Break Points in Life Table Mean Residual Life Times and Estimated Hazard Rates

Abhijeet Jadhav¹ , Rohit R Mutkekar² , S. B. Munoli³

1. Dept. of studies in Statistics, Karnatak University, Dharwad, Karnataka, India.
2. Dept. of Operations Management and Information Technology, Goa Institute of Management, Poriem, India.
3. Dept. of studies in Statistics, Karnatak University, Dharwad, Karnataka, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.5 , pp.7-13, Oct-2023

Online published on Oct 31, 2023

Copyright © Abhijeet Jadhav, Rohit R Mutkekar, S. B. Munoli . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

186 Views    151 Downloads    50 Downloads

Abstract :
The paper is notably focused on statistics and technical aspects of Mean Residual Life Time (MRLT) and Hazard Rate (HR). A polynomial with appropriate degree is fit to the life table MRLT data of countries belonging to different income groups and geological regions. Break points of MRLTs at various age of human life cycle are studied through segmented regression. HRs are estimated using respective MRLTs, break points in estimated HRs are analyzed.

Key-Words / Index Term :
Mean Residual Life Time, Hazard Rate, Life Table, Segmented Regression, Polynomial Regression, Break Points.

References :
[1]. T Bjerkedal, “Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle Bacilli,” American Journal of Hygiene, Vol.72, Issue.1, pp.130-48, 1960. https://doi.org/10.1093/oxfordjournals.aje.a120129.
[2]. David E Matthews, Vernon T Farewell, “On Testing for a Constant Hazard against a Change-Point Alternative,” Biometrics, Vol. 38, Issue. 2, pp.463–68, 1982. https://doi.org/10.2307/2530460.
[3]. H. T. Nguyen, G. S. Rogers, E. A. Walker, “Estimation in change-point hazard rate models,” Biometrika, Vol.71, Issue.2, pp.299-304, 1984. https://doi.org/10.1093/biomet/71.2.299.
[4]. Calabria R, Gianpaolo Pulcini, “On the asymptotic behaviour of mean residual life function,” Reliability Engineering, Vol. 19, pp. 165-170, 1987. https://doi.org/10.1016/01438174(87)90001-1.
[5]. Clive R Loader, “Inference for a hazard rate change point,” Biometrika, Vol.78, Issue.4, pp.749–757, 1991. https://doi.org/10.1093/biomet/78.4.749.
[6]. Gangaji Maguluri, Cun-Hui Zhang, “Estimation in the Mean Residual Life Regression Model,” Journal of the Royal Statistical Society: Series B (Methodological), Vol.56, Issue.3, pp.477-489, 1994. https://doi.org/10.1111/j.2517-6161.1994.tb01994.x
[7]. Jae-Hak Lim, Dong Ho Park, “Trend change in mean residual life,” IEEE transactions on reliability, Vol.44, Issue.2, pp.291-296, 1995. Doi. 10.1109/24.387381.
[8]. Barbara Toson, Allan Baker, “Life expectancy at birth: methodological options for small populations”, London: Office for National Statistics, 2003.
[9]. Vito M. R. Muggeo, “Estimating regression models with unknown break-points,” Statistics in Medicine, Vol.22, Issue.19, pp.3055-3071, 2003. https://doi.org/10.1002/sim.1545.
[10]. David Strauss, Pierre Vachon, Robert Shavelle, “Estimation of future mortality rates and life expectancy in chronic medical conditions”, J Insur Med., Vol.37, Issue.1, pp.20-34, 2005. PMID: 15895695.
[11]. L. B. Shrestha, “Life expectancy in the United States”, Congressional Information Service, Library of Congress, 2005.
[12]. Jean-François Dupuy, “Estimation in a change-point hazard regression model,” Statistics & probability letters, Vol.76, Issue.2, pp.182-190, 2006. https://doi.org/10.1016/j.spl.2005.07.013.
[13]. Lai, Chin-Diew, Min Xie, “Mean Residual Life - Concepts and Applications in Reliability Analysis,” Stochastic Ageing and Dependence for Reliability, Springer, New York, NY, pp.109-138. 2006.
[14]. Vito M. R. Muggeo, “Segmented: an R package to fit regression models with broken-line relationships,” R news, Vol.8, Issue.1, pp.20-25, 2008.
[15]. Melody S Goodman, Yi Li, and Ram C Tiwari, “Detecting multiple change points in piecewise constant hazard functions,” Journal of applied statistics, Vol.38, Issue.11, pp.2523-2532, 2011. https://doi.org/10.1080%2F02664763.2011.559209.
[16]. Elisabeta Jaba, Christiana Brigitte Balan, Ioan-Bogdan Robu, “The Relationship between Life Expectancy at Birth and Health Expenditures Estimated by a Cross-country and Time-series Analysis,” Procedia Economics and Finance, Vol.15, pp.108-114, 2014. https://doi.org/10.1016/S2212-5671(14)00454-7.
[17]. J. Vijay Anto and Lilly George, “Survival Modeling and Analysis for Time to Failures of Aircraft Glass,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.2, pp.252-257, 2019.
https://doi.org/10.26438/ijsrmss/v6i2.252257.
[18]. Bing Wang, Xiaoguang Wang, Lixin Song, “Estimation in the single change-point hazard function for interval-censored data with a cure fraction,” Journal of Applied Statistics, Vol.47, Issue.2, pp.231-247, 2020.
https://doi.org/10.1080%2F02664763.2019.1635571.
[19]. Karin Modig, Roland Rau, Anders Ahlbom, “Life expectancy: what does it measure?,” British Medical Journal Open, Vol.10, Issue.7, pp.e035932, 2020. http://dx.doi.org/10.1136/bmjopen-2019-035932.
[20]. Hassan Piriaei, Gholamhossein Yari, Rahman Farnoosh, “E-Bayesian estimations for the cumulative hazard rate and mean residual life based on exponential distribution and record data,” Journal of Statistical Computation and Simulation, Vol.90, Issue.2, pp.271-290, 2020.
https://doi.org/10.1080/00949655.2019.1678623.
[21]. Suhas Bhat, S. B. Munoli, “Estimation of change points in hazard rates,” Advances and Applications in Statistics, Vol.75, pp.79-90, 2022. https://doi.org/10.17654/0972361722028.
[22]. Ezhilvanan Mani, Kannadasan Karuppaiah, Vinoth Raman, "Statistical Models for Predicting the Expected Time of Diabetes Mellitus Using Exponentiated Gamma Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.4, pp.30-34, 2023.