Frailty Models Under Xgamma Distribution with Application to Survival Data

Ashok Kumar Palanisamy; Muthukumar Madaswamy

doi:doi:10.11648/j.mcs.20230804.11

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Frailty Models Under Xgamma Distribution with Application to Survival Data

Ashok Kumar Palanisamy, Muthukumar Madaswamy

Published in Mathematics and Computer Science (Volume 8, Issue 4)

Received: 26 July 2023 Accepted: 14 August 2023 Published: 31 August 2023

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Abstract

Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.

Published in	Mathematics and Computer Science (Volume 8, Issue 4)
DOI	10.11648/j.mcs.20230804.11
Page(s)	87-93
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Xgamma Distribution, Hazard Function, Survival Analysis, Parametric Frailty Models, Marginal LOG-Likelihood, Clustered Data Analysis

References

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[4]	Vaupel JW, Manton KG, Stallard E, “The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality”. Demography, 16 (3), 439-454, 1979.
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[17]	David D. Hanagal, “Modeling Survival Data Using Frailty Models. Industrial and Applied Mathematics”. Springer Nature Singapore Pte Ltd (295 Pages). DOI: 10.1007/978-981-15-1181-3, 2011.
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APA Style

Ashok Kumar Palanisamy, Muthukumar Madaswamy. (2023). Frailty Models Under Xgamma Distribution with Application to Survival Data. Mathematics and Computer Science, 8(4), 87-93. https://doi.org/10.11648/j.mcs.20230804.11

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ACS Style

Ashok Kumar Palanisamy; Muthukumar Madaswamy. Frailty Models Under Xgamma Distribution with Application to Survival Data. Math. Comput. Sci. 2023, 8(4), 87-93. doi: 10.11648/j.mcs.20230804.11

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AMA Style

Ashok Kumar Palanisamy, Muthukumar Madaswamy. Frailty Models Under Xgamma Distribution with Application to Survival Data. Math Comput Sci. 2023;8(4):87-93. doi: 10.11648/j.mcs.20230804.11

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@article{10.11648/j.mcs.20230804.11,
  author = {Ashok Kumar Palanisamy and Muthukumar Madaswamy},
  title = {Frailty Models Under Xgamma Distribution with Application to Survival Data},
  journal = {Mathematics and Computer Science},
  volume = {8},
  number = {4},
  pages = {87-93},
  doi = {10.11648/j.mcs.20230804.11},
  url = {https://doi.org/10.11648/j.mcs.20230804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230804.11},
  abstract = {Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.},
 year = {2023}
}

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TY  - JOUR
T1  - Frailty Models Under Xgamma Distribution with Application to Survival Data
AU  - Ashok Kumar Palanisamy
AU  - Muthukumar Madaswamy
Y1  - 2023/08/31
PY  - 2023
N1  - https://doi.org/10.11648/j.mcs.20230804.11
DO  - 10.11648/j.mcs.20230804.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 87
EP  - 93
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20230804.11
AB  - Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.
VL  - 8
IS  - 4
ER  -

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Author Information

Ashok Kumar Palanisamy

Department of Statistics, PSG College of Arts and Science, Coimbatore, India
Muthukumar Madaswamy

Department of Statistics, PSG College of Arts and Science, Coimbatore, India

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Plain Text BibTeX RIS

APA Style

Ashok Kumar Palanisamy, Muthukumar Madaswamy. (2023). Frailty Models Under Xgamma Distribution with Application to Survival Data. Mathematics and Computer Science, 8(4), 87-93. https://doi.org/10.11648/j.mcs.20230804.11

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ACS Style

Ashok Kumar Palanisamy; Muthukumar Madaswamy. Frailty Models Under Xgamma Distribution with Application to Survival Data. Math. Comput. Sci. 2023, 8(4), 87-93. doi: 10.11648/j.mcs.20230804.11

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AMA Style

Ashok Kumar Palanisamy, Muthukumar Madaswamy. Frailty Models Under Xgamma Distribution with Application to Survival Data. Math Comput Sci. 2023;8(4):87-93. doi: 10.11648/j.mcs.20230804.11

Copy | Download

@article{10.11648/j.mcs.20230804.11,
  author = {Ashok Kumar Palanisamy and Muthukumar Madaswamy},
  title = {Frailty Models Under Xgamma Distribution with Application to Survival Data},
  journal = {Mathematics and Computer Science},
  volume = {8},
  number = {4},
  pages = {87-93},
  doi = {10.11648/j.mcs.20230804.11},
  url = {https://doi.org/10.11648/j.mcs.20230804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230804.11},
  abstract = {Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.},
 year = {2023}
}

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TY  - JOUR
T1  - Frailty Models Under Xgamma Distribution with Application to Survival Data
AU  - Ashok Kumar Palanisamy
AU  - Muthukumar Madaswamy
Y1  - 2023/08/31
PY  - 2023
N1  - https://doi.org/10.11648/j.mcs.20230804.11
DO  - 10.11648/j.mcs.20230804.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 87
EP  - 93
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20230804.11
AB  - Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.
VL  - 8
IS  - 4
ER  -

Copy | Download