Analysis of a Biased Coin Design Model
Ibrahim Arogundade Mentor: Aliakbar Montazer Haghighi Mathematics Department
Goal Using simulation, this project analyzes the prescription of dose levels to a patient whose disease requires a period of repeated use of the same medicine with different dose levels, such as an oncology patient. Basic Terminologies A patient (or a subject) is to go under repeated treatments for a disease that requires possible repeated use of medicine with different dose levels. Prescribing each dose level needs a period to act. We refer to this period as a unit of time. The subject is to return to the physician after each treatment for assessment. Dose levels are under certain restrictions. We suppose there are ten possible dose levels 1, 2, L ,10 , level 1 being the weakest and level 10 being the strongest. Usually, levels 3 or lower may not be much effective but safe. On the other hand, levels 8 or higher are highly toxic and dangerous, yet needed to take a chance on emergency cases. Hence, based upon the first assessment, if the disease is very mild, level 3 or lower is prescribed. However, if the disease has progressed too much, level 8 or higher may be specified. Thus, we assume that there are three different options to determine the first dose level. (i) If the features of the patient show a mild case, dose level k is assigned. The level k = 1, 2, or 3, is randomly selected. (ii) If the subject shows a progressed case, dose level K is assigned. The level K = 8, 9, or 10 is randomly determined. (iii) If the first assessment is not indicative of too weak or highly progressed, dose level d is assigned. The level d = 4, 5, 6, and 7 is randomly selected. After a unit of time, the patient returns for a follow-up visit. Required tests will be done to assess the result of the dose level prescribed previously. There are two possible cases: (i) The dose was not effective but harmful because it negatively affected the patient's health. This case is referred to as toxicity, and the subject is referred to as toxic. (ii) The dose was not harmful; that is, it either positively affected the patient's health, or it did not affect it at all. Either case is referred to as non-toxicity, and the subject is referred to as non-toxic. At this point, the physician has to decide about a new dose level based on the two cases of toxicity and non-toxicity cases. There are three possible cases to prescribe the next dose level: (i)
move down one level,
(ii)
stay put or
(iii)
move up one level.
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