Change point estimation of hazard rates in contaminated Birnbaum-Saunders models with an application to tuberculosis survival data

Farouq Mohammad A. Alam; Farouq Mohammad A. Alam

doi:10.3934/math.20251149

AIMS Mathematics

2025, Volume 10, Issue 11: 26106-26131. doi: 10.3934/math.20251149

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Change point estimation of hazard rates in contaminated Birnbaum-Saunders models with an application to tuberculosis survival data

Farouq Mohammad A. Alam ^,

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received: 23 August 2025 Revised: 21 October 2025 Accepted: 29 October 2025 Published: 12 November 2025
MSC : 62F10, 62N05

In reliability and survival analysis, the hazard rate is a key statistical measure that quantifies the instantaneous risk of an event occurring at a given time. Detecting a change point in the hazard rate is particularly important in biomedical and reliability studies, as it may indicate a shift in the underlying failure mechanism or disease progression. This paper addresses the estimation of hazard rate change points under the contaminated Birnbaum-Saunders model, a positively skewed lifetime distribution originally derived from material fatigue theory but now widely applied in diverse fields. Several estimation methods were considered, and their performance was compared in terms of estimation efficiency and robustness when the data are subject to contamination. To assess finite-sample properties, extensive Monte Carlo simulations were carried out, highlighting the strengths and limitations of each estimator under varying contamination levels. In addition to the simulation study, the proposed methods were applied to a real biomedical dataset involving the survival times of guinea pigs (cavia corcellus) injected with different dosages of Mycobacterium tuberculosis, the pathogen that causes tuberculosis. The application demonstrates the practical value of the comparative results and provides insight into disease progression under varying infection intensities. Overall, the study contributes to the literature by offering both methodological evaluation and an applied perspective on change point estimation in hazard rates.
- point estimation,
- change point estimation,
- hazard rate,
- Birnbaum-Saunders distribution,
- survival data analysis
Citation: Farouq Mohammad A. Alam. Change point estimation of hazard rates in contaminated Birnbaum-Saunders models with an application to tuberculosis survival data[J]. AIMS Mathematics, 2025, 10(11): 26106-26131. doi: 10.3934/math.20251149

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Abstract

In reliability and survival analysis, the hazard rate is a key statistical measure that quantifies the instantaneous risk of an event occurring at a given time. Detecting a change point in the hazard rate is particularly important in biomedical and reliability studies, as it may indicate a shift in the underlying failure mechanism or disease progression. This paper addresses the estimation of hazard rate change points under the contaminated Birnbaum-Saunders model, a positively skewed lifetime distribution originally derived from material fatigue theory but now widely applied in diverse fields. Several estimation methods were considered, and their performance was compared in terms of estimation efficiency and robustness when the data are subject to contamination. To assess finite-sample properties, extensive Monte Carlo simulations were carried out, highlighting the strengths and limitations of each estimator under varying contamination levels. In addition to the simulation study, the proposed methods were applied to a real biomedical dataset involving the survival times of guinea pigs (cavia corcellus) injected with different dosages of Mycobacterium tuberculosis, the pathogen that causes tuberculosis. The application demonstrates the practical value of the comparative results and provides insight into disease progression under varying infection intensities. Overall, the study contributes to the literature by offering both methodological evaluation and an applied perspective on change point estimation in hazard rates.

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