A clinical trial was conducted among 178 patients with advanced melanoma (a type of skin cancer). There were two treatment groups. Group A received Interleukin-2. Group B received Interleukin-2 plus a vaccine. Six percent of Group A patients and 17% of group B patients had a complete or partial response to treatment. One issue is that some patients experience side effects and have to discontinue treatment. It was estimated that 21% of patients receiving Interleukin-2 plus a 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 Interleukin-2 if arrhythmia developed but not the vaccine and that the probability of a positive response to the treatment would be the same as group A (i.e., 6%)Suppose we have 10 patients who receive Interleukin-2 plus vaccine of whom 2 develop arrhythmia and 8 do not. What is the probability that exactly 2 of the 10 patients will get a positive response to treatment?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A clinical trial was conducted among 178 patients with advanced melanoma (a type of skin cancer). There were two treatment groups. Group A received Interleukin-2. Group B received Interleukin-2 plus a vaccine. Six percent of Group A patients and 17% of group B patients had a complete or partial response to treatment. One issue is that some patients experience side effects and have to discontinue treatment. It was estimated that 21% of patients receiving Interleukin-2 plus a 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 Interleukin-2 if arrhythmia developed but not the vaccine and that the probability of a positive response to the treatment would be the same as group A (i.e., 6%)Suppose we have 10 patients who receive Interleukin-2 plus vaccine of whom 2 develop arrhythmia and 8 do not. What is the probability that exactly 2 of the 10 patients will get a positive response to treatment?
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