Cancer A clinical trial was conducted among 178 patients with advanced melanoma

Question

Cancer

A clinical trial was conducted among 178 patients with advanced melanoma (a type of skin cancer) (Schwartzentruber, et al. [18]). There were two treatment groups. Group A received lnterleukin-2. Group B received lnterleukin-2 plus a vaccine. Six percent of Group A patients and 16% of group B patients had a complete or partial response to treatment. Suppose we seek to extrapolate the results of the study to a larger group of melanoma patients.

4.101

lf 20 melanoma patients are given lnterleukin-2 plus a vaccine, what is the probability that exactly 5 of them will have a positive response to treatment (either complete or partial response)?

4.102

lf 20 melanoma patients are given lnterleukin-2 plus a vaccine, what is the probability that at least 3 of them will have a positive response to treatment? One issue is that some patients experience side effects and have to discontinue treatment. lt was estimated that 19% of patients receiving lnterleukin-2 plus vaccine developed an arrhythmia (irregular heartbeat) and had to discontinue treatment. Since the side effect was attributable to the vaccine, assume that the patients would continue to take lnterleukin-2 if arrhythmia developed but not the vaccine and that the probability of a positive response to treatment would be the same as group A (i.e., 6%).

Explanation / Answer

4.101

P( Exact 5) = 20C5 * p^5 * q*15 = 20!/(15!*5!) * 0.16^5* 0.84^15 = 0.1189

4.102

P( at least 3) = 1-P(0)-P(1)-P(2) = 1- 0.84^20 - 20* 0.16*0.84^19 - (20*19/2) * 0.84^18*0.16^2 = 0.6420

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