| Peer-Reviewed

A Simple Stochastic Stomach Cancer Model with Application

Received: 3 December 2017     Accepted: 12 December 2017     Published: 11 April 2018
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Abstract

Survival analysis majors mainly on estimation of time taken before an event of interest takes place. Time taken before an event of interest takes place is a random process that takes shape overtime. Stochastic processes theory is therefore very crucial in analysis of survival data. The study employed markov chain theory in developing a simple stochastic stomach cancer model. The model is depicted with a state diagram and a stochastic matrix. The model was applied to stomach cancer data obtained from Meru Hospice. Transition probability theory was used in determining transition probabilities. The entries of the stochastic matrix T were estimated using the Aalen-Johansen estimators. The time taken for all the people under the study to transit to death was estimated using the limiting matrix.

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 3)
DOI 10.11648/j.ajtas.20180703.13
Page(s) 112-117
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), 2018. Published by Science Publishing Group

Keywords

Stochastic Stomach Cancer Model, State Diagram, Stochastic Matrix, Transition Probabilities, Limiting Matrix

References
[1] B. M. Dehkordi, A. Safae, M. A. Pourhoseingholi, R. Fatemi, Z. Tsbeie, M. R. Zali( 2008): Statistical Comparison of Survival Models for Analysis of Cancer Data. Asian Pacific journal of Cancer prevention 2008. July-September; 9(3): 417-20.
[2] V. Vallinayagam, S. Prathap, P. Venkatesan (2014): Parametric Regression Models in the Analysis of Breast Cancer Survival Data. International journal of Science and Technology volume 3 No 3, March 2014.
[3] F. E. Ahmed, P. W. Vos and D. Holbert (2007): Modelling Survival in Colon Cancer; a methodological review. Biomed Central- Molecular cancer 2007, di:10.1186/1476-4598-6-15.
[4] D. B. Jun, K. Kim ( 2013): Survival analysis of lung and bronchus cancer patients segmented by demographic characteristics. KAIST Business School Working Paper series, KCB-WP-2013-029.
[5] D. B. Jun, K. Kim ( 2014): Survival analysis of lung and bronchus cancer patients segmented by demographic characteristics. KAIST Business School Working Paper series, KCB-WP-2014-026.
[6] U. Erisoglu, M. Erisoglu and H. Erol (2011): A Mixture Model of Two different Didistributions Approach to the Analysis of Heterogeneous Survival Data. International Journal of Computational and Mathematical Sciences, 5:2 2011.
[7] C. Yu, R. Greiner, H. Lin: Learning Patient-specific Cancer Syrvival Distributions as a Sequence of Dependent Regressors.
[8] H. A. Glick 2007: Introduction to Markov Models. Kyung Hee University July 2007.
[9] J. Jung 2006: Estimationof Markov Transition Probabilities between Health States in the HRS Datas. Research gate:228419924 (2006).
[10] E. L. Abner, R. J. Charnigo and R. J. Kryscio 2014: Markov chain and Semi-Markov chain models in time-to-event analysis. Journal Of Biomedical And Biostatistics; Suppl 1(E001): 19522-doi: 10.4172/2155-6180. SI-e001.
[11] T. Heggland 2015: Estimaitng transition probabilities for the illness- death model. Faculty of Mathematics and Natural Sciences University of Oslo.
[12] M. Snijders 2017:Prediction for Transition Probabilities in Multi-State models. Utrecht University.
[13] L. M. Machado, J. de Una-Alvarez, Carmen Cadarso-Suarez and Perk Andersen 2010: Multi-state models for analysis of time to event data. Statisical Methods in medical Research. 2009 Apri: 18(2): 195-222.
[14] American Cancer Society (2012). Cancer Facts & Figures 2012: American Cancer Society.
[15] Sirpa Heinavaara (2003). Modelling Survival of Patients with Multiple Cancers. Statistics in Medicine 2002 Nov 15;21(21).
[16] Kenya Cancer Network (2013). Kenya Cancer Statistics and National Strategy Report 2013.
[17] World Health Organization (2009). Cancers.
[18] Ministry of Public Health and Sanitation (2014). National Cancer Control Strategy.
[19] Tiwari Rc, Jernal A, Murray T, Ghafoor A, Samuels A, Ward E, Feuer EJ, Thun MJ(2004): Cancer Statistics 2004. Cancer Journal fo Clinicians 2004. 54(1): 8-29.
Cite This Article
  • APA Style

    Josphat Mutwiri Ikiao, Nyongesa Kennedy, Robert Muriungi Gitunga. (2018). A Simple Stochastic Stomach Cancer Model with Application. American Journal of Theoretical and Applied Statistics, 7(3), 112-117. https://doi.org/10.11648/j.ajtas.20180703.13

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    ACS Style

    Josphat Mutwiri Ikiao; Nyongesa Kennedy; Robert Muriungi Gitunga. A Simple Stochastic Stomach Cancer Model with Application. Am. J. Theor. Appl. Stat. 2018, 7(3), 112-117. doi: 10.11648/j.ajtas.20180703.13

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    AMA Style

    Josphat Mutwiri Ikiao, Nyongesa Kennedy, Robert Muriungi Gitunga. A Simple Stochastic Stomach Cancer Model with Application. Am J Theor Appl Stat. 2018;7(3):112-117. doi: 10.11648/j.ajtas.20180703.13

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  • @article{10.11648/j.ajtas.20180703.13,
      author = {Josphat Mutwiri Ikiao and Nyongesa Kennedy and Robert Muriungi Gitunga},
      title = {A Simple Stochastic Stomach Cancer Model with Application},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {7},
      number = {3},
      pages = {112-117},
      doi = {10.11648/j.ajtas.20180703.13},
      url = {https://doi.org/10.11648/j.ajtas.20180703.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180703.13},
      abstract = {Survival analysis majors mainly on estimation of time taken before an event of interest takes place. Time taken before an event of interest takes place is a random process that takes shape overtime. Stochastic processes theory is therefore very crucial in analysis of survival data. The study employed markov chain theory in developing a simple stochastic stomach cancer model. The model is depicted with a state diagram and a stochastic matrix. The model was applied to stomach cancer data obtained from Meru Hospice. Transition probability theory was used in determining transition probabilities. The entries of the stochastic matrix T were estimated using the Aalen-Johansen estimators. The time taken for all the people under the study to transit to death was estimated using the limiting matrix.},
     year = {2018}
    }
    

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    T1  - A Simple Stochastic Stomach Cancer Model with Application
    AU  - Josphat Mutwiri Ikiao
    AU  - Nyongesa Kennedy
    AU  - Robert Muriungi Gitunga
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    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
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    AB  - Survival analysis majors mainly on estimation of time taken before an event of interest takes place. Time taken before an event of interest takes place is a random process that takes shape overtime. Stochastic processes theory is therefore very crucial in analysis of survival data. The study employed markov chain theory in developing a simple stochastic stomach cancer model. The model is depicted with a state diagram and a stochastic matrix. The model was applied to stomach cancer data obtained from Meru Hospice. Transition probability theory was used in determining transition probabilities. The entries of the stochastic matrix T were estimated using the Aalen-Johansen estimators. The time taken for all the people under the study to transit to death was estimated using the limiting matrix.
    VL  - 7
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Author Information
  • Department of Mathematics, Meru University of Science and Technology, Meru, Kenya

  • Department of Mathematics, Masinde Murilo University of Science and Technology, Kakamega, Kenya

  • Department of Mathematics, Meru University of Science and Technology, Meru, Kenya

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