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Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring

Author

Listed:
  • Mei Li

    (Faculty of Science, Kunming University of Scicence and Technology, Kunming 650500, China)

  • Wei Ning

    (Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA)

  • Yubin Tian

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages.

Suggested Citation

  • Mei Li & Wei Ning & Yubin Tian, 2024. "Change Point Test for Length-Biased Lognormal Distribution under Random Right Censoring," Mathematics, MDPI, vol. 12(11), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1760-:d:1409366
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    References listed on IDEAS

    as
    1. Yuhao Deng & Chong You & Yukun Liu & Jing Qin & Xiao‐Hua Zhou, 2021. "Estimation of incubation period and generation time based on observed length‐biased epidemic cohort with censoring for COVID‐19 outbreak in China," Biometrics, The International Biometric Society, vol. 77(3), pages 929-941, September.
    2. Wang, Pingping & Tang, Yincai & Joo Bae, Suk & He, Yong, 2018. "Bayesian analysis of two-phase degradation data based on change-point Wiener process," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 244-256.
    3. Cai, Xia & Tian, Yubin & Ning, Wei, 2019. "Change-point analysis of the failure mechanisms based on accelerated life tests," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 515-522.
    4. Anthony Joe Turkson & Francis Ayiah-Mensah & Vivian Nimoh & Niansheng Tang, 2021. "Handling Censoring and Censored Data in Survival Analysis: A Standalone Systematic Literature Review," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2021, pages 1-16, September.
    5. Xia Cai & Khamis Khalid Said & Wei Ning, 2016. "Change-point analysis with bathtub shape for the exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2740-2750, November.
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