Statistical inference for the partial area under ROC curve for the lower truncated proportional hazard rate models based on progressive Type-II censoring

Abstract

This paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes.

Keywords:

• Bayesian inference
• bootstrap
• generalized pivotal inference
• progressive Type-II censoring
• proportional hazard rate model

2010 Mathematic Subject classifications:

• 62N01
• 62N02

Acknowledgments

The authors would like to thank the editor, associate editor and the anonymous reviewer for their helpful comments and suggestions, which led to the improved presentation of this article significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Yichuan Zhao acknowledges the support from NSF Grant [grant number DMS-2317533] and the Simons Foundation Grant [grant number 638679].