International Journal of Theoretical and Applied Mathematics

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The Type I Generalized Half Logistic Survival Model

Received: 26 October 2016    Accepted: 10 November 2016    Published: 09 December 2016
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Abstract

In this paper, a three parameter probability distribution function called type I generalized half-logistic distribution is introduced to model survival or time to event data. The survival function, hazard function and median survival time of the survival model were established. Estimation of the parameters of the model was done using the maximum likelihood method. We then applied the type I generalized half-logistic survival model to a breast cancer survival data. The derived result from type I generalized half logistic survival model was compared with the results of some common existing parametric survival models, and this revealed that the type I generalized half-logistic survival model clearly demonstrates superiority over these other models.

DOI 10.11648/j.ijtam.20160202.17
Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2, December 2016)
Page(s) 74-78
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), 2024. Published by Science Publishing Group

Keywords

Parameter, Survival Function, Hazard Function, Model, Half Logistic Distribution, Survival Time

References
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[8] Sama, W., Dietz, K., Smith. T. (2006): Distribution of Survival Times of Deliberate Plasmodium Falciparum Infections in Tertiary Syphilis Patients. Transaction of the Royal society of Tropical Medicine and Hygiene, 100: 811-816.
[9] Kannan, N., Raychaudhuri, A., Pilamanis, A. A. (1998): A Log Logistic Model for Altitude Decomposition Sickness. Aviation, Space and Environmental Medicine 69:965-970.
[10] Miller, R. G. (1976): Least squares regression with censored data. Biometrika 63, 449-464.
[11] Buckley, J. and James, I. (1979): Linear regression with censored data. Biometrika 66, 429-436.
[12] Koul,H., Susarla, V. and Van Ryzin, J. (1981): Regression Analysis with Randomly Right Censored Data. Annals of Statistics 8, 1276-1288.
[13] Christensen, R. and Johnson, W. (1988): Modeling Accelerated Failure Time with a Dirichlet Process. Biometrika 75, 793-704.
[14] Kuo, L. and Mallick, B. (1997): Bayesian Semiparametric Inference for Accelerated Failure Time Model. Canadian Journal of Statistics 25, 457-472.
[15] Walker, S. and Mallick, B. K. (1999): A Bayesian Semiparametric Accelerated Failure Time Model. Biometrics 55, 477-483.
[16] Aalen, O. O. (2000): Medical statistics-no time for complacency. Statistical Methods in Medical Research 9, 31-40.
[17] Mohammad, A. T., Zoran, B., David, K. W. and Karan, P. S. (2007): Hypertabastic Survival Model. [http://www.biomedcentral.com/content/supplementary/1742-4682-4-40-S1.doc]
[18] Torabi, H. and Bagheri, F. L. (2010): Estimation of Parameters for an Extended Generalized Half Logistic Distribution Based on Complete Censored data. JIRSS Vol. 9, No. 2, pp 171-19.
[19] Alireza, A. (2012): Breast Cancer Survival Analysis : Applying the Generalized Gamma Distribution under Different Conditions of the Propotional Hazads and Accelerated Failure Time Assumptions. International Journal of Preventive Medicine, Vol 3, No 9.
[20] Balakrishnan, N. (1985): Oder statistics from the Half Logistic Distrinution. Journal of Statistics and Computer Smulation, 20, 27-309.
[21] Balakrishnan, N. and Puthenpura, S. (1986): Best Linear Unbiased Estimators of Location and Scale Parameters of the Half Logistic Distribution. Journal of Statistical Computation and Simulation, 25, 193-204.
[22] Olapade, A. K. (2003): On Characterizations of the Half Logistic Distribution. InterStat, February Issue, 2, http://interstat.stat.vt.edu/ InterStat/ARTICLES/2003articles/F06002.pdf
[23] Balakrishnan, N. and Wong, K. H. T. (1991): Approximate MLE’s for the Location and Scale Parameters of the Half-Logistic Disribution with Type II Right Censoring. IEEE Transactions on Reliability, 40(2), 140-145.
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Author Information
  • Department of Statistics, Federal Polytechnic of Oil and Gas, Bonny, Nigeria

  • Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria

  • Department of Surgery, Ladoke Akintola University of Technology Teaching Hospital, Osogbo, Nigeria

Cite This Article
  • APA Style

    Phillip Oluwatobi Awodutire, Akintayo Kehinde Olapade, Oladapo Adedayo Kolawole. (2016). The Type I Generalized Half Logistic Survival Model. International Journal of Theoretical and Applied Mathematics, 2(2), 74-78. https://doi.org/10.11648/j.ijtam.20160202.17

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    ACS Style

    Phillip Oluwatobi Awodutire; Akintayo Kehinde Olapade; Oladapo Adedayo Kolawole. The Type I Generalized Half Logistic Survival Model. Int. J. Theor. Appl. Math. 2016, 2(2), 74-78. doi: 10.11648/j.ijtam.20160202.17

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    AMA Style

    Phillip Oluwatobi Awodutire, Akintayo Kehinde Olapade, Oladapo Adedayo Kolawole. The Type I Generalized Half Logistic Survival Model. Int J Theor Appl Math. 2016;2(2):74-78. doi: 10.11648/j.ijtam.20160202.17

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  • @article{10.11648/j.ijtam.20160202.17,
      author = {Phillip Oluwatobi Awodutire and Akintayo Kehinde Olapade and Oladapo Adedayo Kolawole},
      title = {The Type I Generalized Half Logistic Survival Model},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {2},
      number = {2},
      pages = {74-78},
      doi = {10.11648/j.ijtam.20160202.17},
      url = {https://doi.org/10.11648/j.ijtam.20160202.17},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijtam.20160202.17},
      abstract = {In this paper, a three parameter probability distribution function called type I generalized half-logistic distribution is introduced to model survival or time to event data. The survival function, hazard function and median survival time of the survival model were established. Estimation of the parameters of the model was done using the maximum likelihood method. We then applied the type I generalized half-logistic survival model to a breast cancer survival data. The derived result from type I generalized half logistic survival model was compared with the results of some common existing parametric survival models, and this revealed that the type I generalized half-logistic survival model clearly demonstrates superiority over these other models.},
     year = {2016}
    }
    

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    T1  - The Type I Generalized Half Logistic Survival Model
    AU  - Phillip Oluwatobi Awodutire
    AU  - Akintayo Kehinde Olapade
    AU  - Oladapo Adedayo Kolawole
    Y1  - 2016/12/09
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    DO  - 10.11648/j.ijtam.20160202.17
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
    SP  - 74
    EP  - 78
    PB  - Science Publishing Group
    SN  - 2575-5080
    UR  - https://doi.org/10.11648/j.ijtam.20160202.17
    AB  - In this paper, a three parameter probability distribution function called type I generalized half-logistic distribution is introduced to model survival or time to event data. The survival function, hazard function and median survival time of the survival model were established. Estimation of the parameters of the model was done using the maximum likelihood method. We then applied the type I generalized half-logistic survival model to a breast cancer survival data. The derived result from type I generalized half logistic survival model was compared with the results of some common existing parametric survival models, and this revealed that the type I generalized half-logistic survival model clearly demonstrates superiority over these other models.
    VL  - 2
    IS  - 2
    ER  - 

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