A clinical trial is designed to identify the better of two experimental treatments. The trial consists...

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A clinical trial is designed to identify the better of two experimental treatments. The trial consists of several stages. At each stage two new patients are selected ran- domly from a common pool of patients and one is given treatment 1, and the other is given treatment 2. The stage is complete when the result of each treatment is known = the number of as a success or a failure. At the end of the nth stage we record Xn successes under treatment 1 minus those on treatment 2 observed on all the stages so far. The trial stops as soon as Xn reaches +k or -k, where k is a given positive integer. If the trial stops with Xn k, treatment 1 is declared to be better than 2, else treatment 2 is declared to be better than 1. Now suppose the probability of success of the ith treatment is pi, i 1, 2. Suppose p₁ > p2. Assume that the results of the successive stages are independent. Compute the probability that the clinical trial reaches correct decision, as a function of p1, p2, and k. - - A clinical trial is designed to identify the better of two experimental treatments. The trial consists of several stages. At each stage two new patients are selected ran- domly from a common pool of patients and one is given treatment 1, and the other is given treatment 2. The stage is complete when the result of each treatment is known = the number of as a success or a failure. At the end of the nth stage we record Xn successes under treatment 1 minus those on treatment 2 observed on all the stages so far. The trial stops as soon as Xn reaches +k or -k, where k is a given positive integer. If the trial stops with Xn k, treatment 1 is declared to be better than 2, else treatment 2 is declared to be better than 1. Now suppose the probability of success of the ith treatment is pi, i 1, 2. Suppose p₁ > p2. Assume that the results of the successive stages are independent. Compute the probability that the clinical trial reaches correct decision, as a function of p1, p2, and k. - -

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Answer The probability that the clinical trial reaches the correct decision can be calculated using the binomial distribution The binomial distribution is a probability distribution that counts the nu... View the full answer