distributions are considered in order to fit the times. A simulation study is carried out to perform comparisons between different scenarios of dependence, different specifications of prior distributions, and comparisons with the maximum likelihood inference. Finally, we apply the proposed approach to a tuberculosis treatment adherence dataset of an HIV cohort from Alvorada‐RS, Brazil. Results show that cure and abandonment outcomes are negatively correlated, that is, as long as the chance of abandoning the treatment increases, the chance of tuberculosis cure decreases.

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Section: Simulation Resultsmentioning

confidence: 99%

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Schneider,

dos Reis,

Gottselig

et al. 2023

Statistics in Medicine

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show abstract

“…While their works give a good starting point, the independence model, 26 the Marshall–Olkin bivariate Rayleigh model 27 and the Marshall–Olkin bivariate general class of inverse exponentiated model 66 are too specific for modeling failure times of competing risks. Therefore, we recently have developed copula‐based models for dependent competing risks, 67 permitting flexible dependence models 68 . Bivariate competing risks without left‐truncation and right‐censoring is equivalent to “dependent censoring”, where copula models were applied 69,70 …”

Section: Discussionmentioning

confidence: 99%

Left‐truncated and right‐censored field failure data: Review of parametric analysis for reliability

Emura

Michimae

2022

Quality & Reliability Eng

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In field reliability analyses, a data collection period is given to monitor the failure events from the field. Left‐truncation arises due to early failures occurring before the data collection period, and right‐censoring arises for late failures occurring beyond the monitoring period. Naïve analyses of left‐truncated and right‐censored data lead to biased estimation of the population lifetime of interest. A variety of models and methods have been developed to analyze the left‐truncated and right‐censored data for field reliability analyses. The goal of the paper is to review the existing models and methods for fitting left‐truncated and right‐censored data. Our review includes the existing statistical models, such as the exponential, Weibull, lognormal, gamma, Gompertz, Lomax, and spline models. We comprehensively review the statistical issues of maximum likelihood estimation, model selection, residual lifetime prediction, and Bayesian methods. Some of these methods are illustrated through the field reliability analysis of the electric power transformer dataset.

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“…Note that in this paper we assume that the two competing failures are independent. In future work, the simple step-stress accelerated dependent competing failure model will be considered, such as Copula [ 37 , 38 ], which is one of the popular models for releasing the restriction.…”

Section: Discussionmentioning

confidence: 99%

E-Bayesian and H-Bayesian Inferences for a Simple Step-Stress Model with Competing Failure Model under Progressively Type-II Censoring

Wang

Yan

Chen

2022

Entropy

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In this paper, we discuss the statistical analysis of a simple step-stress accelerated competing failure model under progressively Type-II censoring. It is assumed that there is more than one cause of failure, and the lifetime of the experimental units at each stress level follows exponential distribution. The distribution functions under different stress levels are connected through the cumulative exposure model. The maximum likelihood, Bayesian, Expected Bayesian, and Hierarchical Bayesian estimations of the model parameters are derived based on the different loss function. Based on Monte Carlo Simulations. We also get the average length and the coverage probability of the 95% confidence intervals and highest posterior density credible intervals of the parameters. From the numerical studies, it can be seen that the proposed Expected Bayesian estimations and Hierarchical Bayesian estimations have better performance in terms of the average estimates and mean squared errors, respectively. Finally, the methods of statistical inference discussed here are illustrated with a numerical example.

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Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

Cited by 13 publications

References 55 publications

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Left‐truncated and right‐censored field failure data: Review of parametric analysis for reliability

E-Bayesian and H-Bayesian Inferences for a Simple Step-Stress Model with Competing Failure Model under Progressively Type-II Censoring

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