Patients in a clinical trial for a new cancer treatment are classified as permanently cured, in remission (the cancer is present, but not growing), sick (the cancer is growing), or deceased. After one year of treatment, 1/3 of sick patients go into remission, another 1/3 are permanently cured, and, unfortunately, 1/3 are deceased. Patients in remission also receive treatment after a year of which 1/4 remain in remission, 1/2 are permanently cured, and 1/4 decline to the sick condition. 1. Formulate a Markov Chain model for the health of a patient in the trial described above. 2. Does your model from part (a) have a steady-state distribution? Explain why or why not? 3. Use your model from part (a) to determine the probability that a patient in the trial is eventually cured.
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Patients in a clinical trial for a new cancer treatment are classified as permanently cured, in remission (the cancer is present, but not growing), sick (the cancer is growing), or deceased. After one year of treatment, 1/3 of sick patients go into remission, another 1/3 are permanently cured, and, unfortunately, 1/3 are deceased. Patients in remission also receive treatment after a year of which 1/4 remain in remission, 1/2 are permanently cured, and 1/4 decline to the sick condition.
1. Formulate a Markov Chain model for the health of a patient in the trial described above.
2. Does your model from part (a) have a steady-state distribution? Explain why or why not?
3. Use your model from part (a) to determine the probability that a patient in the trial is eventually cured.
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