Prognosis of Cancer – A Semi Markov Process
Manjula S Dalabanjan1, Pratibha Agrawal2, Deepthi T3, M. D. Suranagi4

1Manjula S Dalabanjan, Associate Professor, Department of Mathematics, DBIT, Bengaluru, India.
2ratibha Agrawal, Professor, Department of Mathematics, AMCEC, Bengaluru, India.
3Deepthi T*, Assistant Professor, Department of Mathematics, BIET, Hyderabad, India.
4M. D. Suranagi, Professor, Veterinary College, Karnataka Veterinary, Animal and Fisheries Sciences University, Bidar, India.

Manuscript received on May 26, 2021. | Revised Manuscript received on June 02, 2021. | Manuscript published on June 30, 2021. | PP: 146-150 | Volume-10 Issue-5, June 2021. | Retrieval Number:  100.1/ijeat.E26950610521 | DOI: 10.35940/ijeat.E2695.0610521
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: Cancer begins in cells, the building blocks that make up tissues. Tissues make up the organs of the body. The buildup of extra cells often forms a mass of tissue called a growth, polyp or tumor. Tumors can be benign (non cancerous) or malignant (cancerous). Benign tumors are not as harmful as malignant tumors. The transformation of normal cells into cancer cells is called Carcinogenesis.Cancer is one of the major health problems persisting world-wide. Urbanization, industrialization, changes in lifestyles, population growth and ageing all have contributed for epidemiological transition in the country. The absolute number of new cancer cases is increasing rapidly due to growth in size of the population The stages of cancer are considered as different states of a Markov Process. Discrete-time Markov chains have been successfully used to investigate treatment programs and health care protocols for chronic diseases like HIV, AIDS, Hypertension etc. In this study, the process of carcinogenesis was classified into 6 states. The history of every patient is recorded in the form of a data segment starting from initial state.The transitional states and absorbing states are well defined. Since all the patients under study do not reach the last state at a given point of time, the process was studied as a Semi Markov Process. Maximum likelihood estimation of the transitional probabilities, the survival function, the hazard function and the waiting time distribution of patients in different states were studied. This kind of statistical methodology used to study the prognosis of cancer can be applied to real-time data of cancer patients. 
Keywords: Markov Property, Cancer, Stages, Transition Probabilities, Maximum Likelihood Estimation, Semi Markov Model, Distribution function. AMS Classification: 62G32