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Generalized log-logistic proportional hazard model with applications in survival analysis

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  • Shahedul A. Khan

    (University of Saskatchewan)

  • Saima K. Khosa

    (University of Saskatchewan)

Abstract

Proportional hazard (PH) models can be formulated with or without assuming a probability distribution for survival times. The former assumption leads to parametric models, whereas the latter leads to the semi-parametric Cox model which is by far the most popular in survival analysis. However, a parametric model may lead to more efficient estimates than the Cox model under certain conditions. Only a few parametric models are closed under the PH assumption, the most common of which is the Weibull that accommodates only monotone hazard functions. We propose a generalization of the log-logistic distribution that belongs to the PH family. It has properties similar to those of log-logistic, and approaches the Weibull in the limit. These features enable it to handle both monotone and nonmonotone hazard functions. Application to four data sets and a simulation study revealed that the model could potentially be very useful in adequately describing different types of time-to-event data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0054-z
    DOI: 10.1186/s40488-016-0054-z
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    References listed on IDEAS

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    1. Fushing Hsieh & Yi-Kuan Tseng & Jane-Ling Wang, 2006. "Joint Modeling of Survival and Longitudinal Data: Likelihood Approach Revisited," Biometrics, The International Biometric Society, vol. 62(4), pages 1037-1043, December.
    2. Rizopoulos, Dimitris, 2010. "JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i09).
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    2. 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.
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    4. Adam Braima S. Mastor & Abdulaziz S. Alghamdi & Oscar Ngesa & Joseph Mung’atu & Christophe Chesneau & Ahmed Z. Afify, 2023. "The Extended Exponential-Weibull Accelerated Failure Time Model with Application to Sudan COVID-19 Data," Mathematics, MDPI, vol. 11(2), pages 1-26, January.

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