On generalized progressive hybrid censoring in presence of competing risks

Abstract

The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Computational Statistics and Data Analysis, 2509-2528, 2006, has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Cho, Sun and Lee (Statistical Methodology, 23, 18-34, 2015) recently introduced generalized progressive censoring which ensures to get a pre specified number of failures. In this paper we analyze generalized progressive censored data in presence of competing risks. For brevity we have considered only two competing causes of failures, and it is assumed that the lifetime of the competing causes follow one parameter exponential distributions with different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters and also provide their exact distributions. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals can be obtained. Asymptotic and bootstrap confidence intervals are also provided for comparison purposes. We further consider the Bayesian analysis of the unknown parameters under a very flexible Beta-Gamma prior. We provide the Bayes estimates and the associated credible intervals of the unknown parameters based on the above priors. We present extensive simulation results to see the effectiveness of the proposed method and finally one real data set is analyzed for illustrative purpose., if T * = Z k:m:n , P (T < Z k:m:n < Z m:m:n , D 1 = i) dz 1 . . . dz k .

Inference for two‐parameter Rayleigh competing risks data under generalized progressive hybrid censoring

“…and Liu and Shi 49 for some interesting results under different censoring schemes. Bayesian inference for competing risks models based on GPHC schemes has also received some attention among researchers, (see Koley and Kundu, 16 Wang 32 ). Here we obtain Bayesian estimates of the unknown parameters of when data are observed using the GPHC scheme.…”

“…The covariate case has received relatively less attention due to model identification problem (see Kalbeish and Prentice 5 and Crowder 6 for further details). In the past two decades, competing risks models have received a considerable attention of many researchers (see, e.g., Kundu et al., 3 Balasooriya and Low, 7 Balakrishnan and Han, 8 Pareek et al., 9 Pascual, 10 Cramer and Schmiedt, 11 Mazucheli and Achcar, 12 Han and Kundu, 13 Wu et al., 14,15 Koley and Kundu 16 ). Recently, Wang 17 and Wu et al 15 .…”

“…This procedure stops when the termination time max is reached, and by this time all the remaining live units are removed from the experiment. One may refer to Cho et al., 25 Gorny and Cramer, 26 Lee et al., 27 Koley and Kundu, 16 Elshahhat, 28 Kang and Lee, 29 Kotb, 30 Sen et. al 31 .…”

Bayesian Analysis of Nakagami Distribution under Generalized Type-II Progressive Hybrid Censoring Scheme

“…Seo and Kim (2017) proposed a robust Bayesian point estimation approach founded on a hierarchical structure for two parameter exponential distribution under GTPH. Koley and Kundu (2017) analysed generalized progressively censored data in the presence of competing risk. Kotb (2018) gave Bayesian prediction bounds for exponential type distribution under generalized progressively hybrid censored (GPH) scenario.…”

Analysis of progressive Type‐II censoring in presence of competing risk data under step stress modeling

“…It should be mentioned that the results here are close to those results obtained by Xie, Balakrishnan, and Han (2008) without the presence of any competing causes of failures. The proposed model is connected to Type‐I progressively hybrid censored competing risks data considered by Kundu and Joarder (2006) and a more general hybrid censoring model in this regard discussed by the authors in Kundu and Koley (2017). But so far no body has considered the model, under this most general set up.…”