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Drug testing in athletes. Due to inaccuracies in
Chapter 3, Problem 84E(choose chapter or problem)
Problem 84E
Drug testing in athletes. Due to inaccuracies in drugtesting procedures (e.g., false positives and false negatives) in the medical field, the results of a drug test represent only one factor in a physician’s diagnosis. Yet, when Olympic athletes are tested for illegal drug use (i.e., doping), the results of a single positive test are used to ban the athlete from competition. In Chance (Spring 2004), University of Texas biostatisticians D. A. Berry and L. Chastain demonstrated the application of Bayes’s Rule for making inferences about testosterone abuse among Olympic athletes. They used the following example: In a population of 1,000 athletes, suppose 100 are illegally using testosterone. Of the users, suppose 50 would test positive for testosterone. Of the nonusers, suppose 9 would test positive.
a. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.)
b. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result. (This probability represents the specificity of the drug test.)
c. If an athlete tests positive for testosterone, use Bayes’s Rule to find the probability that the athlete is really doping. (This probability represents the positive predictive value of the drug test.)
Questions & Answers
QUESTION:
Problem 84E
Drug testing in athletes. Due to inaccuracies in drugtesting procedures (e.g., false positives and false negatives) in the medical field, the results of a drug test represent only one factor in a physician’s diagnosis. Yet, when Olympic athletes are tested for illegal drug use (i.e., doping), the results of a single positive test are used to ban the athlete from competition. In Chance (Spring 2004), University of Texas biostatisticians D. A. Berry and L. Chastain demonstrated the application of Bayes’s Rule for making inferences about testosterone abuse among Olympic athletes. They used the following example: In a population of 1,000 athletes, suppose 100 are illegally using testosterone. Of the users, suppose 50 would test positive for testosterone. Of the nonusers, suppose 9 would test positive.
a. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.)
b. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result. (This probability represents the specificity of the drug test.)
c. If an athlete tests positive for testosterone, use Bayes’s Rule to find the probability that the athlete is really doping. (This probability represents the positive predictive value of the drug test.)
ANSWER:
Solution
Step 1 of 3
Let U be the the athlete using testosterone
Let T be the test is positive
a) We have to find the probability that the drug test for testosterone will yield a positive result for users
Given that out of 100 users 50 would test positive for testosterone
Then P(sensitivity of drug)=P(P/U)
=50/100
=0.5
Hence the probability of sensitivity of drug is 0.5