A Simple Stochastic Stomach Cancer Model with Application

Josphat Mutwiri Ikiao; Nyongesa Kennedy; Robert Muriungi Gitunga

doi:doi:10.11648/j.ajtas.20180703.13

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A Simple Stochastic Stomach Cancer Model with Application

Josphat Mutwiri Ikiao, Nyongesa Kennedy, Robert Muriungi Gitunga

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 3)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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[11]	T. Heggland 2015: Estimaitng transition probabilities for the illness- death model. Faculty of Mathematics and Natural Sciences University of Oslo.
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[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.
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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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TY  - JOUR
T1  - A Simple Stochastic Stomach Cancer Model with Application
AU  - Josphat Mutwiri Ikiao
AU  - Nyongesa Kennedy
AU  - Robert Muriungi Gitunga
Y1  - 2018/04/11
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180703.13
DO  - 10.11648/j.ajtas.20180703.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 112
EP  - 117
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180703.13
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
IS  - 3
ER  -

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Author Information

Josphat Mutwiri Ikiao

Department of Mathematics, Meru University of Science and Technology, Meru, Kenya
Nyongesa Kennedy

Department of Mathematics, Masinde Murilo University of Science and Technology, Kakamega, Kenya
Robert Muriungi Gitunga

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - A Simple Stochastic Stomach Cancer Model with Application
AU  - Josphat Mutwiri Ikiao
AU  - Nyongesa Kennedy
AU  - Robert Muriungi Gitunga
Y1  - 2018/04/11
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180703.13
DO  - 10.11648/j.ajtas.20180703.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 112
EP  - 117
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180703.13
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
IS  - 3
ER  -

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