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Bayesian and Frequentist Approaches for a Tractable Parametric General Class of Hazard-Based Regression Models: An Application to Oncology Data

Author

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  • Abdisalam Hassan Muse

    (Institute for Basic Sciences, Technology and Innovation (PAUSTI), Pan African University, Nairobi 62000-00200, Kenya
    Faculty of Science and Humanities, School of Postgraduate Studies and Research, Amoud University, Borama 25263, Somalia)

  • Samuel Mwalili

    (Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi 62000-00200, Kenya)

  • Oscar Ngesa

    (Department of Mathematics and Physical Sciences, Taita Taveta University, Voi 635-80300, Kenya)

  • Christophe Chesneau

    (Department of Mathematics, LMNO, CNRS-Université de Caen, Campus II, Science 3, 14032 Caen, France)

  • Afrah Al-Bossly

    (Department of Mathematics, College of Science and Humanities in AL-Kharj, Prince Sattam Bin Abdulaziz University, AL-Kharj 11942, Saudi Arabia)

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in AL-Kharj, Prince Sattam Bin Abdulaziz University, AL-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

In this study, we consider a general, flexible, parametric hazard-based regression model for censored lifetime data with covariates and term it the “general hazard (GH)” regression model. Some well-known models, such as the accelerated failure time (AFT), and the proportional hazard (PH) models, as well as the accelerated hazard (AH) model accounting for crossed survival curves, are sub-classes of this general hazard model. In the proposed class of hazard-based regression models, a covariate’s effect is identified as having two distinct components, namely a relative hazard ratio and a time-scale change on hazard progression. The new approach is more adaptive to modelling lifetime data and could give more accurate survival forecasts. The nested structure that includes the AFT, AH, and PH models in the general hazard model may offer a numerical tool for identifying which of them is most appropriate for a certain dataset. In this study, we propose a method for applying these various parametric hazard-based regression models that is based on a tractable parametric distribution for the baseline hazard, known as the generalized log-logistic (GLL) distribution. This distribution is closed under all the PH, AH, and AFT frameworks and can incorporate all of the basic hazard rate shapes of interest in practice, such as decreasing, constant, increasing, V-shaped, unimodal, and J-shaped hazard rates. The Bayesian and frequentist approaches were used to estimate the model parameters. Comprehensive simulation studies were used to evaluate the performance of the proposed model’s estimators and its nested structure. A right-censored cancer dataset is used to illustrate the application of the proposed approach. The proposed model performs well on both real and simulation datasets, demonstrating the importance of developing a flexible parametric general class of hazard-based regression models with both time-independent and time-dependent covariates for evaluating the hazard function and hazard ratio over time.

Suggested Citation

  • Abdisalam Hassan Muse & Samuel Mwalili & Oscar Ngesa & Christophe Chesneau & Afrah Al-Bossly & Mahmoud El-Morshedy, 2022. "Bayesian and Frequentist Approaches for a Tractable Parametric General Class of Hazard-Based Regression Models: An Application to Oncology Data," Mathematics, MDPI, vol. 10(20), pages 1-41, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3813-:d:943574
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    References listed on IDEAS

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    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    2. Li Li & Timothy Hanson & Jiajia Zhang, 2015. "Spatial extended hazard model with application to prostate cancer survival," Biometrics, The International Biometric Society, vol. 71(2), pages 313-322, June.
    3. Denwood, Matthew J., 2016. "runjags: An R Package Providing Interface Utilities, Model Templates, Parallel Computing Methods and Additional Distributions for MCMC Models in JAGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i09).
    4. Francisco Louzada-Neto, 2001. "Bayesian Analysis for Hazard Models with Non-constant Shape Parameter," Computational Statistics, Springer, vol. 16(2), pages 243-254, July.
    5. Shahedul A. Khan & Saima K. Khosa, 2016. "Generalized log-logistic proportional hazard model with applications in survival analysis," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-18, December.
    6. Natalie V. R. Mendoza & Edwin M. M. Ortega & Gauss M. Cordeiro, 2016. "The exponentiated-log-logistic geometric distribution: Dual activation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(13), pages 3838-3859, July.
    7. Zafar Mahmood & Taghreed M Jawa & Neveen Sayed-Ahmed & E M Khalil & Abdisalam Hassan Muse & Ahlam H. Tolba & Dost Muhammad Khan, 2022. "An Extended Cosine Generalized Family of Distributions for Reliability Modeling: Characteristics and Applications with Simulation Study," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-20, February.
    8. Ibrahim Alkhairy & M. Nagy & Abdisalam Hassan Muse & Eslam Hussam & Sameh S. Askar, 2021. "The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences," Complexity, Hindawi, vol. 2021, pages 1-14, December.
    9. Leemis, Lawrence M. & Shih, Li-Hsing & Reynertson, Kurt, 1990. "Variate generation for accelerated life and proportional hazards models with time dependent covariates," Statistics & Probability Letters, Elsevier, vol. 10(4), pages 335-339, September.
    10. Ying Qing Chen, 2001. "Accelerated Hazards Regression Model and Its Adequacy for Censored Survival Data," Biometrics, The International Biometric Society, vol. 57(3), pages 853-860, September.
    11. Ke Wang & Xin Ye & Jie Ma, 2018. "An empirical analysis of post-work grocery shopping activity duration using modified accelerated failure time model to differentiate time-dependent and time-independent covariates," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-17, November.
    12. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.
    13. Shahedul A. Khan & Nyla Basharat, 2022. "Accelerated failure time models for recurrent event data analysis and joint modeling," Computational Statistics, Springer, vol. 37(4), pages 1569-1597, September.
    14. Zhang, Jiajia & Peng, Yingwei, 2009. "Crossing hazard functions in common survival models," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2124-2130, October.
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