Prognosis of Cancer - A Semi Markov Process

Cancer begins in cells, the building blocks thatmake up tissues. Tissues make up the organs of the body. Thebuildup of extra cells often forms a mass of tissue called agrowth, polyp or tumor. Tumors can be benign (non cancerous)or malignant (cancerous). Benign tumors are not as harmful asmalignant tumors. The transformation of normal cells intocancer cells is called Carcinogenesis.Cancer is one of the majorhealth problems persisting world-wide. Urbanization,industrialization, changes in lifestyles, population growth andageing all have contributed for epidemiological transition in thecountry. The absolute number of new cancer cases is increasingrapidly due to growth in size of the population The stages ofcancer are considered as different states of a Markov Process.Discrete-time Markov chains have been successfully used toinvestigate treatment programs and health care protocols forchronic diseases like HIV, AIDS, Hypertension etc. In this study,the process of carcinogenesis was classified into 6 states. Thehistory of every patient is recorded in the form of a data segmentstarting from initial state.The transitional states and absorbingstates are well defined. Since all the patients under study do notreach the last state at a given point of time, the process wasstudied as a Semi Markov Process. Maximum likelihoodestimation of the transitional probabilities, the survival function,the hazard function and the waiting time distribution of patientsin different states were studied. This kind of statisticalmethodology used to study the prognosis of cancer can be appliedto real-time data of cancer patients.